3.2.1 External wall insulation

Insulating the building externally decreases the possibility of thermal bridges. These are local regions of the earth wall (or adjoined structure/feature) in which heat transport is comparatively high and any applied insulation is ineffective. Thermal bridges can either be physical (e.g. where an uninsulated steel lintel conducts heat and bypasses the insulation) or geometric (e.g. on wall corners where the external surface area is greater than the internal). Thermal bridging is discussed in detail in Section 3.4. Furthermore when the insulation is located to the outside of a building’s load-bearing wall, the structural components are better protected from extreme temperature variations and condensation risk. This reduces the possibility of damage due to thermal stress and water vapour saturation (Krus et al., 2005).

The thermal storage capacity is also improved by external insulation in heavyweight structures, especially in modern earth buildings or in reinforced concrete structures where stored heat is less able to transport through the wall and escape to the outdoor environment. One effect of this is that external insulation will limit the overheating frequency during hot summer months, since the wall fabric is not heated by external gains and is therefore more able to absorb excess internal heat gains. Where the insulation is external, it needs to also protect the building fabric from the influences of rain ingress and wind; unless the structure is overclad with a rain screen. This leads to the necessity of using water-resistant renders over external insulation and normally comprises a proprietary system.

Due to the external exposure of the water-repellent plaster, which is thermally decoupled from the load-bearing wall by the insulating material, it must resist high temperature variations. These variations are a consequence of diurnal temperature variation, wind exposure and long wave radiant heat gains and losses. On clear nights, the external boundary layer will typically be below the dewpoint temperature which leads to a high risk of condensation and potentially mould growth. In terms of applying external insulation to an existing building, one will face relatively high installation costs where scaffolding is necessary. External insulation can change the building’s appearance, to the point where it may become unsympathetic to the local character, whilst in some cases also increasing the building’s footprint. SRE walls do not require protection from the weather and, due to their attractive sedimentary appearance and natural earthen colour, the external aesthetics form part of the appeal to designers and clients. For this reason, external insulation is generally not favoured and cavity insulation is used instead (see below). Unstabilised rammed earth, however, does need to be protected from the outdoor environment and so, despite the significant extra costs, protective waterproof external render systems can be applied that also incorporate the desired level of insulation. Similarly, rain skin cladding or double skin façades can also be applied in this situation.

3.2.2 Internal wall insulation

Internal insulation is often the most viable in terms of costs when insulating a building retrospectively, because this method is relatively easy to apply and does not require additional weather protective coverings. It is often the best thermal solution for buildings that are of masonry construction in colder climates and only used intermittently as it reduces the re-warming time by reducing the thermal admittance of the internal surfaces. Using this approach a room can be heated fairly quickly as the external wall layer does not need to be heated in order to achieve a satisfactory operative temperature. Compared to external insulation or cavity wall insulation (Section 3.2.3), this method is least desirable in modern earth buildings or in reinforced concrete structures in hot climates where the internal insulation will decouple the thermal mass of the building and therefore not contribute to lowering the overheating frequency. An exception to this occurs where adequate thermally massive internal (e.g. partition) walls, or dense large floor slabs and exposed concrete soffits/upper floors, are available to dampen the diurnal temperature swing.

The usage of internal insulation is less appropriate in terms of fire protection where flammable and toxic insulation materials are used, such as those that are based on organic foams such as polystyrene or polyurethane (Krus et al., 2005). In high-density urban locations, where ground is expensive, the reduction of the treated floor area through the use of internal insulation is another drawback. The practical problems associated with relocating occupants are another issue that is often overlooked during the retrospective installation of internal insulation. However, the biggest technical problems one will face with internal insulation are related to the occurrence of thermal bridges, condensation risks and the reduced possibilities for drying out of the load-bearing wall material beneath. Internal insulation is rarely specified for modern earth building designs because it removes one of the principle advantages offered by the material, i.e. passive buffering of indoor air temperature and relative humidity.

3.2.3 Cavity wall insulation

Cavity wall insulation refers to insulation that is placed between the outer and the inner shell of an external wall; typically in masonry constructions but also in situ or pre-cast materials such as concrete and stabilised earth. A cavity wall presents advantages similar to externally insulated structures that often benefit from reduced overheating hours in summer due to the retention of thermal mass in the inner leaf (Krus et al., 2005).

Amongst the disadvantages of cavity insulation is the fact that the air space in between the outer and inner leaves of the wall may be filled with a porous insulation material. The air (or gas) trapped inside the small pores remains the actual insulator, significantly reducing natural convection, and thus reduces heat losses and the associated heating costs significantly (Langdon, 2010). The material used can either be loose fill (e.g. glass fibre, rock wool or a fibrous material such as cellulose insulation or glass wool (see Table 3.1)) or it can be solid fill – either full or partial (e.g. expanded urethane or polystyrene).

Cavities present technical challenges when retrofitting as moisture penetration due to bridging and/or interstitial condensation can sometimes occur. In the case of minor defects in the construction process, or bad workmanship, the external wall layer may not be sufficient in terms of resistance to rainwater penetration – a situation that leads consequently to the danger of capillary moisturisation and humidification of the insulation. In this case it is essential to use a hydrophobic or water-repellent insulation material. This situation can equally apply to stabilised compressed earth block walls, where an unfilled air cavity has been left in place as part of the construction, or if the earth wall forms part of a composite cavity wall construction, e.g. with internal/external timber frame and cladding.

In the UK, cavity wall construction was introduced as a method to stop wind-driven rain from penetrating to the inside surfaces of masonry walls (Howell, 2008). The Energy Savings Trust started to financially support the injection of insulation material in cavities. This funding continues today in many parts of the UK. The current scheme, which is the third of its kind, is driven by the UK carbon emission target and has been in place since 2008. In this process the partially ventilated cavity air layer in between the outer and inner leaves that originally gave only limited thermal insulation is now filled with an insulating material (Table 3.1). The question that remains is if cavities were intentionally built as air voids, but subsequently filled at a later stage in the buildings life, how does this alter the dew point and hygroscopic characteristics of the wall?

The thermal resistance of the post-filled cavity wall is of course limited by the thermal conductivity of the blown loose fill insulation medium (e.g. ~ 0.04 W/m K for glass fibre) and the thickness of the air cavity (typically around 50 mm) and so any ambitious retrofit U-value targets are likely to require additional internal/external insulation.

The initial idea of the cavity is to stop water penetrating through the wall to the inside of the house. Since 1974, the Building Regulations have required new build houses to contain insulation material in the cavity (Building Regulation, part L), and in theory this should give an ideal way of insulating the building as long as it is correctly detailed. As a result a number of different insulation products have been developed that can be fixed on to the inner leaf of a cavity wall, leaving a small air gap to prevent rainwater from being directly wicked across the wall. For this reason the (often hydrophobic) insulation material allows the rainwater and any condensate build up to drain downwards, under the influence of gravity and the presence of vertical aligned fibres. However, most problems occur in cases where insulation was retrospectively added to create a fully filled cavity resulting in damp problems due to a non-water-repellent material being used such as mineral or glass fibre. What happens as a result is that moisture is transferred back to the inner leaf of the construction and houses become damp and mouldy on their inside, and consequently the buildings become structurally damaged and uninhabitable.

The problem of rainwater crossing the cavity wall insulation is well documented (BRE Building Guide). It is stated that:

It has also been revealed that ‘single-leaf brick walls always leak when exposed to wind-driven rain’ (Stirling, 2000). The leakage occurs at the vertical joints between adjacent bricks, because of the drying shrinkage in the mortar (Stirling, 2000). This can be a particular problem for clay brick or concrete block masonry walls, as the BRE studies have shown, since the hydraulic conductivity (i.e. pressure-driven moisture ingress) and sorptivity (i.e. capillary-driven moisture ingress) are typically very high for these materials, especially in the case of decorative facing bricks as used on the external leaf of the cavity wall. This problem can be overcome if the materials are treated with waterproofing agents, however these are typically high volatile organic compound (VOC) solvent-based surface treatments (e.g. silicone emulsions) that penetrate and fill the material’s pore network. High-quality engineering brick, polished stone or walls of considerable thickness do not suffer the same level of moisture penetration. In the case of insulated SRE walls, the insulation used is a solid fill of interlocking boards usually made from extruded polystyrene (XPS), polyisocyanurate (PI) or expanded polyurethane (PU) (see Table 3.1). All are suited/designed for solid wall applications where the use of cavities is not possible and the insulation has to resist compression (e.g. during compaction of the adjacent earth material) and be resistant to moisture ingress or damage. SRE is high density (typically > 95% Proctor compaction) and so has very low permeability and sorptivity (Walker and Stace, 1996; Hall and Djerbib, 2004). Particularly for cavity rammed earth walls, where the inner and external leaves are usually a minimum of 175 mm thick in a load-bearing wall, the mix design must also include a hydrophobic admixture. This has the effect of significantly reducing liquid transport and effectively rainproofing the wall material, but leaving the macropore network open such that vapour permeability is largely unaffected. For more details of hydrophobic admixtures refer to Chapter 10. Note that masonry cavity walls typically have an inner/outer leaf thickness of 102.5 mm for fired clay brick or 100 mm for concrete block.

Condensation will always form on the coldest surface in a wall construction, which is typically found at the window/wall connection or areas of thermal bridges. Cold spots resulting from geometric or construction-related thermal bridges reduce the localised moisture-holding capacity of the air resulting in water vapour condensing, a phenomenon commonly referred to as ‘interstitial condensation’.

A number of different materials used for cavity insulation are shown in Table 3.1. Commonly used in the UK are mineral wool fibre, bonded polystrene beads or insulation foams.

Figures 3.1, 3.2 and 3.3 show typical SRE solid cavity wall cross-sections during construction of Straightways farm, Devon, UK in 2007 by earth Structures (Europe) Ltd. Note that proprietary formwork systems have to be modified to allow the central insulation board to be mounted securely and allow compaction of the earth on either side. The two separate wall leaves are mechanically tied as for masonry walls but instead with specially designed stainless steel staples that become bonded with the compacted earth during compaction. This ties the two leaves together (both of which are supported by a common foundation) in order to prevent buckling, i.e. vertical bending moments. In cases of high wind loading or multi-storey walls, additional vertical restraint can be added, for example through the incorporation of stanchions. Where structural steel stanchions or similar framework members are included in the external wall fabric, continuity of the insulation can be achieved with careful detailing to avoid any risk of thermal bridging. Construction of stabilised insulated (cavity) earth walls in seismic regions (e.g. North West America) requires additional detailing and support in order to reduce ‘mass mobilisation’ and the likelihood of cavity tie failure/buckling. Figure 3.4 shows a stablised insulated rammed earth (SIREWALL) construction detail which addresses all of these concerns by incorporating a rigid cross-braced steel framework to tie the two leaves together, coupled with vertical restraint from the reinforced foundation slab and puddle earth cap.

3.3.1 Two-dimensional calculations

Several factors have to be addressed when calculating a two-dimensional flow and, in particular, 2D thermal bridges. A major requirement is that the model conforms to the geometrical requirements stated in BS EN ISO 10211:2007. Once an accurate model of the desired problematic area has been created, materials have to be assigned in accordance with the architect’s specifications. Thermal conductivity values of the material can be found in BN EN ISO 10456 (British Standards Institution, 2009). Where these are not listed, values that conform to CE testing procedures should be used in favour of manufacturers’ stated values, which are in many cases misleading. Finally, appropriate boundary conditions in terms of temperatures and surface resistance of the corresponding environments are to be assigned in accordance with EN ISO 120011-1 (Ben Larbi, 2005). Once the model has been implemented, calculation of the thermal coupling coefficient and linear thermal transmittance can be executed according to the specified requirements. It is therefore appropriate to define the components contributing to the total (two-dimensional) heat exchange between both environments (Ward and Sanders, 2007).

Thermal coupling coefficient (L_2D) is defined as the heat flow rate per temperature difference between internal and external environments. According to EN ISO 10211:2007, 2D thermal coupling coefficients can be calculated as shown in Equation 3.2:

[3.2]

Linear thermal transmittance, known as the Psi value (Ψ), is the residual heat flow when the one-dimensional heat flow (all elements inc.) is subtracted from the total heat flow per unit temperature difference, i.e. the 2D thermal coupling coefficient (Ward and Sanders, 2007) as shown Equation 3.3:

[3.3]

Point thermal transmittance, known as the Chi value (χ), is the residual heat flow when the one-dimensional heat flow and the linear transmittance are subtracted from the three-dimensional coupling coefficient (Ward and Sanders, 2007).

3.3.2 Total heat flow

Total heat transfer through the building envelope can be defined by Equation 3.4.

[3.4]

The first term A_i · U_i represents the thermal transmittance through the area of the plane element. If only this term is considered, then the problem becomes one-dimensional. It is commonly the most significant source of heat loss within Equation 3.4 (Ward and Sanders, 2007) and occurs at plane elements including roofs, external walls, floors, and doors/windows (Kuhnenne, 2008). The second term l_k · Ψ _k represents the sum of all linear thermal bridges in the envelope, where Ψ is the linear thermal coefficient and l is the length of the thermal bridge. Ψ can be estimated by subtracting the thermal transmittance component A · U from the two-dimensional coupling coefficient defined previously as L_2D (Ward and Sanders, 2007). This term is relevant to heat transfer that occurs at thermal bridges including eaves and corners, i.e. a geometric thermal bridge (Kuhnenne, 2008) as shown by Figure 3.5.

The third term χ_j represents the point thermal bridges within the structure. They occur as a result of the interaction of the linear thermal bridges or where the residual heat flow at either boundary is three dimensional. Usually, they can be omitted from the total heat transfer calculation because their contribution is insignificant. However, in certain situations, they have to be included for a more accurate solution, e.g. at penetrations where the point thermal bridges are either frequent or very large, such as poorly insulated structural frame elements including steel stanchions. Therefore calculating accurate U and Ψ will be of major interest when comparing the value of computational packages (Ward and Sanders, 2007) and is of significant importance in the design of low energy buildings.

3.3.3 Humidity and condensation

One of the main problems associated with thermal bridges aside from the thermal losses are the cold regions of minimum temperatures on the internal surfaces of the building. Lowered temperatures can lead to condensation, which is an undesirable effect in contemporary design. Condensation leads to mould growth and premature deterioration of the construction materials (Kuhnenne, 2008). It is therefore vital to numerically determine the temperatures on the internal surface of the model. Once the minimum temperature on the internal surface is known, the temperature factor f_Rsi can be estimated. The temperature factor must be a minimum value of 0.7 in order to avoid condensation and mould growth (Kuhnenne, 2008). The temperature factor f_Rsi can be defined by Equation 3.5.

[3.5]

θ_si,min is the threshold internal surface temperature below which condensation can occur. Note that condensation depends upon the predefined internal relative humidity within the model (Kuhnenne, 2008).

3.5.1 Reverberation time

The most commonly used simplified model to calculate reverberation time, is that of the Wallace Sabine approximation. This assumes the speed of sound to be constant at 343.3 m/s, and at 20 °C the term 2.76/t^0.5 = 0.161 s/m. If sound is reflected off a surface several times, the reverberation time is the time required for reflections to decay by 60 dB. The reverberation time is frequently stated as a single value, however, it can be assessed based on three versions of the diffuse-field theory (Citherlet and Macdonald, 2003). Typically, the reverberation time differs depending on the frequency band being measured. The frequency-dependent reverberation time can therefore be expressed by Equation 3.5.

[3.6]

The Wallace Sabine equation states that t_r is directly proportional to the volume, V, of the room, but inversely proportional to the room’s effective surface area, A_f^tot. The effective surface area is the sum of the individual products of an area covered by a particular material multiplied by the material’s absorption coefficient (α) as shown in Equation 3.7.

[3.7]

The reverberation time in a room is thus affected by the size and shape of the enclosure and the materials used in the construction of the room. Furthermore, every object that is in the room will impact on the reverberation time, including occupants and furniture. The theoretical model, from which these equations are derived, requires the decaying sound field to be perfectly diffuse. According to Citherlet and Macdonald (2003):

3.5.2 Acoustic absorption

Sound is absorbed because of its reflections at the enclosure boundaries during the propagation. At each successive reflection, the enclosure boundaries and all objects within the enclosure absorb a fraction of the sound energy. The fraction of absorbed sound is dependent upon the frequency of the emitted sound and the capacity of the reflecting material to absorb this frequency. For instance, concrete is a rather poor sound absorber compared to fibreboard, as shown in Fig. 3.8. The total absorption is the product of the absorption coefficient of all materials multiplied by the area. In practice this calculation has to be conducted at a number of different frequencies due to the fact that the absorption coefficient is not constant across frequencies. The absorption coefficient of a material is a number between 0 and 1 that indicates the proportion of sound absorbed by the surface compared to the proportion which is reflected back into the room. For example, in the situation of an open window without any sound reflections whereby sound would pass straight outside, this would be a perfect absorber and have an absorption coefficient of 1. The opposite of this might be a thick concrete ceiling, which is smooth and painted, and is from an acoustic point of view the equivalent of a mirror and has an absorption coefficient close to 0. The absorption coefficient varies with the frequency and so the reverberation time is a function of frequency. Some contractors have experimented by manipulating the surface texture of rammed earth walls, by adjusting the soil particle grading, in an attempt to alter the acoustic absorption coefficient SIREWALL (2011). This is an interesting avenue for further research as no detailed experimental data are currently available and yet could have significant potential for application in performing arts buildings, recording studios and other similar building typologies.

3.5.3 Correlation with thermal inertia

Thermal inertia describes the combined effect of heat storage capacity within the wall and the thermal resistance to movement of heat through the wall. The following equation refers solely to thermal mass and does not take into account the thermal resistance of the wall, however it is an often-used formula to describe the thermal inertia of a material. Table 3.2 shows the impact of different materials and frequencies of the absorption coefficient. The thermal inertia, I, of a material is defined as the square root of the product of the material’s thermal conductivity, density and specific heat capacity. It therefore quantifies the capacity of a material to store surrounding heat and to release it when surrounding temperature drops, as defined in Equation 3.8:

[3.8]

Note also that this is a simplified equation and does not, for example, describe solar absorption coefficients as either part of the boundary equation or the limits of 24-hour cycling.

In contrast to its acoustic performance, concrete has a higher capacity to store heat (thermal inertia) than fibreboard, because of its higher density and thermal conductivity. This higher thermal inertia generally increases absorption of solar gains, and reduction in internal heat gains may improve occupants’ thermal comfort, especially for spaces with large glazed areas and no cooling plant. To provide a well-designed building, a balance must be found between acoustic absorption and thermal inertia. Earth brick walls make a significant contribution towards achieving adequate acoustic performance (Morton et al., 2005). The performance of earth brick walls is very good in terms of thermal and acoustic performance and could be enhanced by avoiding flanking transmission. It is also good practice to repair initial shrinkage cracks, which may affect acoustic performance. The reason why soil functions particularly well in terms of thermal inertia is due to the combination of relatively high volumetric heat capacity and thermal conductivity. With its low thermal diffusivity, earth walls possess the ability to dampen and delay internal thermal variations in response to external inflows.

3.5.4 Acoustics and building performance simulation

It is important to realise that with regard to building acoustics it is all about getting the shell of the building right in the first instance. It is almost impossible to retrofit proper acoustic performance (May, 2009). Elsewhere as in Europe traditionally, buildings typically consisted of heavy monolithic constructions such as masonry walls with earthen or stone floors. With the advent of concrete blocks and monolithic construction, the first models for the prediction of sound isolation were based on a simple mass law where only transmission through the partition between two rooms was considered (Schoenwald, 2008). A large number of building simulation tools that provide computational models to predict sound isolation and acoustics in buildings are now widely available. The weighted Sound Reduction Index (R_w) of a solid wall is strongly dependent on the dry density of the material. SRE is a monolithic wall fabric where the dry density (ρ_d) is typically high, ranging between 1900 and 2200 kg/m³. According to the ‘acoustic mass rule’ for solid walls, as defined by BS 8233 (British Standards Institution, 1999), R_w can be calculated using:

[3.9]

According to the Building Regulations (2000) Approved Document E: ‘Resistance to the passage of sound’, the laboratory values for new internal walls within houses, flats and rooms for residential purposes must have a minimum R_w of 40 dB. A typical 300 mm thick solid SRE wall (without insulation), would have a weighted Sound Reduction Index (R_w) of 58.3 dB, assuming dry density to be 2100 kg/m³. A brief summary of a number of the simulation software tools that could be used to better predict the acoustic performance of buildings are listed in Table 3.4.

1. FEM (finite-element method) such as Ansys, LSDyna, Nastran, Abaqus

2. Multibody system such as ADAMS, Dymola, Partial Flow Code PFC

3. CAS (computer Algebra system) such as Maple, Matlab/Simulink

4. CFD (computational fluid dynamics).

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f frequency (Hz)

I thermal inertia, also known as thermal effusivity, β (W s^1/2/m² K)

l length (m)

m' wall surface mass (kg/m²)

V volume (m³)

T absolute temperature, e.g. of air (K)

A_f^tot total equivalent area of an enclosure for frequency f (m²), that includes absorption due to boundaries, furniture, occupants and air.

Q total heat flow (W/m)

U Thermal transmittance (W/m² K)

θ_i Internal temperature (°C)

θ_e External temperature (°C)

θ_si,min Threshold internal surface temperature (°C)

Ψ linear thermal transmittance

χ point thermal transmittance