(A) Long‐Term Degradation

Studies conducted by Elias (2000) and Allen and Bathurst (2003) have indicated that long‐term degradation of geosynthetics in the in‐soil environment in typical reinforcement applications is very small. Of particular interest is a field‐scale experiment described in Section 4.2.3 and shown in Figure 4.29. The experiment conducted by the Public Research Institute (PWRI) of Japan is enlightening especially in regard to the influence of long‐term degradation of geosynthetic reinforcement. The experiment was initially designed to examine the failure surface of a 6.0‐m high GRS wall. After the wall was constructed, layers of geogrid reinforcement embedded in the wall were severed at preselected sections. The horizontal movement of the wall due to cutting of the reinforcements was essentially zero until the cutting approached approximately 0.2H from the wall face (H = wall height), at which time lateral movement increased by about 10 mm. The PWRI experiment suggests that stress relaxation in geosynthetic reinforcement might have completed at the time of cutting (within three days after construction). If stress relaxation is to reduce reinforcement loads to a very small value or zero, the geosynthetic reinforcement would no longer be serving any reinforcing function shortly after construction, hence long‐term degradation of the reinforcement will no longer be an issue. Cutting of reinforcements in the experiment can be viewed as an extreme form of degradation, in that the reinforcement is degraded into pieces.

(B) Installation Damage

Studies performed to investigate installation/construction damage of geosynthetics (e.g., Hufenus et al., 2005) have indicated that most installation damage does not severely affect the load–deformation behavior of woven geotextiles and geogrids, if at all, until damage levels become quite high. In applications where tensile resistance of reinforcement at low elongations is relevant (typical in GRS walls), the effects of moderate installation damage has been found to be very small. It has been suggested that RF_ID in Eqn. (5‐11) be designated as being close to unity, on the order of 1.0 to 1.1.

Allen and Bathurst (1996) have provided convincing evidence that installation damage would have little, if any, effect on creep strains and creep rates for typical levels of installation damage in full‐scale geosynthetic reinforced retaining walls. They concluded that in many cases, installation damage will have a negligible effect on the long‐term strength at working stress levels (i.e., the geosynthetic behaves as if it is not damaged).

(C) Creep

Geosynthetics, being polymeric materials, are generally considered susceptible to creep under sustained loads. Stress level, polymer type, manufacturing method, and temperature have been known to affect the creep potential of geosynthetics. When evaluating the creep potential of geosynthetic reinforcement in reinforced soil structures, however, it can be misleading to evaluate the creep potential based on laboratory tests performed by applying a sustained load directly to a geosynthetic specimen, as has been stipulated in the prevailing design guides. This is because the interaction between geosynthetic reinforcement and the time‐dependent deformation behavior of the confining soil must be taken into account when evaluating the long‐term creep behavior of geosynthetic reinforced soil structures. If the confining soil has a tendency to deform faster than the geosynthetic reinforcement (in isolation or subject to a confining pressure for pressure‐sensitive geosynthetics), the geosynthetic reinforcement will impose a restraining effect on the time‐dependent deformation of the soil through interface bonding forces. Conversely, if the confining soil tends to deform slower than the geosynthetic reinforcement (in isolation or subject to a confining pressure for pressure‐sensitive geosynthetics), the confining soil will then restrain the creep deformation of the reinforcement. This restraining effect is a direct result of soil–reinforcement interaction wherein redistribution of stresses in the confining soil and changes in tensile loads in the reinforcement will occur over time in an interactive manner (Wu and Helwany, 1996).

Creep of geosynthetics and geosynthetic reinforced soil mass has been discussed in some detail in Section 4.2.2. Field measured data have strongly suggested that creep deformation of geosynthetic reinforcement will not be a design issue when well‐compacted granular fill is used as backfill in the reinforced soil zone (Crouse and Wu, 2003; Allen and Bathurst, 2003).

(D) Discussion on Long‐Term Design Strength and Recommendations

To account for installation damage, creep, and durability of geosynthetic reinforcement, the prevailing design guides have suggested that the design strength be obtained by applying a combination of reduction factors to the short‐term strength (Eqn. (5‐11)). The value of the combined reduction factor typically depends on whether a geosynthetic is on a preapproved list; this value is typically about 5% of short‐term strength for non‐preapproved geosynthetics, and 15% for preapproved geosynthetics. This is hardly a sound approach, for three reasons.

• Soil–reinforcement interaction is known to be critical to creep of geosynthetic reinforcement, yet the approach is based on tests where loads are applied directly to geosynthetics specimens without any regard to soil–geosynthetic interaction (see Sections 4.2.1(B) and 4.2.2).
• There is no evidence that a compounding effect of installation damage and creep would occur. In fact there is evidence to the contrary (e.g., Allen and Bathurst, 1996; Greenwood, 2002), hence multiplication of individual reduction factors in Eqn. (5‐11) is not justified.
• Creep is a deformation problem resulting from soil–geosynthetic interaction, yet the approach employs simplistic reduction factors, of which the values are not based on a reliable and sufficiently large database, to account for influences of these factors on complicated long‐term creep deformation.

It is an indisputable fact that creep of geosynthetic reinforcement in a GRS is strongly influenced by time‐dependent deformation behavior of the soil surrounding the geosynthetic reinforcement. A rational assessment of long‐term design strength, therefore, must take the confining soil into account. If the time‐dependent behavior of a given backfill is in question, a laboratory test such as the SGIP test (Wu and Helwany, 1996; Ketchart and Wu, 2002), shown in Figures 4.23 and 4.25, is recommended for evaluation of the potential creep deformation of a GRS structure.

When a GRS wall is constructed with well‐compacted granular backfill, long‐term deformation and stability are generally not major design concerns. In this case, the use of a single combined factor to account for long‐term effects, uncertainty, and ductility is recommended. The value of this combined factor needs to be a function of soil properties and, to a lesser extent, geosynthetic type. Moreover, as noted in Section 5.3.1, when designing a GRS wall, the required minimum values of reinforcement stiffness, reinforcement strength and ductility strain still need to be specified.

For GRS walls with well‐compacted granular fill, the required minimum tensile stiffness in the direction perpendicular to the wall face () can be determined by Eqn. (5‐3) (Note: Use 2% for bridge abutments and 3% for non‐load‐carrying walls are recommended). On the other hand, the required minimum reinforcement strength (T_ult) can be obtained by imposing a ductility and long‐term factor F_dl on the required minimum tensile stiffness to ensure sufficient ductility and satisfactory long‐term performance, i.e., (Eqn. (5‐4)). In addition, the tensile strain corresponding to T_ult on the load–deformation curve of the geosynthetic needs to be greater than the ductility strain (5–7% for most applications, based on a limited database) to ensure sufficient ductility.

The following values for ductility and long‐term factor F_dl in Eqn. (5‐4) are recommended for design of GRS walls constructed with well‐compacted granular fill materials:

• Plasticity index (PI) is 3 or less:
  • F_dl = 3.5 for all geosynthetics
• Plasticity index (PI) is between 4 and 6:
  • F_dl = 5.5 for polypropylene geosynthetics
  • F_dl = 5.0 for polyethylene geosynthetics
  • F_dl = 4.0 for polyester geosynthetics

(A) Research and Case Histories

1. Reinforced Soil Walls with Uniform Reinforcement Length

   When it comes to short reinforcement lengths, the research by Fumio Tatsuoka and the Japan Railway (Tatsuoka et al., 1992, 1997; Tatsuoka, 2008) was among the first. Beginning in the mid‐1980s, Tatsuoka and his associates at the Japan Railway Technical Research Institute developed a GRS wall system with full‐height rigid facing, referred to as the CIP‐FHF (cast‐in‐place full‐height facing) system (Section 3.4.3). Due to its superior performance in resisting strong earthquakes and heavy rainfalls over conventional cantilever walls and metallic reinforced earth walls, the CIP‐FHF system became the “default” wall type for retaining walls constructed by the Japan Railway. To date, over 120 km of CIP‐FHF GRS walls have been built all over Japan with great success.

   As noted in Section 3.4.3, the CIP‐FHF system involves a two‐stage construction procedure. In the first stage, a GRS wall with geosynthetic reinforcement of 0.3–0.4H in length and typical spacing of 0.3 m is constructed using stacked gravel gabions as facing. The wall is allowed to deform under its self‐weight before starting the second stage of construction, which involves installing full‐height rigid concrete facing (cast‐in‐place) over the gabion face GRS wall. The rigid concrete facing is attached to the reinforced soil mass via protruded steel bars that are embedded in the GRS mass during the first stage. Despite the short reinforcement lengths of 0.3–0.4H, none of the walls have ever experienced failure. Both granular and cohesive backfills have been used in the construction of CIP‐FHF wall systems. Tatsuoka and his associates suggested that overturning may be the most critical mode of failure for reinforced soil walls with short reinforcement lengths of 0.3–0.4H, whereas lateral sliding is typically the governing failure mode for walls with reinforcement lengths of 0.6–0.7H.

   In a rebuttal to Tatsuoka’s comments regarding CIP‐FHF GRS walls vs. reinforced earth walls (with steel strips as reinforcement), Segrestin (1994), of Terre Armée International, stated that a number of reinforced earth walls with reinforcement length as low as 0.45H had been constructed successfully. Segrestin also stated that a very tall (10.5‐m high) reinforced earth wall with reinforcement length of 0.48H had demonstrated satisfactory performance. Segrestin maintained that the basic mechanism and behavior of reinforced soil structures with reinforcement lengths between 0.4H and 0.7H were identical, and this had been validated by a finite element parametric study conducted by Terre Armée.

   Bastick (1990) conducted finite element analysis of MSE walls undergoing changes due to reduced reinforcement length. It was found, similar to Terre Armée’s finding, that the performance of an MSE wall would remain practically the same as long as the reinforcement lengths were kept above 0.4–0.5H and the reinforcement spacing stayed the same. The finding was confirmed by a full‐scale experiment with reinforcement length of 0.48H loaded to an average surcharge of 840 kPa.

   There are two distinct situations when very short reinforcement lengths find their way into reinforced soil walls: (a) walls with a constrained fill zone, where a rock or heavily overconsolidated soil outcrop or an existing nailed wall is present in the back of the reinforced soil wall, in which the space constraint makes the commonly used reinforcement length of 0.6–0.7H impractical (Lawson and Yee, 2005), and (b) walls with the end of reinforcement being anchored by metal plates or geosynthetic loops (Fukuoka et al., 1986; Brandl, 1998). Situation (a) is in line with the scope of this subject and will be elaborated further.

   Lawson and Yee (2005) proposed a design‐and‐analysis method for reinforced soil retaining walls involving a constrained fill zone. Within the constrained reinforced fill zone, the full active failure wedge is unable to develop because of the close proximity of the rigid zone behind the reinforced fill. In this method, the magnitude of horizontal thrust acting on the wall face, P_h , is evaluated as . Lawson and Yee concluded that for walls with reinforcement lengths greater than 0.5H, the Rankine active wedge can fully develop within the granular fill zone, hence the lateral earth pressure coefficient, K, is equal to K_A. However, if reinforcement length is less than 0.5H, the full active wedge cannot develop fully and the magnitude of the lateral earth pressure coefficient will decrease with decreasing reinforcement lengths.

   A glaring example of reduced lateral thrust for walls with a constrained fill zone is a very tall wall constructed by Lin et al. (1997) in Taiwan, a country where very heavy seasonal rainfall occurs annually. The wall was 39.5 m high, constructed in six tiers (three 8‐m tall tiers and three shorter tiers). The geogrid reinforcement length was 1.5 m, or 0.19H. All tiers, despite having to carry the soil weight from upper tiers, performed satisfactorily even with the very short reinforcement length. It is interesting to note that the reinforcement length of 0.19H happens to coincide with the finding of a numerical study (Vulova, 2000; Vulova and Leshchinsky, 2003). The numerical study also agreed well with Tatsuoka’s assertion that overturning will be the control failure mode for a MSE wall with short reinforcement lengths.

   Morrison et al. (2006) performed centrifuge tests on shored MSE walls where a constrained fill zone is present due to the shoring and reported the following:

   • Reinforcement lengths in the range of 0.25–0.6H generally produce stable wall systems.
   • Reinforcement lengths of 0.25H or smaller generally produce outward deformation followed by an overturning collapse of the MSE mass under increasing gravitational levels.
   • For reinforcement lengths less than 0.6H, deformation produced a “trench” at the shoring interface, interpreted to be the result of tension; the trench was not observed with reinforcement lengths of 0.6H or greater.
   • A conventional MSE wall with retained fill and a reinforcement length of 0.3H was observed to be stable up to an acceleration level of 80g, which represents a prototype height of approximately 27 meters.

   It has been suggested that a shorter reinforcement length may result in larger lateral displacements and likely larger settlement as well. A finite element study conducted by Chew et al. (1991) showed that reducing reinforcement length from 0.7H to 0.5H caused about a 50% increase in lateral deformation. Ling and Leshchinsky (2003) reported that, with a reinforcement length of 0.5H, a reinforced soil wall would produce satisfactory performance considering the maximum displacement mobilized in the reinforcement layers. A study by Liu (2012) suggested that the larger lateral displacement when shorter reinforcement is used may be a result of larger lateral deformation of the soil behind the reinforced zone.

   It is of interest to note that a reinforced soil mass with closely spaced reinforcement and well‐compacted fill tends to behave as a coherent mass. This behavior was observed in two loading experiments of full‐scale concrete block facing GRS bridge abutment walls, referred to as the NCHRP GRS test abutments (Wu et al., 2006, 2008). Two different woven geotextiles of different values of stiffness and strength were used as reinforcement, each 3.15 m long and on 0.2 m spacing. The backfill was a non‐plastic silty sand, and the abutment was loaded by applying increasing vertical loads onto a strip footing near the front face. A tension crack was observed on the wall crest in both experiments. The tension crack was located exactly at the extent of the reinforced zone (i.e., 3.15 m from the backface of the facing blocks) under an applied pressure between 150 and 200 kPa. The location of the tension cracks suggests that the reinforced soil mass behaves as a coherent mass for GRS walls with closely spaced reinforcement. This also explains why eccentricity (lift‐off) has been the most critical failure mode with short reinforcement lengths of 0.3–0.4H, especially for walls with closely spaced reinforcement. The only exception is when a constrained fill zone is present.

2. Reinforced Soil Walls with a Truncated Base

   A reinforced soil wall with shortened reinforcement lengths in the lower part of the wall, known as a truncated‐base wall, is often used when excavation to allow for uniform reinforcement lengths is cost prohibitive. The reduction in reinforcement lengths commonly takes one of two forms: stepped truncation (reducing lengths in groups of 2 to 4 reinforcement layers) and trapezoidal truncation (reducing lengths approximately linearly with depth).

   A truncated base for MSE walls is allowed in the FHWA NHI manual. The manual provides general guides for a truncated base, and states that this provision should only be considered if the base of the MSE wall is founded on rock or competent soil; competent soil is a soil which exhibits minimal post‐construction settlement. For foundation soil less than competent, a ground improvement technique may be used prior to construction.

   The British Standard BS 8006 design manual (BSI, 1995) for MSE walls also allows use of a truncated base. It states that a truncated base (or trapezoidal) wall should only be considered where foundations are formed by excavation into rock or other competent foundation conditions exist. The manual prescribes a minimum reinforcement length of 0.4H for the lower portion of the wall. Hong Kong’s Geoguide 6 (GEO, 2002) essentially follows the FHWA NHI manual, except it stipulates that soil arching needs to be accounted for in the design.

   Japan Railway allows reinforcement with truncated lengths in the lower part of a GRS wall be used when the costs of excavation to allow for full‐length reinforcement are high (Tatsuoka et al., 1992, 2005; Morishima et al., 2005). The walls constructed with a truncated base have been reported to have performed satisfactorily during heavy rainfall and severe earthquake events.

   Segrestin (1994) of Terre Armée International reported on the applications of truncated‐base walls with steel‐strip reinforcement in situations where constrained fill is present. It has been reported that wider metal strips, or more often an increased number of strips, have been employed in truncated base reinforced earth walls.

   The Colorado Department of Transportation constructed a 7.6‐m high GRS wall with a truncated base in the DeBeque Canyon along Interstate Highway 70 (Wu, 2001). For comparison purposes, a 10‐m long control section was also constructed with full‐length reinforcement throughout (termed “the control wall”). A road base material was used as backfill, and the wall was situated over a firm foundation. Lateral displacements of the control wall (reinforcement length = 5 m) and the truncated‐base wall (reinforcement length at base = 1.1 m, or 0.14H), taken 6 months after construction, were found to be very similar, both on the order of 3–6 mm, with the maximum displacement being 8 mm. Adams et al. (2011a) of the Federal Highway Administration also reported a number of GRS abutments with a truncated base. The GRS abutments have been reported to have performed satisfactorily.

   Lee et al. (1994) conducted a forensic study on a series of failed walls founded on rock and concluded that the resistance against sliding failure is reduced by the truncated base due to a smaller base area. They noted that soil arching due to the rock behind the fill would reduce vertical stress above the back of the lower reinforcements, hence can lead to overestimation of resistance to pullout failure.

   Thomas and Wu (2000) conducted a finite element study on the behavior of GRS walls with a truncated base. The major findings of the study are as follows:

   • When designing a GRS wall with a truncated base, external stability should be thoroughly checked; truncated base walls are more likely to experience lateral sliding failure and lift‐off failure. The length of reinforcement at the lowest level of a truncated base wall should be at least 0.35H or 0.9 m.
   • Fill type and fill compaction play an especially important role in the performance of GRS walls with a truncated base. The use of cohesive backfill should be completely avoided for truncated base walls.
   • The foundation soil needs to be sufficiently stiff (with little post‐construction settlement) to permit construction of truncated‐base walls.

(B) Discussions and Concluding Remarks

A minimum reinforcement length of 0.6–0.7H (H = height of the wall at the wall face) has been used in most design guides for GRS/GMSE walls with a uniform reinforcement length throughout. However, walls with uniform reinforcement lengths as small as 0.3–0.4H have consistently been shown to be stable, and studies have suggested that GRS walls with reinforcement length between 0.4H and 0.7H behave approximately the same. For situations where a uniform reinforcement length is employed, a minimum reinforcement length of 0.6H is well justified. A minimum reinforcement length of 0.7H is overly conservative, especially for closely spaced reinforcement (spacing not more than 0.3 m). Care must be exercised to prevent tension crack on the wall crest if the wall is to carry significant vertical loads near the wall face (e.g., bridge abutments). Extending the top 1 to 2 layers of reinforcement well beyond the assumed failure plane would help in eliminating the tension cracks.

Use of shorter reinforcement for reinforced soil walls, with a uniform reinforcement length of 0.35–0.5H, will result in larger lateral movement than those with a uniform reinforcement length of 0.6H, and is recommended only if the following four conditions are met:

1. The wall will not be subject to heavy edge loads, such as a bridge abutment wall.
2. Free‐draining granular backfill is employed and well compacted.
3. The foundation is competent (little post‐construction settlement).
4. External stability, especially against lift‐off (eccentricity) failure and lateral sliding failure, is thoroughly checked.

Use of a truncated base is a viable measure when the cost of excavation to allow for uniform reinforcement length is impractical. There is strong evidence based on a large number of case histories and research studies that a truncated base wall will perform satisfactorily as long as the base of a reinforced soil wall is founded on competent foundation, and external stability, especially sliding and eccentricity (i.e., lift‐off) stability, is ensured. The reinforcement length at the lowest level should generally be at least 0.3H. However, it can be significantly smaller (as small as 0.1H has been used routinely by the Japan Railway) if a constrained fill is involved (i.e., there is firm existing overconsolidated soil within a short distance behind the wall).

Step 1: Establish wall profile and check design assumptions

A wall profile should be established from the grading plan of the wall site. The following design assumptions should be verified:

• wall face is vertical or near vertical; i.e., no more than 10° off the vertical, or steeper than a batter of 1 (horizontal) to 7 (vertical)
• wall crest is essentially horizontal
• backfill is granular and free‐draining
• wall is constructed over a firm foundation; i.e., very small post‐construction settlement
• live loads are essentially vertical
• no concern for seismic loads

If any of the design assumptions are not satisfied or if the wall geometry cannot be approximated as an equivalent system that satisfies the design assumptions, the design method should not be used.

Step 2: Determine backfill properties ϕ and γ

The drained friction angle of the fill material, ϕ (more precisely ϕ'), can be estimated conservatively by an experienced soils engineer or determined by performing appropriate direct shear or triaxial tests. The unit weight, γ, can be estimated or determined by a test. Generally, the unit weight at 95% Standard Proctor relative compaction (i.e., 95% of AASHTO T‐99 maximum unit weight) is specified. However, other densities may also be specified as long as the friction angle ϕ is consistent with the density.

Step 3: Develop a lateral earth pressure diagram due to overburden plus surcharge

The friction angle ϕ determined in Step 2 can be used to calculate the coefficient of earth pressure at rest, , and determine the lateral earth pressure diagram along the height of the wall due to overburden (soil self‐weight) plus surcharge (see Figure 5.18). The lateral earth pressure at depth z (measured from the crest) is:

(5‐16)

where K₀ is the coefficient of earth pressure at rest, and q is the vertical surcharge pressure uniformly applied on the wall crest.

Step 4: Develop a lateral earth pressure diagram due to live loads

Boussinesq theory allows determination of stress at any point within a semi‐infinite elastic soil mass due to a single point vertical load applied on the crest (the top surface of the soil mass). Boussinesq theory also allows lateral stress within a soil mass to be determined, which can be regarded as being equal to lateral earth pressure on a virtual wall face. Boussinesq theory is used in the USFS design method to determine lateral earth pressure due to loads applied on the crest of a reinforced soil wall.

For a concentrated vertical live load P applied on the crest, the lateral earth pressure at depth z on the wall face can be evaluated by the Boussineq equation:

(5‐17)

where σ_h(l) is the lateral earth pressure on the wall face at depth z due to a concentrated vertical live load P applied at a point with a horizontal distance x from the wall face (distance measured in the orientation perpendicular to wall face), and R is the radial distance from the point where P is applied to the point where σ_h(l) is being calculated. The lateral pressure profile due to live loads, σ_h(l) , is commonly evaluated at 0.6‐m (2‐ft) vertical intervals (i.e., z = 0.6 m, 1.2 m, or 2 ft, 4 ft, etc.) along the height of the wall. The lateral pressure profile due to live loads (see Figure 5.18) can be obtained from the influence diagram shown in Figure 2.11. The diagrams are conservative (see Section 2.2.6) for evaluation of σ_h(l). When multiple live loads are present, σ_h(l) can be obtained by superimposing earth pressure due to each live load. An example for calculating lateral earth pressure due to an eight‐wheel 40‐kip (178 kN) dual tandem axle truck can be found in Steward et al. (1977) and Koerner (2005), and is given (with modifications) in Section 5.4.2. Normally, more than one section along the wall should be checked to determine the most critical section. The values of live loads P can be determined as the larger value between 1.5 × (legal loads) and 1.2 × (heavy loads).

Step 5: Develop a combined lateral earth pressure diagram

The lateral earth pressure diagrams determined from Steps 3 and 4 are superimposed to form a combined lateral earth pressure diagram, similar to that shown in Figure 5.18.

Step 6: Determine the vertical spacing of reinforcement layers

The vertical spacing between reinforcement layers, s_v, is determined as:

(5‐18)

where T_ult is the ultimate strength of the reinforcement; F_s is the factor of safety, which should at least be 1.2–1.5, depending on the confidence level in the value of T_ult ; and σ_h is lateral earth pressure at the mid‐depth of a layer, as obtained from the combined pressure diagram (Step 5). The value of T_ult may be specified by either Method A, the wide cut strip tensile test, or Method B, a combination of grab tensile and 25‐mm (1‐in.) cut strip tests. The tests should be performed with the reinforcement in its weakest principal direction, and Method A is generally preferred over Method B.

To account for long‐term creep potential, a reduction factor should be applied to the tensile strength obtained from the tests. The value of the reduction factor depends on the test method, the polymer type, and style of the reinforcement, as follows:

When Method A is used for determination of T_ult , the following conditions should be observed:

• The aspect ratio (the ratio of width to gauge length) of the test specimen should be 2 or greater. The minimum gauge length (between grips of test specimen) should be 100 mm (4 in.).
• The test should be performed at a constant strain rate of 10% per minute.
• The test should be performed at 65 + 2% relative humidity and 21 ± 1°C (70 ± 2°F) temperature.
• The test specimen should be soaked in water for at least 12 hours and maintained surface damp during the test.
• The grips used in the test should not weaken the specimen and should be able to hold the specimen without slippage. Tests which fail at the grips should be disallowed. If slippage cannot be sufficiently limited, elongation must be measured between points on the specimen rather than between the grips.
• Test results should include applied tensile force per unit width of specimen vs. strain curve, failure load per unit width, and strain at failure.

When using Method B to determine T_ult , the smaller value of the following two strengths should be used: (i) 90% of the 25‐mm (1‐in.) cut strip strength or (ii) 33% of the grab tensile strength.

Step 7: Determine the length of reinforcement required to develop pullout resistance

As shown in Figure 5.19, the total length of reinforcement, L, required to prevent pullout failure from occurring is equal to the sum of the anchored length behind the potential failure plane, L_e , and the length within the potential failure zone, L_f . For a reinforcement located at depth z below the crest,

(5‐19)

in which

(5‐20)

(5‐21)

where H is the wall height and z is the depth of the reinforcement layer being considered. The safety factor against pullout failure, F_s , should be at least 1.5–1.75. A minimum value of should be used.

When different soils are used above and below a reinforcement layer, the equation for calculating L_e is modified as:

(5‐22)

where ϕ_a and ϕ_b are the friction angles of the soils above and below the reinforcement layer, respectively.

Following the equations above, the reinforcement layers near the base can be shorter than near the top to satisfy the internal stability requirement of a reinforced soil structure. However, due to external stability considerations (Step 9), particularly with respect to sliding and bearing capacity, and to avoid confusion in the actual reinforcement placement sequence in the field, all reinforcement layers are usually taken as being of a uniform length.

Step 8: Determine the wrapped length of reinforcement into the wall face

The wrapped length of reinforcement into the wall face, L_o (see Figure 5.19) can be determined as:

(5‐23)

The minimum value of safety factor, F_s, is 1.2–1.5. The minimum value of L_o is 0.9 m (3 ft). It is very important to abide by this minimum L_o value.

Step 9: Check external stability

The external stability of the reinforced soil wall against overturning failure, base sliding, bearing failure, and overall slope failure should be checked. The checks should be carried out by treating the reinforced soil mass as a rigid wall.

• For overturning failure check, stabilizing and destabilizing overturning moments about the toe of the wall should be calculated to determine the safety factor against overturning failure. Typically, a minimum safety factor of 1.5 is needed.
• For base sliding failure check, stabilizing and destabilizing forces along the base of the wall should be calculated to determine the safety factor against sliding failure. Typically, a minimum safety factor of 1.5 is needed.
• For bearing failure check, the applied resultant load (typically an inclined resultant load) at the base of the wall (due to self‐weight of the wall, externally applied loads on the crest, and lateral earth thrust against the reinforced soil mass) and the load‐carrying capacity of the ground beneath the base of the wall should be calculated (by using the bearing capacity equations for shallow foundation, e.g., NAVFAC, 1986; Terzaghi et al., 1996) to determine the safety factor against bearing failure. Typically, a minimum safety factor of 3.0 is needed.
• For overall slope failure check, slope stability software is usually needed to evaluate the safety factors of the different assumed slip planes of the wall, involving soil behind and below the reinforced soil mass, and determine the minimum safety factor against overall slope failure. Typically, a minimum safety factor of 1.3 is needed.

If any of the required minimum safety factors are not met, one of the following two measures (or combination of the measures) could be taken to achieve required safety margins: (i) revise the design, such as decrease reinforcement spacing, increase reinforcement length, decrease wall height, etc., or (ii) improve the soil, including use of better reinforced fill material, improve fill compaction, improve the foundation soil, etc.

Step 1: Establish wall profile and check design assumptions

A typical cross‐section of the wall is shown in Figure 5.20. The design assumptions listed in Step 1 of Section 5.4.1 are verified, including granular backfill and a firm foundation.

Step 2: Determine backfill properties ϕ and γ

The backfill is granular, with moist unit weight γ = 115 lb/ft³, c' = 0 and ϕ' = 37° at 95% of AASHTO T‐99 maximum density.

Step 3: Develop a lateral earth pressure diagram due to soil self‐weight plus surcharge

The coefficient of earth pressure at‐rest,

The lateral earth pressure at depth z due to self‐weight and surcharge is:

This lateral earth pressure is tabulated under σ_h (o) in Table 5.4 and plotted in Figure 5.22.

Step 4: Develop a lateral earth pressure diagram due to live loads

The lateral earth pressure due to the eight‐wheel live load of 40 kips can be determined conservatively with the aid of the lateral earth pressure influence diagram shown in Figure 2.11. The earth pressure due to the live load in 2‐ft increments of the wall height is evaluated at two selected vertical sections: Sections A and B (see Figure 5.21; Table 5.5). The earth pressure is found to be larger in Section A than in Section B, thus the pressure at Section A is used in the design. The earth pressure due to the live load is tabulated under σ_h(l) in Table 5.4 and plotted in Figure 5.22.

Step 5: Develop a combined lateral earth pressure diagram

A combined earth pressure diagram is obtained by superimposing the earth pressures obtained in Steps 3 and 4. The combined earth pressure along the wall height is tabulated under σ_h in Table 5.4 and plotted in Figure 5.22.

Step 6: Determine the vertical spacing of reinforcement layers

For the trial reinforcement (a polyester needled geotextile), the ultimate strength is reduced by a factor of 0.7, per Step 6 of Section 5.4.1, thus . Using a safety factor F_s of 1.5, the vertical spacing, s_v , is:

The required minimum vertical spacing along the wall height is tabulated in Table 5.4. A uniform vertical spacing of 1.5 ft (or 18 in.) is selected.

Step 7: Determine the length of reinforcement

With F_s = 1.5, the required anchored length behind the potential failure plane, L_e , and the length within the potential failure wedge, L_f , are:

Note that the length L_e must at least be 0.9 m (3 ft), thus is selected. The values of L_e and L_f as well as the total reinforcement length L () along the wall height are listed in Table 5.4. A uniform length of 2.7 m (9 ft) is selected for all reinforcement layers.

Step 8: Determine the wrapped length of reinforcement

The wrapped length, L_o, into the wall face is:

The values of L_o along the wall height are also listed in Table 5.4. All the L_o values are found to be less than the minimum required length of 0.9 m (3 ft), therefore L_o of 0.9 m (3 ft) is selected for all reinforcement layers.

Step 9: Check external stability

External stability against overturning failure, base sliding, bearing failure, and overall slope failure need to be checked before accepting the design.

Step 1: Determine the friction angle (ϕ) and unit weight (γ) of the fill in and behind the reinforced zone

The friction angle (ϕ) should be estimated conservatively by an experienced soils engineer or determined by performing direct shear tests (AASHTO T236‐72) or triaxial tests (AASHTO T234‐74) on project‐specific fill materials. The soil strength should be evaluated at residual stress levels. In the absence of reliable project‐specific soil data, maximum friction angles of 30° and 34° should be used for external stability analysis and internal stability analysis, respectively.

Step 2: Determine the depth of embedment

Minimum embedment at the front face of the wall (measured from the adjoining finished ground surface to the bottom of footings) should be at least 2 ft (0.6 m), and greater than the maximum frost penetration depth at the wall site. In addition, the following requirements must be satisfied (H = wall height, measured from the bottom of the lowest block to the top of the fill behind the facing):

• For a horizontal ground surface in front of the wall: minimum embedment = H(ft)/20 (for walls) and H(ft)/10 (for abutments).
• For a sloping ground surface in front of the wall: minimum embedment = H(ft)/10 for a 3H:1V slope, H(ft)/7 for a 2H:1V slope, and H(ft)/5 for a 1.5H:1V slope, and there needs to be a minimum horizontal bench of 4 ft (1.2 m) in front of the wall.

For walls constructed along rivers and streams, the foundation depth must be at least 2 ft (0.6 m) below the potential scour depth.

Step 3: Select a tentative reinforcement length

A tentative reinforcement length of at least 0.7H (H = wall height measured from the bottom of the lowest block to the top of the fill behind the facing near the top of the wall) should be selected, and no less than 8 ft (2.4 m) for strip‐ or grid‐type reinforcement. Unless substantial evidence is presented to justify variation in reinforcement length, the length of reinforcement should be uniform throughout the entire wall.

Step 4: Determine the forces acting on the reinforced soil mass

The reinforced soil mass is treated as a rigid body for external stability computations. All forces acting on the reinforced soil mass, including body force due to self‐weight of the reinforced mass and forces acting on the reinforced soil mass, should be determined. The forces for walls with a level crest and an inclined crest are shown in Figures 5.23(a) and (b), respectively.

Step 5: Check stability against overturning

For walls with a level crest, the safety factor against overturning (about point O, Figure 5.23(a)) is calculated as:

(5‐24)

As shown in Figure 5.23(a), L is the length of the reinforced zone, H is the wall height, V₁ is the body force (self‐weight) of the reinforced soil mass, F₁ is lateral force due to the fill behind the reinforced mass, and F₂ is lateral force due to a uniform traffic surcharge load, q, which is assumed to act only beyond the reinforced zone in computations involving resisting forces/moments for external stability check.

For walls with an inclined crest, the safety factor against overturning (about point O) can be calculated as:

(5‐25)

As shown in Figure 5.23(b), L is the length of the reinforced zone, H is the wall height, h is the height of the fill above the end of the reinforcement, V₁ and V₂ are body forces of the reinforced soil mass, and F_H and F_V are, respectively, the horizontal and vertical components of the lateral thrust F due to fill behind the reinforced mass.

The minimum value of FS_overturning should be at least 2.0 for all walls. If the safety margin is found insufficient, the safety factor may be increased by increasing the reinforcement length.

Step 6: Check stability against base sliding

For walls with a level crest, the safety factor against sliding is calculated as:

(5‐26)

Note that the uniform traffic surcharge load, q, is assumed to act only beyond the reinforced zone in the computation of resistance to base sliding in the external stability check.

For walls with an inclined crest, the safety factor against sliding is calculated as:

(5‐27)

where parameter δ is the friction angle between the backfill and foundation. The value of δ can be assumed to be the internal friction angle of the backfill or the foundation soil, whichever is smaller. The value of FS_sliding must be at least 1.5. If the safety margin is found to be insufficient, the safety factor may be increased by increasing the roughness at the base of the wall (i.e., at the backfill–foundation contacting surface) or by increasing the reinforcement length.

Step 7: Check overall stability of slopes in the vicinity of the wall

Overall slope stability encompassing the entire wall and the stability of the inclined sloping crest (if present) should be checked by using the limiting equilibrium methods of analysis, such as the modified Bishop, simplified Janbu, or Spencer methods of analysis. The recommended minimum factors of safety are listed in Table 5.6. If the safety margin is found to be insufficient, the slope should be stabilized by an appropriate method (e.g., TRB, 1996).

Step 8: Check bearing capacity of wall foundation

Bearing capacity of the wall foundation should be checked by considering the bottom of the reinforced soil mass as a rigid footing. The footing has a width of L, which is the length of the reinforcement at the foundation level, and is subjected to a concentrated eccentric load. The eccentricity, e, measured from the centerline of the reinforced soil mass (see Figure 5.23), can be calculated as:

(5‐28)

where M_r and M_d are, respectively, resisting moment and driving moment for overturning of the reinforced soil mass (as determined in Step 5), and R_V is the resultant of vertical forces (; for walls with a level crest, ). The eccentricity must stay within the middle third of the reinforced soil mass, i.e.,

(5‐29)

The bearing pressure, , must have a safety factor of at least 2, i.e.,

(5‐30)

If the safety margin is found to be insufficient, the safety factor may be increased by improving the foundation soil (using techniques such as compaction, staged construction, preloading, wick drain, grouting, etc.) or by increasing the reinforcement length.

Step 9: Select reinforcement and determine the limit state tensile load and serviceability tensile load

Upon selecting a particular reinforcement for the wall, a series of controlled laboratory creep tests will need to be conducted. The tests should be performed for a minimum duration of 10,000 hours for a range of load levels on samples of the selected reinforcement. The samples should be tested in the anticipated loading direction, in either a confined or an unconfined condition, and typically at an assumed in‐ground temperature of 70°F. The test results are to be extrapolated over the required design life using the procedures outlined in ASTM D2837.

From the laboratory creep tests, two tensile loads may be determined: limit state tensile load (T_limit) and serviceability state tensile load (T_service). The limit state tensile load is the highest load level at which the log time vs. creep‐strain rate relationship continues to decrease with time within the design life without inducing either brittle or ductile failure. The serviceability state tensile load, on the other hand, is the load level at which total strain will not exceed 5% within the design life. The design life is typically 75 years. Designated critical walls, however, may be designed for a 100‐year service life.

Step 10: Determine the allowable tensile load of reinforcement

The allowable tensile load in the reinforcement, T_a , is the lesser of two allowable tensile loads at limit state (T_al) and at serviceability state (T_as). The allowable limit state tensile load, T_al , is determined as:

(5‐31)

where T_limit is the limit state tensile load determined in Step 9; F_D is a durability safety factor to account for such effects as aging, chemical degradation, biological degradation, temperature variations, environmental stress cracking, and plasticization; F_C is a construction damage safety factor; and F_S is an overall safety factor to account for uncertainties in structure geometry, fill properties, reinforcement manufacturing variations, and externally applied loads. The minimum value of F_S is 1.5, whereas F_D and F_C should be determined by tests simulating the anticipated field conditions. If the facing of a wall is composed of dry stacked concrete blocks and facing connection strength is lower than T_al , the allowable tensile load at limit state (T_al) should be reduced further to account for possible connection failure.

On the other hand, the allowable serviceability state tensile load, T_as , is determined as:

(5‐32)

where T_service is determined in Step 9, F_D is the durability safety factor, and F_C is the construction damage safety factor.

Step 11: Develop a combined lateral earth pressure diagram due to overburden pressure, surcharge, and live loads

Similar to Step 5 of the U.S. Forest Service method (Section 5.4.1), the lateral earth pressure diagrams due to gravity, uniform normal surcharge, and live loads are superimposed to form a combined lateral earth pressure diagram.

Step 12: Determine vertical spacing of reinforcement layers

Vertical spacing between reinforcement layers, s_v , is determined as:

(5‐33)

where T_a is the allowable tensile load determined in Step 10 and σ_h is the lateral earth pressure at the mid‐depth of the reinforcement layer, obtained from the combined pressure diagram determined in Step 11.

For walls of low to medium height (say, 10–15 ft or 3.0–4.5 m), a uniform vertical spacing is generally selected for all reinforcement layers. In such a case, the value of s_v only needs to be evaluated at the depth where σ_h is largest. If the value of s_v turns out to be too small (say, less than the typical block height of 8 in. or 0.2 m), a different reinforcement with a larger allowable tensile load may be selected.

Step 13: Check stability against pullout failure

Similar to the USFS method shown in Figure 5.19, the anchored length behind the potential failure plane (L_e) needed to prevent pullout failure from occurring is equal to the total reinforcement length (L) minus the length within the potential failure zone. For a reinforcement layer at depth z below the crest,

(5‐34)

where H is wall height and z is the depth of the reinforcement layer being considered.

The safety factor against pullout failure for the reinforcement layer being considered is evaluated as:

(5‐35)

where σ_v is the vertical stress at the depth of the reinforcement and f is the friction coefficient between backfill and reinforcement; , in which δ = friction angle at the backfill–reinforcement interface. In the absence of reliable test data, δ can be taken as 2/3 of the internal friction angle of the backfill, ϕ. The safety factor against pullout for every reinforcement layer as determined from Eqn. (5‐35) must be at least 1.5, and the anchored length L_e must be at least 3 ft. If the safety factor is less than 1.5, the reinforcement length may be increased.

Step 1: Determine friction angle, ϕ′, and unit weight, γ, for the fill in and behind the reinforced zone

The fill has a moist unit weight γ = 115 lb/ft³ and c' = 0, ϕ' = 37°.

Step 2: Determine depth of embedment

Consider the following three conditions: (i) minimum embedment depth, measured from the finished ground surface to the bottom of the wall footings, should be at least 2 ft; (ii) minimum embedment for horizontal ground surface in front of the wall = H/20, i.e., 0.6 ft; and (iii) the embedment depth of the wall, measured from the finished ground surface to the bottom of the wall footings, should not be less than the maximum frost penetration depth at the wall site (4 ft). For 1‐ft thick footings, the wall height (H), measured from the leveling pad of the footings, will be 12 + 4 – 1 = 15 (ft).

Step 3: Select a tentative reinforcement length

A tentative length of 0.7H, or 10.5 ft, is selected for the entire wall.

Step 4: Determine the forces acting on the reinforced soil mass

As depicted in Figure 5.25, the reinforced soil mass is subjected to three resultant forces: (i) weight of the reinforced soil mass, V₁ = 18,100 lb/ft, (ii) lateral earth thrust due to retained earth, F₁ = 3,234 lb/ft, and (iii) lateral force due to traffic surcharge, F₂ = 938 lb/ft.

Step 5: Check stability against overturning

The factor of safety against overturning is calculated as:

The safety factor is greater than the minimum required value of 2.0 (OK).

Step 6: Check stability against base sliding

The safety factor is greater than the minimum required value of 1.5 (OK).

Step 7: Check overall stability of slopes in the vicinity of the wall

Using the simplified Bishop method for stability analysis of slopes encompassing the entire wall, the minimum safety factor against overall slope failure can be determined. The safety factor needs to be at least 1.5.

Step 8: Check the bearing capacity of wall foundation

The eccentricity measured from the centerline of the reinforced soil mass is:

Alternatively,

The value e is less than L/6 = 1.75 ft (OK).

The applied bearing pressure σ_v = 18,100/[10.5/2 – 2(1.60)] = 2,480 (lb/ft²). For blow count (N) = 30, ϕ = 36°, hence N_γ = 50 and N_q = 32. Therefore, the ultimate bearing capacity is:

Thus,

The bearing capacity safety factor is greater than the minimum required value of 2.0 (OK).

Step 9: Select reinforcement and determine the limit state tensile load and serviceability tensile load

A polypropylene woven geotextile is selected as the reinforcement. For a design life of 75 years, the geotextile reinforcement has a limit state tensile load T_limit = 2,500 lb/ft and a serviceability state tensile load T_service = 1,500 lb/ft, as determined from a series of controlled laboratory creep tests.

Step 10: Determine the allowable tensile load of reinforcement

The allowable limit state tensile load, T_al , is determined as:

The allowable serviceability state tensile load, T_as, is determined as:

Thus, the allowable tensile load, T_a = 500 lb/ft.

Step 11: Develop a combined lateral earth pressure diagram due to overburden pressure, surcharge, and live loads

The lateral earth pressure at depth z is:

where the coefficient of active earth pressure, .

In the absence of live loads, the maximum lateral earth pressure will occur at the base of the wall (i.e., at z = 15 ft), which is equal to 494 lb/ft².

Step 12: Determine the vertical spacing of reinforcement layers

Select uniform spacing for all reinforcement layers,

Step 13: Check stability against pullout failure

The smallest anchored length behind the potential failure surface is at the uppermost reinforcement layer, for which . This L_e value is greater than the minimum required value of 3.0 ft (OK).

The minimum safety factor against pullout failure is:

The safety factor is greater than the minimum required value of 1.5 (OK).

Step 1: Establish design parameters

• Establish abutment geometry and loads (ref. Figure 5.26):
  • the wall is composed of a lower wall (load‐bearing wall) and an upper wall (back wall), with concrete block facing
  • total abutment height, H', is the sum of lower wall height and upper wall height
  • load‐bearing wall (lower wall) height, H₁, is measured from the base of the embedment to the top of the load‐bearing wall
  • back wall (upper wall) height, H₂
  • equivalent traffic surcharge, q
  • bridge vertical dead load, DL
  • bridge vertical live load, LL
  • bridge horizontal load
  • bridge span and type (simple or continuous span)
  • length of approach slab
  • If there is a strong likelihood that erosion or other untoward events at the wall base will not be an issue throughout the design life, embedment of a GRS abutment wall needs only be a nominal depth (say, one block height, typically 8 in.). If the foundation contains frost susceptible soils (i.e., silts, silty tills, etc.), they should be excavated to at least the maximum frost penetration line and replaced with a non‐frost susceptible soil. If the GRS abutment is situated in a stream environment, scour/abrasion/channel protection measures should be undertaken.
• Establish trial design parameters:
  • sill width, B (a minimum sill width of 0.6 m (12 in.) is recommended)
  • clear distance between the backface of facing and the front edge of sill, d (a clear distance d = 0.3 m (6 in.) is recommended; the fill compaction within the clear distance is generally less than the rest of the fill)
  • sill type (isolated sill or integrated sill, the former refers to a sill that is a separate unit from the upper wall of the abutment, whereas the latter refers to a sill that is integrated with the upper wall as a combined unit)
  • facing type (dry‐stacked concrete blocks, timber, natural rocks, wrapped geosynthetics, or gabions) and facing block size (for concrete block facing)
  • vertical facing is recommended, although batter of facing with a minimum front batter of 1/35 to 1/40 is commonly used (if a batter is employed, a typical minimum setback of 5–6 mm between successive courses of facing blocks is common for block height of 200 mm (or 8 in.))
  • reinforcement spacing (the default value of reinforcement spacing is 0.2 m (8 in.). For wrapped‐faced geotextile walls, temporary walls or walls where facing may be added subsequently, a reinforcement spacing of 0.15 m (6 in.) is recommended. Reinforcement spacing greater than 0.4 m (16 in.) is not recommended under any circumstances).

Step 2: Determine geotechnical engineering properties

• Check to ensure that the selected fill satisfies the following criteria: 100% passing 100 mm (4 in.) sieve, 0–60% passing No. 40 (0.425 mm) sieve, and 0–15% passing No. 200 (0.075 mm) sieve; and plasticity index (PI) ≤ 6.
• Determine reinforced fill parameters, including:
  • moist unit weight of the reinforced fill
  • the design friction angle of the reinforced fill, ϕ_design, should be taken as one (1) degree lower than the friction angle obtained from direct shear tests, , where ϕ_test is determined by a single set of the standard direct shear tests performed on the portion passing 2 mm (No. 10) sieve, with the specimen compacted to 95% of AASHTO T‐99, Methods C or D, at the optimum moisture content. If multiple sets of direct shear tests are performed, the smallest friction angle could be used in design. For instance, if two sets of tests are performed; one showing a friction angle of 35° and the other 37°, the design friction angle will be 35°. On the other hand, if a single set of tests shows that a soil has a friction angle of 35°, then the design friction angle will be taken as 34°.
• Determine retained earth parameters:
  • friction angle of the retained earth
  • moist unit weight of the retained earth
  • coefficient of active earth pressure of the retained earth.
• Determine foundation soil parameters:
  • friction angle of the foundation soil
  • moist unit weight of the foundation soil
  • allowable bearing pressure of the foundation soil, q_af .
• Determine allowable bearing pressure of the reinforced fill:

  The allowable bearing pressure of the reinforced fill, q_allow, can be determined by a 3‐step procedure as follows:

  1. Use Table 5.7 to determine the allowable bearing pressure for an abutment in the following conditions: (i) the sill is an integrated sill, (ii) sill width = 1.5 m, (iii) a sufficiently strong reinforcement is employed (with minimum required values of stiffness and strength to be determined in Step 9, below), and (iv) the abutment is constructed over a competent foundation (satisfying the bearing pressure requirement in Step 7, below).
  2. Select a sill width for the abutment and use Figure 5.27 to determine a sill width correction factor for the selected sill width. Calculate a corrected allowable bearing pressure, which is equal to the allowable pressure determined in Step 1 above, and multiply by the correction factor. A minimum sill width of 0.6 m is recommended.
  3. If an isolated sill is used, a reduction factor of 0.75 should be applied to the corrected allowable bearing pressure in Step 2, above. No correction is needed for an integrated sill.

The 3‐step procedure for determination of allowable bearing pressure is illustrated in Example 1 and Example 2 below. Note that the allowable bearing pressure determined by the procedure described above is applicable only to GRS abutments founded on a competent foundation and with a sufficiently strong reinforcement.

Step 3: Establish design requirements

• Establish external stability design requirements:
  • factor of safety against reinforced fill base sliding ≥ 1.5
  • eccentricity ≤ L/6 (L = length of reinforcement at base of reinforced zone)
  • average sill pressure ≤ allowable bearing pressure of the reinforced fill, q_allow
  • average contact pressure at the foundation level ≤ allowable bearing pressure of the foundation soil, q_af
• Establish internal stability design requirements:
  • factor of safety against reinforcement pullout, FS_pullout, of every reinforcement layer should be no less than 1.5
  • connection strength is not a design concern if (i) the reinforcement spacing is kept no greater than 0.2 m, (ii) the fill is compacted to the specified value (see Section 6.2.3), and (iii) the average applied pressure on the sill does not exceed the recommended allowable pressure determined in Step 2 above
  • for reinforcement spacing of 0.4 m, facing connection failure should be checked to ensure facing stability (see Section 5.3.5); moreover, for walls with light‐weight concrete block facing, the contact surfaces of the top 2 to 3 courses of the facing block should be bonded together by pouring concrete mix through the course or using adhesives to improve facing stability (see Section 6.2.4 and Figure 6.1)
  • studies have suggested that concrete reinforced soil walls will be much stronger if the facing blocks are interconnected through the hollow cells (by use of rebar and cement) after all facing units are in place.

Step 4: Choose facing type and reinforcement spacing

Facing type, including wrapped geotextile facing, dry‐stacked concrete block facing, timber facing, natural rock facing and gabion facing, may be selected. Reinforcement spacing between 0.15 m (6 in.) and 0.4 m (16 in.) can be selected. However, smaller reinforcement spacing is highly recommended. For concrete block facing, reinforcement spacing should be a multiple of a single block height.

Step 5: Determine a trial reinforcement length

• A trial reinforcement length, L, can be taken as 0.7 × total abutment wall height (, see Figure 5.26).
• The reinforcement length may be truncated in the bottom portion of the wall (see Section 5.3.6) provided that the foundation is competent (as defined earlier in this section). The recommended configuration for the truncated base is: reinforcement length = 0.35H' (H' = total abutment height) at the foundation level and increases upward at about a 45° angle.
• The allowable bearing pressure of the sill (reinforced fill), as determined in Step 2, should be reduced by 10% for a wall with a truncated base.
• When reinforcement is truncated in the bottom portion, the external stability of the wall (i.e., sliding failure, overall slope failure, eccentricity failure, and foundation bearing failure) in Steps 6 and 7 must be thoroughly examined.

Step 6: Size abutment footing/sill

• Establish a trial sill configuration (e.g., establish the value of B, d, H₂ , t, b, fw and fh, Figure 5.28).
• Determine the forces acting on the sill (e.g., see Figure 5.28) and calculate the factor of safety against sliding, FS_sliding , which needs to be ≥ 1.5.
• Check the sill eccentricity requirement: The load eccentricity at the base of the sill, e', needs to be ≤ B/6 (B = width of sill).
• Check the allowable bearing pressure of the reinforced fill; the applied contact pressure on the base of the sill (reinforced fill) should be ≤ q_allow , as determined in Step 2.

Step 7: Check external stability of reinforced fill (for the trial reinforcement length selected in Step 5)

• Determine the forces needed for evaluating the external stability of the abutment, e.g., V₄ , V₅ , V_q , F₃ , F₄ (see Figure 5.29) and l₁, the influence depth due to the horizontal forces in the upper wall (see Figure 5.30).
• Calculate the factor of safety against sliding of the reinforced zone, FS_sliding , which needs to be ≥ 1.5.
• Check the eccentricity requirement for the reinforced volume, e, which needs to be ≤ L/6 (L = length of reinforcement).
• Check the allowable bearing pressure of the foundation soil:
  • Determine the influence length D₁ at the foundation level (, see Figure 5.30) and compare it to the effective reinforcement length, .
  • Determine the contact pressure on the foundation level, p_contact , calculated by dividing the total vertical load in the reinforced volume by D₁ or L', whichever is smaller.
  • The contact pressure p_contact needs to be ≤ q_af .

If the bearing pressure of the foundation soil supporting the bridge abutment is only marginally acceptable or slightly unacceptable, a reinforced soil foundation (RSF) may be employed to increase the bearing capacity and reduce potential settlement. A typical RSF is formed by excavating a pit at the planned location of bridge abutment and backfilled with compacted road base material that is reinforced by the same reinforcement for the reinforced abutment wall on 0.3 m vertical spacing. The pit should typically be 0.5L deep (L = reinforcement length), and at least cover the footprint of the reinforced fill, and should extend no less than 0.25L in front of the wall face. A generic design protocol for RSF has recently been proposed by Wu (2018).

Step 8: Determine internal stability at each reinforcement level

The internal stability is evaluated by computing the factor of safety against the reinforcement pullout failure at each reinforcement level. Rupture failure is addressed later in Step 9. The factor of safety against pullout failure, FS_pullout , at a given reinforcement level is equal to pullout resistance at the reinforcement level divided by T_max, which is the reinforcement tensile thrust at the reinforcement level where the pullout safety factor is being evaluated.

The value of T_max can be calculated as the product of the average Rankine active lateral earth pressure of the reinforcement level and reinforcement vertical spacing. The pullout resistance, on the other hand, derives from the frictional resistance at the soil–reinforcement interface along the portion of reinforcement beyond the potential failure plane. The potential failure plane is taken as the active Rankine failure plane with a uniform vertical surcharge. FS_pullout at all reinforcement levels need to be ≥ 1.5.

Step 9: Determine the required minimum reinforcement stiffness and strength

A required minimum ultimate tensile stiffness and a required minimum tensile strength are needed for specifying the geosynthetic reinforcement to be used in the design of a GRS abutment to ensure sufficient tensile resistance at the service load and a sufficient safety margin against rupture failure.

The tensile stiffness is defined as the tensile resistance at a working strain, namely, the secant modulus of reinforcement at a selected strain under in‐service condition. It is recommended that a tensile strain of 1.0% be taken as the working strain for GRS abutment walls. The required minimum reinforcement stiffness in the direction perpendicular to abutment wall face,  , is determined as:

(5‐36)

where σ_h(max) is the largest lateral stress in the reinforced fill and s_v is the vertical reinforcement spacing. For non‐uniform reinforcement spacing, s_v = (½ distance to reinforcement layer above) + (½ distance to reinforcement layer below).

The required minimum value of the ultimate reinforcement strength in the direction perpendicular to abutment wall face, T_ult , is determined by imposing a combined safety factor on  , i.e.,

(5‐37)

The combined safety factor F_s is used to (i) ensure satisfactory long‐term performance, (ii) ensure sufficient ductility of the abutment, and (iii) account for various uncertainties. Recommended values for the combined safety factor are: F_s = 5.5 for reinforcement spacing ≤ 0.2 m and F_s = 3.5 for reinforcement spacing of 0.4 m (Note: F_s is smaller for s_v = 0.4 m than for s_v ≤ 0.2 m because the influence of spacing is compensated for in Eqn. (5‐36)). These combined safety factors are applicable only to the condition where the backfill material and placement conditions satisfy those given in Section 6.2.3.

Step 10: Design the back/upper wall

If the back wall (upper wall) of a bridge abutment is to be a reinforced soil wall, it should be designed in a manner similar to the load‐bearing wall (lower wall). In most cases, the same fill, same reinforcement, and same fill placement conditions as those of the load‐bearing wall should be employed in the back wall, although the default reinforcement spacing in the approach fill may be increased somewhat, say from 0.2 m to 0.3 m. The length of all the layers of reinforcement should be extended approximately 1.5 m beyond the end of the approach slab to produce a smoother subsidence profile over the design life of the abutment and help eliminate potential bridge bumps. If there is serious space constraint, it is recommended that at least the top two to three layers of reinforcement should undertake this measure.

Step 11: Check angular distortion between abutments or piers

Angular distortion between any two bridge supporting structures (abutments or piers) should be checked to ensure ride quality and structural integrity. Angular distortion = (difference in total settlements between bridge supporting structures)/(span between the bridge supporting structures). The angular distortion should be limited to 0.005 (or 1:200) for simple span structures, and 0.004 (or 1:250) for continuous span structures.

The total settlement of a bridge supporting structure is the sum of foundation settlement (i.e., settlement occurs beneath the abutment) and settlement within the bridge supporting structure. Foundation settlement due to the self‐weight of a GRS abutment/pier and subjected to bridge loads can be estimated by conventional settlement computation methods in soils engineering textbooks or reports (e.g., Terzaghi et al., 1996; Perloff, 1975; Poulos, 2000). Settlement of bridge supporting structures, under the recommended allowable bearing pressure determined in Step 2 (above), can be conservatively estimated as 1.5% of H₁ (H₁ = height of the load‐bearing wall).

In situations where the heights of two load‐bearing walls at the two ends of a bridge are significantly different, preloading or prestressing the load‐bearing walls may be an effective measure to alleviate problems associated with differential settlement. The level of preloading/prestressing and probable reduction in differential settlement due to preloading of a reinforced soil mass can be evaluated by a procedure proposed by Ketchart and Wu (2001, 2002).

If differential settlement is due to differences in foundation settlement, a number of remedial measures (e.g., vibroflotation for granular deposits, wick drain with surcharge for cohesive deposits) for reducing foundation settlement can be employed to mitigate the problem.

Step 1: Establish design parameters

Wall heights and external loads (ref. Figure 5.31):

Trial design parameters (ref. Figure 5.31):

Note: Since a batter of 1/35 corresponds to an angle of 1.6°, which is far less than 10°, the abutment wall can be designed as a vertical wall and the coefficient of earth pressure is to follow the Rankine active earth pressure theory for walls with a vertical backface.

Step 2: Determine geotechnical engineering properties

Reinforced fill:

• The selected fill satisfies the following criteria: 100% passing 100 mm (4 in.) sieve, 0–60% passing No. 40 (0.42 mm) sieve, and 0–15% passing No. 200 (0.074mm) sieve; PI ≤ 6, and maximum soil particle size = 20 mm (3/4 in.).
• The friction angle of the fill is 35°, as determined by one set of standard direct shear test on the portion finer than 2 mm (No. 10) sieve, using a specimen compacted to 95% of AASHTO T‐99, Methods C or D, at optimum moisture content.
• 

  Note: The design friction angle is taken as one degree lower than ϕ_test, i.e., (see Design Procedure Step 2, Section 5.6.1).

Determine allowable bearing pressure of the reinforced fill, q_allow, for following conditions:

• 
• Reinforcement spacing = 0.2 m (uniform reinforcement length with no truncation)
• Integrated sill, sill width = 1.5 m
  1. From Table 5.7, for ϕ = 34° and reinforcement spacing = 0.2 m, allowable bearing pressure is 180 kPa.
  2. From Figure 5.27, correction factor for sill width of 1.5 m is 1.0, thus corrected allowable bearing pressure .
  3. No reduction for an integrated sill, thus

Retained earth:

Foundation soil:

Step 3: Establish design requirements

External stability design requirements:

• Design life = 75 years
• Factor of safety against sliding, FS_sliding ≥ 1.5
• Eccentricity ≤ L/6
• Sill pressure ≤ allowable bearing pressure of the reinforced fill, q_allow = 180 kPa
• Average contact pressure at the foundation level ≤ allowable bearing pressure of the foundation soil, q_a = 300 kPa

Internal stability design requirements:

• Factor of safety against pullout, FS_pullout ≥ 1.5
• Facing connection strength is OK with reinforcement spacing = 0.2 m (see Step 3, Section 5.6.1)

Step 4: Choose facing type and reinforcement spacing

• Concrete blocks, 200 mm (depth) × 200 mm (height) × 400 (width)
• Reinforcement spacing in the load‐bearing wall (the lower wall) = 0.2 m

Step 5: Determine a trial reinforcement length

Trial reinforcement length = 0.7 × total abutment height

Step 6: Size abutment footing/sill

Preliminary sill configuration and forces acting on the sill are shown in Figure 5.32. The dimensions of the sill are:

With the unit weight of concrete, , the forces acting on the sill are determined as:

Check factor of safety against sliding:

Check eccentricity requirement:

Check allowable bearing pressure of the reinforced fill:

Step 7: Check external stability of reinforced fill (for the trial reinforcement length selected in Step 5)

The forces involved in evaluation of external stability of the abutment are shown in Figure 5.31. These forces are calculated as follows.

l₁ is the influence depth due to the horizontal forces in the back wall (see Figure 5.33, cf. Figure 5.30):

Check the factor of safety against sliding for the reinforced volume:

Check the eccentricity requirement for the reinforced volume:

Check the allowable bearing pressure of the foundation soil:

Calculate the effective length D₁ at the foundation level and compare with the effective reinforcement length, L'.

As D₁ at the foundation level is greater than L' , the contact pressure on the foundation level, p_contact , is calculated as follows.

Step 8: Determine internal stability at each reinforcement level

With geosynthetic reinforcement, the coefficient of lateral earth pressure is constant for the entire wall height. The internal stability is evaluated by checking stability against reinforcement pullout failure (Note: rupture failure is to be addressed later in Step 9).

Check reinforcement pullout failure:

• α is a scale effect correction factor, ranging from 0.6 to 1.0 for geosynthetic reinforcement; for geotextile, α is defaulted to 0.6.
• σ_v ∙ L_e is the normal force at the soil–reinforcement interface at depth z (excluding traffic surcharge).
• 
• L_e = length of reinforcement in the resistant zone behind the failure surface at depth z =
• L_a = length of reinforcement in the active zone at depth z   =
• L_i = length of reinforcement within the influence area inside the resistant zone; this length can be measured directly from the design drawing
• m = reinforcement effective unit perimeter; m = 2 for strips, grids, and sheets
• R_c = coverage ratio; R_c = 1.0 for 100% coverage of reinforcement
• σ_h = horizontal pressure at depth z =
• σ_vs = vertical soil pressure at depth z =
• Δσ_v = distributed vertical pressure from sill = ΣV_a/D
  • D = effective width of applied load at depth z
  • For z ≤ z₂ ,
  • 
• Δσ_h = supplement horizontal pressure at depth z
  • For z ≤ l₁,
  • For z > l₁,
• T_max = maximum tensile force in the reinforcement at depth z =
• s_v = vertical reinforcement spacing
• FS_pullout = factor of safety against reinforcement pullout
• FS_pullout =

Let depth z be the depth measured from the top of the load‐bearing wall. We will use reinforcement layer no. 25 at z = 2.5 m (see Figure 5.33) as an example for determination of FS_pullout.

Since , therefore

Since , therefore

Calculate the normal force at z = 2.5 m:

The values of FS_pullout for all reinforcement layers in the load‐bearing wall are summarized in Table 5.8.

Step 9: Determine the required minimum reinforcement stiffness and strength

The required minimum working reinforcement stiffness is determined as:

The required minimum ultimate reinforcement strength is determined as:

The recommended combined safety factor is F_s = 5.5 for reinforcement ≤ 0.2 m, and F_s = 3.5 for reinforcement spacing of 0.4 m.

From Table 3.2, σ_h(max) is 59.84 kN/m², at reinforcement no. 1 at depth z = 7.3 m and with s_v = 0.2 m.

The uniform reinforcement spacing is 0.2 m, hence F_s = 5.5.

A reinforcement with minimum working stiffness, = 12.0 kN/m and minimum ultimate strength (per ASTM D4595 for geotextiles and D6637 for geogrids), T_ult = 66.0 kN/m is required.

Step 10: Design of back/upper wall

Step 11: Check angular distortion between abutments or piers

If the magnitude of settlement between any span of a bridge (i.e., between any adjacent abutments or piers) is expected to be different, angular distortion will need to be checked. For demonstration purposes, the following calculations for angular distortion are made with an assumed value of foundation settlement.

δ_foundation = foundation settlement (as determined by conventional settlement computation methods)

Assume

Assuming the other end of the bridge segment is zero,angular distortion = (δ_total – 0)/span length = 0.1225 m/24 m = 0.0051

Largest tolerable angular distortion for simple span = 0.005

Angular distortion = 0.0051 ≈ 0.005 (OK)

Design Summary:

The configuration for the final design is shown in Figure 5.34.

Abutment configuration:

Load‐bearing wall height, H1	7.5 m
Back wall (upper wall) height	2.2 m
Facing	dry‐stacked concrete blocks (200 × 200 × 400 mm)
Front batter	1/35
Sill type	integrated sill
Sill width	1.5 m
Sill clear distance	0.3 m
Embedment	200 mm (one facing block height)

Reinforcement:

Minimum working stiffness, T_@ ε=1.0% = 12.0 kN/m

Minimum ultimate strength, T_ult = 66.0 kN/m

Length in load‐bearing wall = 7.0 m

Length of top three layers in load‐bearing wall = 7.5 m

Vertical spacing in load‐bearing wall = 0.2 m

Length in back wall = 5.75 m

Vertical reinforcement spacing in back wall = 0.3 m

Step 1: Establish wall profile and verify design conditions

A wall profile for design should be established in consideration of the grading plan at the wall site. When a project involves variation in wall height along the longitudinal direction, the designer should choose proper height intervals to allow for a gradual change in height. An example is given in Figure 5.35.

The conditions for non‐load‐bearing applications listed at the beginning of Section 5.7 should be checked. If the conditions are not met, the design method is not recommended.

Step 2: Determine design parameters for reinforced fill, retained fill, and foundation

Soil parameters needed for design include:

• moist unit weight (γ), Mohr–Coulomb angle of internal friction (at peak strength) (ϕ ), and angle of dilation (ψ) of the compacted fill in the reinforced soil zone
• moist unit weight (γ_rf ) and Mohr–Coulomb angle of internal friction (at peak strength) (ϕ_rf ) of the fill in the retained fill zone (i.e., immediately behind the reinforced soil zone)
• moist unit weight (γ_f) and Mohr–Coulomb strength parameters (at peak strength) (c_f and ϕ_f ) of the foundation soil; for purely cohesive foundation: ϕ_f = 0 and c_f = undrained shear strength, which can be determined by appropriate field or laboratory tests; for granular foundation: c_f = 0, and ϕ_f can be estimated from standard penetration blow count or other in situ shear strength tests.

For a granular fill material, the value of ϕ in a set of direct shear tests should be determined by drawing a best‐fit straight line through the data points and ignoring the cohesion.

Step 3: Determine forces acting on reinforced soil mass

The reinforced soil mass together with block facing (where the block facing is regarded as a façade) should be considered as a rigid body when evaluating external stability. Figures 5.36(a) and (b) show forces acting on and in the reinforced soil mass for external stability evaluation of a GRS wall with a level crest (also referred to as horizontal backslope) and with a sloping crest (also referred to as sloping backslope), respectively. The figure includes body force (e.g., self‐weight), traffic surcharge, and earth thrusts from the retained fill on the reinforced soil mass. The coefficient of Rankine active earth pressure, K_A, in Figure 5.36(a) is calculated as:  .

GRS walls with a break in the crest slope (see Figure 5.37), referred to as a broken crest or broken backslope, can be analyzed as an equivalent sloping crest (shown by a dashed line in Figure 5.37) if the break in the slope is located within 2H from the back of the wall face (H = total wall height measured from the bottom of the lowest block), as suggested by AASHTO (2002, 2014). Alternatively, the actual slope geometry of the broken crest can be analyzed by the Coulomb theory, with the soil–wall friction angle δ as discussed in Section 2.4.

In subsequent steps, the design computations will involve resisting forces/moments and driving forces/moments for evaluation of safety factors. To be on the conservative side, for calculations of resisting forces/moments, the traffic surcharge in the crest area is assumed to begin at the end of the reinforced zone (see Figure 5.36(a)). For calculations of driving forces/moments, on the other hand, the surcharge is assumed to extend over the entire crest area.

Step 4a (for walls with a sloping crest, skip to Step 4b): Determine a tentative reinforcement length of a GRS wall with a level crest

A tentative reinforcement length is obtained by considering two potential failure modes: (i) lateral sliding failure and (ii) eccentricity failure. If all reinforcement layers are to have the same length, the tentative reinforcement length should be the greater of the two lengths obtained from the above two modes of failure. Should construction of the wall involve excavation into rock outcrop or heavily overconsolidated clay, the costs of excavation to accommodate uniform reinforcement length may be impractically high. In such a situation, the use of shorter reinforcement in the lower portion of the reinforced zone (referred to as the truncated base) is allowed, especially if the fill material is free‐draining and the foundation soil is firm. Note that the provision of a truncated base (see Step 5 of the NCHRP design method, Section 5.6.1) will affect external stability, movement of the wall face, etc. Note also that overturning failure check is not needed because it is always less critical than eccentricity failure (lift‐off of reinforced soil mass) as long as the safety factor against overturning is smaller than 3.0. For added conservatism, all reinforcement lengths are to be measured from the back of the wall face.

1. Lateral sliding failure

   To obtain a tentative reinforcement length against lateral sliding failure, an initial trial value of may be assumed. For a GRS wall of uniform reinforcement length (see Figure 5.36(a)), the safety factor against lateral sliding is:

   (5‐38)

   Therefore, the required length of reinforcement (L_t) to resist lateral sliding failure is:

   (5‐39)

   In Eqns. (5‐38) and (5‐39), H is the height of the wall at wall face measured from the bottom of the lowest facing block, and δ is the friction angle between the base of the reinforced zone and the foundation soil. If the lowest layer of reinforcement is on the ground surface, δ will be the friction angle between the geosynthetic reinforcement and the foundation soil, which can be obtained by performing interface shear tests of the two materials. If δ is greater than either ϕ or ϕ_f , the lesser value of ϕ and ϕ_f should be used for δ. In the absence of interface shear test results, may be assumed. The recommended minimum safety factor FS_sliding against lateral sliding failure is 1.5.

2. Eccentricity failure

   The reinforced soil mass in a GRS wall is typically subject to both vertical and horizontal forces acting above the base, hence the resultant force at the base of the reinforced soil mass without introducing a bending moment will usually be eccentric. The line of action of the eccentric resultant force needs to stay within the middle third of the base of the reinforced soil mass to prevent lift‐off of the reinforced soil mass from the foundation soil (i.e., to prevent tension at the contact surface). Using the tentative reinforcement length L_t determined from the lateral sliding failure check, the eccentricity e, measured from the centerline of the reinforced soil mass, is:

   (5‐40)

   The parameters in Eqn. (5‐40) are as defined in Figure 5.36(a). Note that surcharge q is not included in the denominator of Eqn. (5‐40) as it is part of the resisting forces. The e value must not be greater than L_t/6. If , a larger value of L_t should be selected, and the corresponding value of e should be re‐calculated. This procedure needs to be repeated until a value of L_t that satisfies is obtained.

Step 4b (for walls with a level crest, skip to Step 5): Determine a tentative reinforcement length of a GRS wall with a sloping crest

A tentative reinforcement length for GRS walls with a sloping crest needs to be obtained by an iterative procedure. A trial reinforcement length, L_t , is first assumed for determination of the safety factor against the lateral sliding failure at the base of the reinforced soil mass. The safety factor against lateral sliding, FS_sliding , needs to be at least 1.5. If FS_sliding is less than 1.5, a longer trial length should be analyzed until FS_sliding ≥ 1.5 is obtained. The tentative reinforcement length L_t that satisfies the lateral sliding failure criterion is then used to check against eccentricity failure (i.e., lift‐off of reinforced soil mass). The reinforcement length needs to be increased again if it fails to meet the eccentricity failure criterion. When construction of a wall involves excavation into rock outcrop or heavily overconsolidated clay, use of shorter reinforcement in the lower portion of reinforced zone (referred to as the truncated base) to minimize excavation is allowed, especially if the fill material is free‐draining and the foundation soil is firm. Note that the provision of a truncated base (see Step 5 of the NCHRP design method, Section 5.6.1) may affect external stability, movement of wall face, etc. Note also that there is no need to check overturning failure in design because it is always less critical than eccentricity failure as long as the safety factor against overturning is smaller than 3.0. For added conservatism, all reinforcement lengths are measured from the back of the wall face.

1. Lateral sliding failure

   To obtain a tentative reinforcement length against lateral sliding failure, an initial trial value of may be assumed. Using this trial value for L_t, a projected vertical height above the end of reinforced zone, h, is determined as , where β is the angle of the sloping crest with the horizontal plane (see Figure 5.36(b)). The resultant active force F_rf , exerted by retained fill on the reinforced soil mass, inclining counterclockwise at an angle β from the horizontal plane, is:

   (5‐41)

   Once F_rf is determined, its horizontal and vertical components F_H and F_V (see Figure 5.36(b)) can be calculated as , and .

   For a GRS wall of uniform reinforcement length (see Figure 5.36(b)), the safety factor against lateral sliding failure, FS_sliding , is:

   (5‐42)

   In Eqn. (5‐42), δ is the friction angle between the base of the reinforced zone and the foundation soil. If the lowest layer of reinforcement is on the ground surface, δ will be the friction angle between the geosynthetic and foundation soil, and the value of δ can be obtained by performing foundation soil–geosynthetic interface shear tests. If δ is greater than either ϕ or ϕ_f , the lesser of ϕ and ϕ_f should be used as δ in the calculation. In the absence of interface shear test results, may be assumed.

   If FS_sliding < 1.5, the above procedure should be repeated with an increased L_t until a value of L_t that gives FS_sliding ≥ 1.5 is obtained. This can be easily accomplished with the aid of a spreadsheet.

2. Eccentricity failure

   The reinforced soil mass in a GRS wall is typically subject to both vertical and horizontal forces (acting above the base), hence the resultant force at the base of the reinforced soil mass without introducing a bending moment will be eccentric. The line of action of the eccentric resultant force needs to stay within the middle third of the base of the reinforced soil mass to prevent lift‐off of the reinforced soil mass from the foundation soil. The length L_t determined from lateral sliding failure may be used to check eccentricity failure by calculating the eccentricity e (measured from the center line of the reinforced soil mass) to see if it satisfies the eccentricity requirement of :

   (5‐43)

   where R_V is the resultant of vertical forces . If , the tentative length is said to satisfy the eccentricity failure criterion; otherwise, L_t needs to be increased_, and a new value of e needs to be calculated until it meets the eccentricity requirement of .

Step 5: Check stability against foundation bearing failure

Following the work of Meyerhof (1963), the safety factor against the foundation bearing failure, FS_bearing, of the reinforced mass can be determined by the following equation:

(5‐44)

where σ_v is the average reaction pressure at the base, which can be determined as follows.

For a level crest with uniform traffic surcharge q:

(5‐45)

For a sloping crest:

(5‐46)

The value of eccentricity, e, in Eqns. (5‐45) or (5‐46) has been determined in Step 4. Forces W₁, W₂ , and F_V are as defined in Figure 5.36(b). The multipliers i_γ and i_c in Eqn. (5‐44) are defined as:

(5‐47)

The angle of inclination λ is the angle between the vertical plane and the orientation of the resultant of all forces acting on the reinforced soil mass (i.e., the resultant of q, W₁, F₁ and F₂ for walls with a level crest, or the resultant of W₁, W₂ , and F_rf for walls with a sloping crest, see Figure 5.36). The bearing capacity factors, N_γ and N_c are a function of friction angle (ϕ_f) of the foundation soil, as given in Figure 5.38. For a cohesive foundation, N_γ = 0 and N_c = 5.14.

The safety factor against foundation bearing failure, FS_bearing , should be at least 2.5. Note that the side shear of the reinforced zone is ignored for conservatism in the above computations, hence FS_bearing = 2.5 (slightly lower than the commonly used value of 3.0 for footings) is recommended. If the value of FS_bearing is less than 2.5, L_t may be increased until FS_bearing ≥ 2.5 is obtained. Alternatively, the embedment depth of the reinforced soil mass may be increased to increase resistance against foundation bearing failure. An increase in embedment is particularly effective if the foundation soil is granular. In this case, (where D_f = depth of embedment) should be added to the numerator in Eqn. (5‐44) for the calculation of FS_bearing , i.e.,

(5‐48)

The values of N_q as a function of ϕ_f are given in Figure 5.38. If the reinforcement length becomes too large (say, ), especially if the foundation soil is cohesive, a reinforced soil foundation as described in Step 12 may be considered.

For GRS walls with a truncated base, the design computations are very similar to those described above. The detailed procedure is illustrated in Design Example 3 in Section 5.7.2.

Step 6: Select vertical reinforcement spacing and block height

Selecting a small value for vertical reinforcement spacing, in multiples of facing block height between 0.1 m (4 in.) and 0.3 m (12 in.), is recommended to take advantage of tight reinforcement spacing to gain significantly better performance and improved stability (Wu et al., 2010). Uniform spacing throughout is usually selected to avoid confusion during actual installation of geosynthetic reinforcement. For taller GRS walls (say, ), however, use of two or more values of vertical spacing may prove to be justifiable, especially for very long walls. When more than one value of reinforcement spacing is selected, smaller spacing is generally used in lower layers. Alternatively, if reinforcement spacing is to be kept constant for the entire wall, weaker reinforcement may be used for the upper part of the wall.

When reinforcement is not placed at every course of facing blocks, the CTI tail (shortened reinforcement in place of full‐length reinforcement) on every other block may be employed. The CTI tail typically extends only 1.0 m (3 ft) behind the back of facing blocks (see Section 6.1.1). Great care needs to be exercised to avoid confusion on sequencing of reinforcement placement during construction when the CTI tail is used.

Step 7: Determine required tensile stiffness and strength for reinforcement

As noted in Section 5.3.1, both tensile stiffness and tensile strength are needed for the specification and design of geosynthetic reinforcement. Tensile stiffness is defined as the tensile resistance at a reference reinforcement strain. For GRS‐NLB, a reference strain of 3.0% is recommended. Specification of a minimum value for tensile stiffness ensures that the selected reinforcement will be stiff enough to provide satisfactory performance under service loads. The required minimum reinforcement stiffness in the direction perpendicular to the wall face, , can be determined by the following equation (see Section 5.3.1 for background information):

(5‐49)

where = required minimum tensile stiffness at ε = 3% on the load–deformation curve (as obtained from the wide‐width tensile test, ASTM D4595 for geotextiles and D6637 for geogrids), σ_h = horizontal stress in GRS mass at the depth of reinforcement being considered, σ_c = lateral confining pressure of GRS mass at the depth of reinforcement being considered, s_v = reinforcement spacing, and d_max = maximum particle size of the backfill.

The largest value of σ_h typically occurs at the base of the wall and can be estimated by the Rankine active earth pressure theory. For a GRS wall with a level crest and subjected to a uniform surcharge, , where γ is the unit weight of the backfill, H is the height of the wall, q is the uniform surcharge, and K_A is the coefficient of Rankine active earth pressure. For a GRS wall with a sloping crest (slope angle = β, Figure 5.36(b)), the bottom layer of reinforcement is usually subject to the highest horizontal stress, and the largest vale of σ_h is .

For a GRS wall with dry‐stacked concrete block facing, the value of σ_c can be estimated as , where γ_b is the bulk unit weight of the facing block, D is the depth of the facing block (in the direction perpendicular to the wall face), and δ_b is the friction angle between facing blocks (or between the geosynthetic reinforcement and the facing block, if geosynthetic reinforcement is installed between adjacent blocks). The value of σ_c is very small for light‐weight dry‐stacked facing, and can be conservatively assumed to be zero.

In addition to specifying the stiffness requirement, the strength requirement for reinforcement is needed as well. The required minimum value of the ultimate strength of reinforcement in the direction perpendicular to the wall face, T_ult , can be determined by imposing a ductility and long‐term factor, F_dl , on to ensure sufficient ductility (i.e., to prevent sudden collapse) and satisfactory long‐term performance, i.e.,

(5‐50)

From limited experience, the tensile strain corresponding to T_ult needs to be at least 5–7% (referred to as the ductility strain). The ductility and long‐term factor F_dl is a function of soil properties and geosynthetic type. The following values of F_dl are recommended (Note: Plasticity index (PI) of any fill material greater than 6 is not recommended):

• If the plasticity index (PI) of fill material passing No. 40 sieve is 3 or less:
  • F_dl = 3.5 for all geosynthetics
• If the plasticity index (PI) of fill material passing No. 40 sieve is between 4 and 6:
  • F_dl = 5.5 for polypropylene geosynthetics
  • F_dl = 5.0 for polyethylene geosynthetics
  • F_dl = 4.0 for polyester geosynthetics

Note that if more than one reinforcement (i.e., reinforcements of different stiffnesses/strengths) is selected, the σ_h‐value in Eqn. (5‐49) should be evaluated at the bottom of each group of reinforcement layers. Different values of required reinforcement stiffness and reinforcement strength for each group of reinforcement can then be determined.

Step 8: Select geosynthetic reinforcement

Select a geosynthetic product that satisfies the following conditions (cf. Figure 5.9):

1. Stiffness requirement: the tensile stiffness in the direction perpendicular to wall face, (tensile stiffness at 3% strain), must be equal to or greater than the value calculated by Eqn. (5‐49).
2. Strength requirement: the ultimate strength, T_ult , in the direction perpendicular to wall face must be equal to or greater than the value calculated by Eqn. (5‐50).

The load–deformation relationship of geosynthetic product, commonly expressed in terms of load per unit width versus tensile strain, can be determined by conducting a wide‐width tensile test (ASTM D4595 for geotextiles, ASTM D6637 for geogrids). The T_ult value should be the minimum average roll value (MARV) of the product to account for statistical variance. For most geosynthetics that are not sensitive to confining pressure (i.e., woven geotextiles and geogrids), the load–deformation relationship determined by in‐isolation tests can be used for the selection of geosynthetic reinforcement. For confining pressure‐sensitive geosynthetics (i.e., nonwoven needle‐punched geotextiles), the intrinsic confined test proposed by Wu (1991), Ling et al. (1992), and Ballegeer and Wu (1993) is recommended. Note that for pressure‐sensitive geosynthetics, the effect of confining pressure has been found to be much more pronounced on the tensile stiffness than on the ultimate strength. For example, the increase in stiffness (secant modulus) for a nonwoven needle‐punched geotextile under a confining pressure of 80 kPa is found to be about 100%, whereas the corresponding increase in ultimate strength is only about 30%. Note that pressure‐sensitive geosynthetics are generally not selected in the design of GRS walls due to their relatively low stiffness values.

Step 9: Estimate lateral movement of wall face

The lateral displacement profile of the wall face of a block facing GRS wall can be estimated by the following equation (Pham, 2009; Wu and Pham, 2010). The lateral movement Δ_i at a given depth z_i of a GRS wall is:

(5‐51)

where K_reinf = stiffness of the geosynthetic reinforcement (, see Figure 4.19), ϕ_ds = friction angle of soil in the reinforced zone, as obtained from direct shear tests, and ψ = angle of dilation of the soil in reinforced zone. Other parameters are as defined in Section 5.3.3. In the absence of soil dilation data, the angles of dilation ψ can be estimated as 0°, 10°, and 20°, for loose, medium, and dense sands, respectively. The value of ϕ_ds can be estimated from the plane‐strain angle of friction, ϕ_ps , and the angle of dilation, ψ, as (Jewell and Milligan, 1989):

(5‐52)

A vertical face without a batter is recommended for walls of low to medium height (less than 20 ft or 6 m in height) because a batter usually offers little practical benefit in these cases. For walls with a battered face, an empirical facing batter factor Φ_fb , suggested by Allen and Bathurst (2001), may be applied to account for the facing batter. For a facing batter of 8°, Allen and Bathurst (2001) suggest an empirical equation for determination of the lateral earth pressure on the wall face:

(5‐53)

where K_ab and K_av are horizontal components of the active earth pressure coefficient for a battered wall and a vertical wall, respectively, and d is a constant. Allen and Bathurst (2001) found that d = 0.5 would yield the best fit for available T_max data, and recommended using d = 0.5 for determination of Φ_fb. For design of a battered wall, K_ab determined from Eqn. (5‐53) can be used in place of K_A in Eqn. (5‐51) for evaluation of the wall displacement profile. This procedure is illustrated in Design Examples 2 and 3 in Section 5.7.2.

For GRS walls with a sloping crest, the portion of soil above the top of the wall face can be regarded as an equivalent uniform overburden pressure of 0.5 γ L(tan β) for the term q in Eqn. (5‐51). Note that Eqn. (5‐51) ignores the down‐drag force along the contact surface between the back of the wall face and the backfill behind. This will lead to a conservative (i.e., larger than actual) lateral displacement profile.

From Eqn. (5‐51), the maximum lateral displacement of a wall, Δ_max , can readily be determined. If the maximum wall displacement exceeds a prescribed performance limit, measures should be taken to alleviate the problem. Measures to consider include decreasing reinforcement spacing and increasing reinforcement stiffness/strength. Strictly speaking, Eqn. (5‐51) is applicable only to GRS walls with concrete block facing. For GRS walls with other types of facing, Δ_max would be different. Take geotextile wrapped‐faced walls for instance, Δ_max will be about 15% larger than that calculated by Eqn. (5‐51).

Step 10: Check stability against pullout failure

For GRS walls with a level crest and uniform reinforcement length, the safety factor against pullout failure for reinforcement at depth z_i (referred to as reinforcement layer‐i) is:

(5‐54)

where L_t is the most updated value of reinforcement length (up to Step 9), σ _h (max) is the maximum horizontal stress, and δ is the angle of friction at the soil–geosynthetic interface.

For GRS walls with a sloping crest, the sloping soil overburden can be regarded as an equivalent uniform surcharge, and the sloping crest wall considered as an equivalent level crest wall with an added wall height of 0.5 · L_t · (tan β) or subjected to a vertical surcharge pressure of 0.5 · γ · L_t · (tan β).

The coefficient of interface friction, f = tan δ, can be determined from the results of a pullout test by the interface pullout formula (Eqn. (4‐2), Section 4.2.4), i.e.,

(5‐55)

where F_f = applied pullout force at failure (per unit width of reinforcement) in the pullout test, L = total length of the reinforcement specimen used in the pullout test, E = Young’s modulus per unit width of reinforcement, t = nominal thickness of reinforcement, and σ_n = normal stress (overburden) on the reinforcement specimen. In the absence of pullout test results, the angle δ can be assumed as 2/3 of the friction angle of the backfill, i.e., δ = (2/3)ϕ.

The maximum horizontal stress for a given layer of reinforcement at depth z_i (measured from the crest), σ_hi (max), in Eqn. (5‐54) can be determined as:

(5‐56)

As in Step 9, for GRS walls with a battered wall face, an empirical facing batter factor, Φ_fb, suggested by Allen and Bathurst (2001), may be applied to account for the facing batter:

(5‐57)

where K_ab and K_av are the horizontal components of the active earth pressure coefficient for a battered wall and a vertical wall, respectively, and d = 0.5 for the best fit of available T_max data. For a battered wall, the value of K_ab determined from Eqn. (5‐57) can be used in place of K_A in Eqn. (5‐56). Again, wall batter is generally of little practical value for walls of low to medium heights. The maximum tensile force, i.e., the denominator of Eqn. (5‐54), σ_h(max) ∙ s_v , should be calculated for each selected value of vertical spacing. To be conservative, the contribution of surcharge q is ignored in Eqn. (5‐54). For a wall on uniform vertical spacing and with a uniform reinforcement length for all layers, the maximum horizontal stress (σ_h(max)) at the lowest reinforcement layer should be used for calculation of T_max. For a wall of more than one reinforcement spacing, T_max should be calculated at the lowest reinforcement layer of each spacing used in design.

In all prevailing design methods, stability against pullout failure is checked by requiring each and every layer of reinforcement to meet a minimum safety factor against pullout. As discussed in Section 5.3.2, it is not a realistic scenario that a single reinforcement layer is being pulled out while all the adjacent reinforcement layers remain immobilized in a closely spaced reinforced soil mass. In other words, pullout failure cannot occur in a single layer alone when reinforcement layers are tightly spaced. If pullout failure is to occur, it will only occur as a group. To evaluate pullout of reinforcement, a group safety factor as defined in Section 5.3.2 may be used to allow for a more rational evaluation of pullout stability.

It is recommended that the group safety factor be evaluated by the rule of three, i.e., pullout failure will occur if the group safety factor for any three consecutive reinforcement layers is below a prescribed value (see Section 5.3.2). The group safety factor Fs_(group), with its mid‐layer located at depth z_i , is defined as:

(5‐58)

For a level crest with surcharge q:

(5‐59)

(5‐60)

For a sloping crest:

(5‐61)

(5‐62)

where , and the subscripts i–1, i, and i+1 refer to reinforcement layers at depths z_i–1, z_i and z_i+1, respectively. Eqn. (5‐58) states that the group safety factor against reinforcement pullout is the sum of resisting pullout forces for any three consecutive layers divided by the sum of the driving pullout forces for the same three layers. Note again that there is no reinforcement above the top layer or beneath the bottom layer of a wall, hence the values of the non‐existent layers should be taken as zero (i.e., Pr_i–1 = Pd_i–1 = 0 for evaluation of F_s (group) for the top layer, and Pr_i+1 = Pd_i+1 = 0 for evaluation of F_s (group) for the bottom layer). Note also that surcharge q does not appear in Eqn. (5‐59) as it is for calculation of a resisting force, but appears in Eqn. (5‐60) as it is for calculation of a driving force (see Figure 5.23(a)).

If the any of the F_s (group) is less than 1.5, the reinforcement length L_t will need to be increased until all values of F_s (group) are at least 1.5.

Step 11: Check stability against rotational slide‐out failure

Using the updated reinforcement length determined in Step 10, stability against rotational slide‐out failure should be evaluated. This can be carried out by using limiting‐equilibrium based slope stability computer software such as SLOPE‐W, STABL WV, ReSSA, etc.

The rotational slide‐out analysis should include not only analysis of overall slide‐out failure encompassing the entire reinforced soil wall, but also analysis of compound failure (see Figure 5.4), especially in situations where the wall is situated over sloping or soft ground. For a trial slip surface passing through the soil–geosynthetic composite mass, the strength parameters of the reinforced soil mass (c_R and ϕ_R) can be taken as (Wu et al., 2010):

(5‐63)

where K_P = coefficient of Rankine passive earth pressure, T_ult = tensile strength of the reinforcement, as determined in Step 8, s_v = vertical spacing of reinforcement, d_max = maximum particle size of the reinforced fill, and c = cohesion of the soil (c can be ignored if it is small, say less than 10 kPa).

The factor of safety against any trial of rotational slide‐out failure should be at least 1.3. Otherwise, the reinforcement length may be increased to provide an adequate safety margin. Alternatively, a viable ground improvement technique may be employed to improve the strength of the foundation soil when warranted. The design reinforcement length can then be finalized at the completion of this design step. Recall that all reinforcement lengths referred to in the design computations are to measure from the back of facing.

Step 12: Determine facing requirements

Facing requirements involve three aspects: embedment, facing batter, and connection strength.

1. Embedment

   If there is no concern for erosion or other untoward events surrounding the wall base during design life (typically 75 years), the required embedment of a GRS‐NLB wall can be a nominal depth of 0–200 mm, i.e., up to one typical concrete block height. Note that a nominal embedment of ½ to 1 block height can help to prevent outward movement of facing blocks during construction before the wall gets taller.

   Design of shallow foundations requires that the base of the footing be placed below the maximum frost penetration depth to alleviate uneven heaving due to formation of ice lenses in the frost zone. Since heaving of the foundation soil can be absorbed by the reinforced soil mass of a GRS‐NLB wall, and will usually not hinder wall performance, it can be argued that embedding the wall base below the maximum frost penetration depth is unnecessary. However, if the foundation soil contains frost‐susceptible soils (e.g., silty soils, see Holtz et al., 2011 for details), it is recommended that the foundation soils be excavated to the maximum frost penetration depth and replaced with a non‐frost‐susceptible soil. The backfill in the excavated zone can be reinforced by geosynthetic reinforcement to form a reinforced soil foundation (RSF) (Adams et al., 2011a). A typical RSF for GRS abutments involves excavating a pit that is 0.5L deep (L = reinforcement length, determined in Step 11), backfilling it with compacted road base material, and reinforcing it by the same reinforcement used in the reinforced soil wall on 0.2–0.3 m vertical spacing. The lateral extent of the RSF should at least cover the footprint of the reinforced fill and should extend no less than 0.25L in front of the wall face. A generic design protocol for RSF has recently been proposed by Wu (2018).

   For GRS walls constructed along rivers and streams, embedment depths should be at least 0.6 m (2 ft) below the potential scour depth, as determined based on subsurface investigation and hydraulic studies. For GRS walls founded on a slope, a minimum horizontal bench width of 0.3H (H = wall height) should be provided.

   At the base of the wall face, a leveling pad made of compacted granular soil may be formed to help align the first course of facing blocks. Good alignment of the first course of facing blocks is essential to overall alignment of a concrete block GRS wall. An alternative is to use a concrete leveling pad (see Section 6.2.4 about leveling pads).

2. Facing batter

   A vertical face is recommended for low to medium height concrete block walls (not exceeding 20 ft or 6 m in height). The wall face may batter slightly, typically from 1:10 to 1:12 (horizontal to vertical) to help mask minor lateral movement of the wall face. For design computations, slightly battered walls can be considered as vertical walls with only small errors.

3. Connection strength

   The facing of GRS walls should be designed to resist lateral pressure from the reinforced soil mass and to resist down‐drag force resulting from differential settlement between the reinforced soil mass and facing blocks. The connection strength required for a concrete block GRS wall is influenced by reinforcement spacing, constraints on facing movement (including weight of blocks and facing connection enhancement elements), surcharge on crest, reinforcement tensile properties, stress–strain–strength properties of the reinforced fill, relative settlement between facing blocks and reinforced mass, and construction sequence.

   For walls that satisfy the four conditions for the bin pressure diagram (see Section 5.3.5), frictional resistance between concrete blocks has been found to be more than sufficient to satisfy connection stability requirements (i.e., resisting forces are always greater than driving forces at all depths). The four conditions are: (1) the facing offers insignificant restraint to lateral movement of the reinforced soil mass, (2) the fill material behind the facing is free‐draining so that there is little hydraulic pressure involved, (3) the soil–reinforcement interface bonding is maintained under the design load, and (4) the reinforcement is sufficiently stiff. For walls which fail to satisfy any of the four conditions, use of the connection force equations (i.e., Eqns. (5‐12) to (5‐15)) is recommended to check if facing connection stability is satisfied. It is highly recommended that the reinforcement spacing is kept small, preferably on 0.2 m spacing for GRS‐NLB. For closely spaced GRS walls with reinforcement at every facing block and reinforcement spacing not greater than 0.3 m, connection stability is satisfied regardless of wall height (see Section 5.3.5).

   It is recommended that reinforcement sheets be placed in such a way that they cover the top surface area of the facing blocks as much as possible without protruding out of the wall face; in addition, when lightweight blocks are used, the top 2–3 courses of facing blocks be bonded together by concrete mix or mortar. This measure will offer added resistance to the lateral earth thrust under unexpected external loads.

Step 1: Establish wall profile and verify design conditions

The cross‐section of the wall is as depicted in Figure 5.39. The conditions for non‐load‐bearing applications as listed at the beginning of Section 5.7 are verified, including fines content of reinforced backfill = 12% ≤ 20%, liquid limit = 10 ≤ 30, and plasticity index (PI) = 2 ≤ 6.

Step 2: Determine design parameters for reinforced fill, retained fill, and foundation

The values of the soil parameters are:

Step 3: Determine forces acting on reinforced soil mass

The forces acting on the reinforced soil mass for external stability checks are shown in Figure 5.40. The active Rankine earth pressure coefficient of the retained fill, K_A = tan² [45° – (35°/2)] = 0.27.

Step 4: Determine a tentative reinforcement length (for a GRS wall with a level crest)

Tentative reinforcement lengths (L_t) against lateral sliding failure and eccentricity failure are determined as follows:

1. Lateral sliding failure

   Determine L_t against lateral sliding failure:

   
2. Eccentricity failure

   Determine L_t needed to prevent eccentricity failure:

   Using L_t = 3.4 m (as determined in (i), above), the eccentricity, e, can be determined as (Eqn. (5‐40)):

   

   Set

   hence and

Therefore, the tentative reinforcement length needs to be increased from L_t = 3.4 m (determined from lateral sliding failure check) to L_t = 3.6 m (determined from eccentricity failure check).

Step 5: Check stability against foundation bearing failure

From Figure 5.38, for ϕ_f = 38°, bearing capacity factors N_c = 65 and N_γ = 80

Vertical load = (γ H + q) L_t = [(18.0)(6.0) + 12)](3.6) = 432 (kN/m)

Horizontal load = F₁ + F₂ = 87.5 + 19.4 = 106.9 (kN/m)

Angle of inclination for the resultant load, λ = tan^–1 (106.9/432) = 13.9° (< ϕ = 35°)

Hence, i_γ = (1 – λ/ϕ)² = (1 – 13.9°/35°)² = 0.36

From Eqns. (5‐44) and (5‐45)

Since embedment of the wall is to be only nominal, its effect is not included in the calculation of FS_bearing (Note: FS_bearing determined by ignoring the effect of embedment has already been found adequate). The tentative reinforcement length of L_t = 3.6 m, therefore, remains unchanged.

Step 6: Select vertical reinforcement spacing and block height

Uniform spacing of 0.2 m (i.e., s_v = 0.2 m) is selected. The height of each facing block is to be 0.2 m.

Step 7: Determine required tensile stiffness and strength for reinforcement

The confining stress of the reinforced soil mass (σ_c) is:

The maximum lateral stress (σ_h) is:

Required minimum reinforcement stiffness, T_{@ ε = 3.0%} , in the direction perpendicular to wall face is:

PI = 2 ≤ 3, thus the ductility and long‐term factor F_dl = 3.5, hence the required minimum value of ultimate reinforcement strength in the direction perpendicular to the wall face, T_ult, is:

The tensile strain of the selected reinforcement corresponding to Tult ( ≥ 36.4 kN/m) needs to be at least 5–7%.

Step 8: Select geosynthetic reinforcement

Select a geosynthetic product with tensile stiffness T_{@ ε = 3.0%} ≥ 10.4 kN/m and tensile strength T_ult ≥ 36.4 kN/m at tensile strain ≥ 5–7%, both in the direction perpendicular to the wall face. A woven polypropylene geotextile with MARV = 38 kN/m (at ε = 10%) and T_{@ ε = 3.0%} = 12 kN/m is selected.

Step 9: Estimate lateral movement of wall face

The lateral movement Δ_i at depth z_i is:

The reinforcement stiffness, K_reinf , is equal to T_{@ ε = 3.0%}/(3%) = 12 kN/m/(3%) = 400 kN/m. The values of the other parameters are: K_A = 0.27, γ = 18.0 kN/m³, q = 12 kN/m², s_v = 0.2 m, γ_b = 12.6 kN/m³, D = 0.2 m, tan δ_b = 0.4, H = 6.0 m, and ψ = 5°. The direct shear friction angle ϕ_ds can be estimated as:

The lateral movement profile for a vertical wall face is shown in Figure 5.41. From the profile, the maximum lateral movement is found to be 33 mm, smaller than the specified performance limit of 60 mm.

Should a facing batter of 1 (horizontal):12 (vertical) is employed (instead of a vertical wall specified in this example), the K_A value will need to be modified. The empirical correction suggested by Allen and Bathurst (2001) is:

Therefore the term K_A in the equation for Δ_i needs to be replaced by , and the maximum lateral movement will reduce from 33 mm to 25 mm (see Figure 5.41), both meeting the performance limit of 60 mm.

Step 10: Check stability against pullout failure

The pullout resisting force (Pri) and driving force (Pdi) for reinforcement layer‐i are (Eqns. (5‐59) and (5‐60)):

where . Note that surcharge q (=12 kPa) does not appear in the equation for Pr_i , but appears in the equation for Pd_i . The pullout resisting forces and driving forces for all layers are listed in Table 5.9.

Using the rule of three, i.e., the group pullout safety factor for any three consecutive reinforcement layers with its mid‐layer located at depth z_i can be determined as:

The group pullout safety factors of the wall are also listed in Table 5.9. Note that the group safety factor of layer‐i in the table is the safety factor with layer‐i being the mid‐layer of the group. It is seen that the group safety factors for all layers are greater than 1.5, therefore the tentative reinforcement length will stay unchanged.

Step 11: Check stability against rotational slide‐out failure

A limiting‐equilibrium based slope stability program (such as SLOPE‐W, STABL WV, or ReSSA) can be used to evaluate different modes of rotational stability (including overall slide‐out failure and compound failure). The analysis can be carried out with the reinforced soil zone having the following soil–geosynthetic composite strength parameters (because the cohesion of the soil is quite small, c = 0 is assumed):

If the smallest safety factor against rotational slide‐out failure is less than 1.3, the reinforcement length may be increased to raise the safety factor. Alternatively, if the critical rotational failure plane is passing through the foundation soil, a viable ground improvement technique may be employed to improve the strength of the foundation soil.

Step 12: Determine facing requirements

1. Embedment: The GRS wall is to be constructed with a nominal embedment of 0.1 m (half a block height) below the ground surface. This is based on the given information that there is very low probability of erosion or other unfavorable events occurring near the wall base through the design life of the wall.
2. Facing batter: The facing of the GRS wall is to be vertical, no batter.
3. Connection strength requirements: All facing blocks are to be dry‐stacked. Reinforcement is at every course of facing blocks and reinforcement spacing is 0.2 m, hence connection stability is ensured. The top two courses of facing blocks are to be bonded by filling the hollow cells with concrete mix or mortar.

Step 1: Establish wall profile and verify design assumptions

The cross‐section of the wall is shown in Figure 5.42. The conditions for non‐load‐bearing applications as listed at the beginning of Section 5.7 are verified, including fines content of reinforced backfill = 14% ≤ 20%, liquid limit = 10 ≤ 30, and plasticity index (PI) = 2 ≤ 6.

Step 2: Determine design parameters for reinforced fill, retained fill, and foundation

The values of the soil design parameters are:

Step 3: Determine forces acting on reinforced soil mass

The break in the slope is located within 2H from the back of the wall face, hence the broken crest can be converted into an equivalent sloping crest by following the procedure suggested by AASHTO (2002, 2014) (see Figure 5.37). The forces acting on the reinforced soil mass for external stability checks of the equivalent sloping crest are shown in Figure 5.43. The active Rankine earth pressure coefficient of the retained fill, K_A = tan² [45° – (35°/2)] = 0.27. The equivalent sloping crest is denoted by a dashed line in the figure. The angle of the equivalent sloping crest, β = tan^–1 [h₁/(2H)] = 16.3°.

Step 4: Determine a tentative reinforcement length (for a GRS wall with a sloping crest)

A tentative reinforcement length (L_t) is determined by considering two failure modes: lateral sliding failure and eccentricity failure.

1. Lateral sliding failure

   Assume reinforcement length L_t = 0.5H = 0.5 (6.0 m) = 3.0 m. For a GRS wall of uniform reinforcement length, the safety factor against lateral sliding at the lowest layer of reinforcement is (Eqn. (5‐42)):

   

   where h – H = L_t (tan β) = (3.0 m) (tan 16.3°) = 0.9 m, thus h = 6.9 m (see Figure 5.43). The resultant force exerted by the retained fill, Frf (inclined at β counterclockwise from the horizontal) is (Eqn. (5‐41)):

   

   Hence,

   

   From trials that repeated the calculations with increasing value of L_t , or with the aid of a design spreadsheet, it was determined that L_t = 3.5 m would yield F_s = 1.5.

2. Eccentricity failure

   To check eccentricity (lift‐off) failure, the L_t as determined above is first used to calculate eccentricity e. For L_t = 3.5 m, h = H + L_t (tan β) = 6.0 + (3.5) (tan 16.3°) = 7.0 (m). Thus, W₁ = (18.0)(6.0)(3.5) = 378 (kN/m), W₂ = 0.5 (18.0)(3.5)(7.0 – 6.0) = 31.5 (kN/m), F_rf = 2.72 ⋅ h² = 2.72 (7.0)² = 133 (kN/m), F_H = F_rf (cos 16.3°) = 128 (kN/m), and F_V = F_rf (sin 16.3°) = 37 (kN/m).

   From Eqn. (5‐43),

   

Since e = 0.48 m ≤ L_t/6 = 3.5/6 = 0.58 m (OK), thus L_t = 3.5 m remains unchanged.

Step 5: Check stability against foundation bearing failure

From Figure 5.38, for ϕ_f = 38°, bearing capacity factors are N_c = 65 and N_γ = 80

Vertical load = W₁ + W₂ + F_v = 378 + 31.5 + 37 = 446.5 (kN/m)

Horizontal load = F_H = 128 kN/m

Angle of inclination for the resultant load, λ = tan^–1 (128/446.5) = 16.0° (< ϕ = 35°)

Hence, i_γ = (1 – λ/ϕ)² = (1 – 16.0°/35°)² = 0.29

• • i_c = (1 – λ/90°)² = (1 – 16.0°/90°)² = 0.68 and eccentricity e = 0.48 m (from Step 4)

From Eqns. (5‐44) and (5‐46),

Step 6: Select vertical reinforcement spacing and block height

Uniform spacing of 0.2 m (s_v = 0.2 m) is selected. The height of each facing block is to be 0.2 m also.

Step 7: Determine required tensile stiffness and strength for reinforcement

The confining stress of the reinforced soil mass, σ_c , is:

The maximum lateral stress, σ_h , at the wall base is

The required minimum reinforcement stiffness, T_{@ ε = 3.0%}, in the direction perpendicular to the wall face, is:

PI = 2 ≤ 3, thus F_dl = 3.5. The required minimum value of the ultimate reinforcement strength in the direction perpendicular to the wall face, T_ult , is:

Also, the ductility strain of the selected reinforcement at T_ult ( ≥ 38.5 kN/m) needs to be at least 5–7%.

Step 8: Select geosynthetic reinforcement

Select a geosynthetic product with tensile stiffness T_{@ ε = 3.0%} ≥ 11 kN/m and tensile strength T_ult ≥ 38.5 kN/m (at ε ≥ 5–7%), both in the direction perpendicular to the wall face. A woven polypropylene geotextile with MARV = 40 kN/m (at ε = 10%) and T_{@ ε = 3.0%} = 12 kN/m is selected.

Step 9: Estimate lateral movement of wall face

The lateral movement of the wall face, Δ_i , at depth z_i is:

The reinforcement stiffness, K_reinf  is equal to T_{@ ε = 3.0%}/(3%) = 12 kN/m/(3%) = 400 kN/m. Other parameters are: K_A = 0.27, γ = 18.0 kN/m³, q = 0.5 γ L_t (tan β) = 0.5(18.0) (3.5)(tan 16.3°) = 9.2 (kN/m²), s_v = 0.2 m, γ_b = 12.6 kN/m³, D = 0.2 m, tan δ_b = 0.4, H = 6.0 m, and ψ = 5°. The direct shear friction angle ϕ_ds can be estimated as:

To account for facing batter,

The term K_A in the equation for calculating Δ_i is to be replaced by (as opposed to 0.27 for a vertical wall).

The lateral movement profile is shown in Figure 5.44. The maximum lateral movement is determined to be 24 mm, which is smaller than the specified performance limit of 60 mm. Note that a vertical wall without any batter would have sufficed.

Step 10: Check stability against pullout failure

The pullout resisting force (Pr_i) and driving force (Pd_i) for reinforcement layer‐i are (Eqns. (5‐61) and (5‐62)):

where . The pullout resisting force and driving force for each layer of the wall are listed in Table 5.10.

Using the rule of three, the group pullout safety factor for any three consecutive reinforcement layers with its mid‐layer located at depth z_i can be determined as:

The group pullout safety factors at all depths are also listed in Table 5.10. The group safety factor of layer‐i is the safety factor with layer‐i being the mid‐layer of the group. It is seen that the group safety factors for all layers are greater than 1.5, therefore the tentative reinforcement length will stay unchanged.

Step 11: Check stability against rotational slide‐out failure

A limiting‐equilibrium based slope stability program (such as SLOPE‐W, STABL WV, or ReSSA) can be used to evaluate different modes of rotational stability (including overall slide‐out failure and compound failure). The analysis can be carried out with the following soil–geosynthetic composite strength parameters for the reinforced soil mass (because the cohesion of the soil is quite small, c = 0 is assumed):

If the smallest safety factor against any modes of rotational slide‐out failure is less than 1.3, the reinforcement length may be increased to raise the safety factor. Alternatively, if the critical rotational failure plane is passing through the foundation soil, a viable ground improvement technique may be employed to improve the strength of the foundation soil.

Step 12: Determine facing requirements

1. Embedment: Since there is no concern for erosion or other untoward events surrounding the planned location of the wall base during the design life, the GRS wall is to be constructed with a nominal embedment of 0.1 m below the ground surface.
2. Facing batter: The facing of the GRS wall is to have a batter of 1 (vertical) to 12 (horizontal); note that a vertical wall without a batter would suffice.
3. Connection strength requirements: All facing blocks are to be dry‐stacked. Reinforcement is at every course of facing blocks and the reinforcement spacing is 0.2 m, hence connection stability is ensured (see Section 5.3.5). The top two courses of facing blocks are to be bonded by filling the hollow cells with concrete mix or mortar. To ensure facing stability under a sloping crest, the concrete mix may be reinforced with 0.2‐m long steel pins through the cores. All other facing blocks are to be dry‐stacked with their cells filled with compacted fill.

Step 1: Establish wall profile and check design assumptions

The cross‐section of the wall is depicted in Figure 5.45. The conditions for non‐load‐bearing applications as listed at the beginning of Section 5.7 are verified, including fines content of reinforced backfill = 12% ≤ 20%, liquid limit = 10 ≤ 30, and plasticity index (PI) = 2 ≤ 6.

Step 2: Determine design parameters for reinforced fill, retained fill, and foundation

The values of the soil parameters needed for the design are:

Step 3: Determine forces acting on reinforced soil mass

With a trial reinforcement length of 0.5H (L = 0.5H = 3.0 m) in the upper portion of the wall and a trial reinforcement length at the base is set equal to 0.3H (L_B = 0.3H = 1.8 m), the forces acting on the reinforced soil mass of the GRS wall for external stability checks are as shown in Figure 5.46. Note that the active Rankine state can be mobilized in the zone of retained fill (see Section 2.4), hence the lateral earth pressure in the retained fill above the truncated zone is assumed to be in the Rankine active state. The active Rankine earth pressure coefficient of the retained fill, K_A = tan² [45° – (35°/2)] = 0.27.

Step 4: Determine a tentative reinforcement length (for a GRS wall with a level crest)

A tentative reinforcement length is obtained by considering two failure modes: lateral sliding failure and eccentricity failure.

1. Lateral sliding failure
   • For the assumed reinforcement length L = 0.5H = 3.0 m, and reinforcement length at base = 0.3H = 1.8 m (an initial trial),
   • 
   • Driving force for sliding = F₁ + F₂ = 56 + 16 = 72 (kN/m)
   • Factor of safety against lateral sliding FS_sliding = 134/72 = 1.9 > 1.5 (OK)
2. Eccentricity failure

   To check eccentricity failure (i.e., lift‐off at wall base), the tentative reinforcement length can be used for calculation of resultant forces and bending moment at the base of the reinforced soil mass. The calculation can be performed by treating the wall base as a projected horizontal plane, in the same way as for a wall without base‐truncation, except the stabilizing force due to soil weight is now reduced due to truncation. The calculation of the resultant forces and bending moment on the projected wall base for L = 3.0 m and L_B = 1.8 m is shown in Figure 5.47.

   The eccentricity of the resultant force R_V due to the bending moment (M) is

   

   The initial trial tentative reinforcement length of L_t = 0.3 m (i.e., 0.5H) needs to be increased. A new trial reinforcement length of L_t = 0.36  m (or 0.6H) is selected. Using the same procedure illustrated in Figure 5.47, the new eccentricity becomes

   

   The tentative reinforcement length of L_t = 0.36 m (or 0.6H) still fails the eccentricity criterion of e ≤ L_t/6, therefore L_t needs to be increased further. L_t = 3.9 m (or 0.65H) is subsequently tried. Using the same procedure shown in Figure 5.47, the eccentricity for L_t = 3.9 m (or 0.65H) is

   

   Therefore, reinforcement length L_t = 3.9 m (with L_B = 0.18 m) is adopted. Lateral sliding failure is re‐calculated as follows to ensure L_t = 3.9 m is acceptable.

   • 
   • Driving force for sliding = F₁ + F₂ = 37 + 13 = 50 (kN/m)
   • Factor of safety against lateral sliding FS_sliding = 164/50 = 3.3 > 1.5  (OK)

Step 5: Check stability against foundation bearing failure

• Foundation soil: c_f = 9.5 kPa and ϕ = 30°; from Figure 5.38, for ϕ_f = 30°, the bearing capacity factors are N_c = 30 and N_γ = 18
• Vertical load = R_v = V₁ + V₂ +V₃ = 381 kN/m
• Horizontal load = F₁ + F₂ = 50 kN/m
• Angle of inclination for the resultant load with the vertical plane,
• 
• hence,
•    
• Average base pressure, σ_v = R_v/(L_t – 2e) = 381/(3.9 – 2 × 0.6) = 141.1 kN/m²

The safety factor against bearing capacity failure, FS_bearing , is (Eqns. (5‐44) and (5‐45))

Step 6: Select vertical reinforcement spacing and block height

Uniform spacing of 0.2 m (s_v = 0.2 m) is selected. The height of each facing block is also to be 0.2 m.

Step 7: Determine required tensile stiffness and strength for reinforcement

The confining stress of the reinforced soil mass (σ_c) is:

The maximum lateral stress (σ_h) is:

The required minimum reinforcement stiffness, T_{@ ε = 3.0%}, in the direction perpendicular to the wall face is:

PI = 2 ≤ 3, thus the ductility and long‐term factor, F_dl = 3.5. The required minimum value of ultimate reinforcement strength in the direction perpendicular to the wall face, T_ult , is:

Also, the ductility strain corresponding to T_ult ( ≥ 36.4 kN/m) of the selected reinforcement needs to be at least 5–7%.

Step 8: Select geosynthetic reinforcement

Select a geosynthetic product with tensile stiffness T_{@ ε = 3.0%} ≥ 10.4 kN/m and tensile strength T_ult ≥ 36.4 kN/m, both in the direction perpendicular to the wall face. A nonwoven polypropylene geotextile with MARV = 38 kN/m (at ε = 10%), and T_{@ ε = 3.0%} = 12 kN/m is selected.

Step 9: Estimate lateral movement of wall face

Studies have suggested that for walls constructed with well‐compacted free‐draining granular backfill and over a firm foundation, there is not a significant difference between truncated‐base walls and full‐length walls in terms of lateral displacement of the wall face. Compared to a wall with full‐length reinforcement, a truncated‐base wall generally has slightly larger movement in the lower portion of the wall, and slightly smaller movement in the upper portion of the wall. The maximum deflection of a truncated‐base wall is typically about 10% greater than that of a full‐length reinforcement wall.

The lateral movement at the wall face, Δ_i , of a truncated‐base wall at depth z_i is:

The reinforcement stiffness, K_reinf is equal to T_{@ ε = 3.0%}/(3%) = 12 kN/m/(3%) =400 kN/m. The values of the other parameters are: K_A = 0.27, γ = 18.0 kN/m³, q = 12 kN/m², s_v = 0.2 m, γ_b = 12.6 kN/m³, D = 0.2 m, tan δ = 0.4, H = 6.0 m, ψ = 5°, and B_T = 1.0 for z_i < H/2, B_T = 1.1 for z_i ≥ H/2. The direct shear friction angle ϕ_ds can be estimated as:

To account for face batter,

The term K_A in the equation for calculating Δ_i is to be replaced by .

The lateral movement profile is depicted in Figure 5.48. Note that the 10% correction of the calculated movement due to base truncation is made for the lower half of the wall, therefore the deflection profile contains a kink near the mid‐height. A “reasoned” deflection profile near the kink is shown by a dotted line in Figure 5.48. The maximum lateral movement is found to be 27 mm, which is smaller than the specified performance limit of 60 mm. Note that a vertical wall without batter would suffice also.

Step 10: Check stability against pullout failure

The pullout resisting force (Pr_i) and driving force (Pd_i) for reinforcement layer‐i are:

where . Note that surcharge q appears only in the equation for driving force, Pd_i (see Figure 5.36(a)). The pullout resisting force and driving force for each layer are listed in Table 5.11.

Using the rule of three, i.e., the group pullout safety factor for any three consecutive reinforcement layers with its mid‐layer located at depth z_i can be determined as:

The group pullout safety factors for all reinforcement layers of the wall are also listed in Table 5.11. The group safety factor of layer‐i is the safety factor with layer‐i as the mid‐layer of the group. It is seen that the group safety factors at all depths for L_B = 1.8 m and L_t = 3.9 m are greater than 1.5. The layout of reinforcement length is as follows: reinforcement length in the truncated zone is 1.8 m at the base, the length is to increase linearly to 3.9 m at 2.1 m from the base. The reinforcement in the non‐truncated zone is a uniform length of 3.9 m.

Step 11: Check stability against rotational slide‐out failure

A limiting‐equilibrium based slope stability program (such as SLOPE‐W, STABL WV, or ReSSA) can be used to analyze the stability against different modes of rotational failure (including overall slide‐out failure and compound failure). The analysis can be carried out with the reinforced soil mass having the following soil–geosynthetic composite strength parameters (because the cohesion of the soil is quite small, c = 0 is assumed):

If the smallest safety factor against any modes of rotational slide‐out failure is less than 1.3, the reinforcement length may be increased to raise the safety factor. Alternatively, if the critical rotational failure plane is passing through the foundation soil, a viable ground improvement technique may be employed to improve the strength of the foundation soil and raise the safety factor.

Step 12: Determine facing requirements

1. Embedment: Considering that there is no concern for erosion or other untoward events surrounding the planned location of wall base during the design life, the GRS wall is to be constructed with a nominal embedment of 0.1 m below the ground surface.
2. Facing batter: The facing of the GRS wall is to have a face batter of 1 (horizontal) to 10 (vertical). Note that a vertical wall without any batter will also suffice.
3. Connection strength requirements: All facing blocks are to be dry‐stacked. Reinforcement is at every course of facing blocks and reinforcement spacing is 0.2 m, hence connection stability is ensured. The top two courses of facing blocks are to be bonded by filling the hollow cells with concrete mix. All other facing blocks are to be dry‐stacked with their core filled with compacted fill.