Civil Engineering March 2021 | Vol 29 No 2

Civil Engineering March 2021 61 designs are refined in RS3 if the geometry is complicated. The use of 3D FE suites will become more prevalent in future in the design of these walls. These software packages are expensive and necessitate sufficient user competency and understanding of all the input require- ments and soil and structural element behaviour. Such competency and under- standing is difficult to acquire if the software is not frequently used, the developers are not consulted for guidance, and if the user does not have a good understanding of structural design. Care should therefore be exercised by the design engineer and hand calculations and/or a second analysis method used to confirm outputs from FE analyses. A quick hand calculation to determine the required tensile force (T), ignoring the effects of passive resistance due to embed- ment, friction between wall and soil, and the effect of cohesion is given by: T = 0.5K a γH 2 FoS(S h ) where K a is the coefficient of active earth pressure γ is the unit weight of the retained soil H is the height of the retained soil FoS is a factor of safety of typically 1.5 S h is the horizontal spacing of grouted anchors A simple wedge stability analysis can also be used (upper bound theorem). The designer always needs to ensure that the prestress applied to the top grouted anchor would not result in passive failure. If passive failure over the top portion of the wall is not considered problematic, the T-force can generally be divided by the proposed number of anchors over the exposed height of the wall (ULS). As discussed in Part 1 of this series, different designers use either factored or unfactored (T calculated without a factor of safety (FoS)) lock-off loads for grouted anchors. REDUCED PASSIVE RESISTANCE AND ACTIVE PRESSURES BELOW EXCAVATION LEVEL The following question was asked: How do you consider reduced pas- sive resistance and active pressure below the excavation depth using 2D plain strain or BOE Winkler spring software? This question was asked to gauge whether it is understood that when soldier piles are spaced more than three diameters apart in cohesionless soil (Figure 2), or one diameter apart in cohesive soil in an undrained scenario, reduced passive resistance per run- ning meter will result below the excavation depth. Additionally, a reduction in active pressure could also result below the excava- tion level. When considering a plate element (material properties derived per meter length of wall, A wall = A pile c c spacing and I wall = I pile c c spacing ) in a 2D plane strain FE analysis, modelling a widely spaced soldier pile wall, increased passive resistance and active pressure will result per linear meter of wall below the embedded portion. This increased resistance could result in reduced moments developing in the piles and reduced grouted anchor loads. Three respondents indicated that they do not consider the 3D effect while three indicated that they do consider this 3D ef- fect using either Brom’s or the Wang Reece formulation. The user of plane strain FE packages is cautioned against this potential unsafe design assumption as it could result in reduced structural forces. Although these considerations are incorporated into DeepEx and Wallap, it is unclear how the respondents will account for this phenom- enon in a plane strain FE model. It is advised that the designer of these systems consider the achieved passive resistance considering failure mechanism as detailed by Wang and Reese’s equations (FHWA, 1999) to ensure wedge failure, overlapping wedge failure and plastic flow does not occur. FRICTION BETWEEN WALL AND SOIL The interface friction that develops between a piled wall and the soil reduces the horizontal component of earth pressure acting on the wall and results in a vertical force component that needs to be resisted in end bearing or side shear below the excavation level. This reduction is generally beneficial. In addition to this, the passive resistance over the embedded portion of the wall normally increases due to friction. In geotechnical FE suites, interface friction is modelled using an interface element of zero thickness. This interface element models relative displacements and elastic shear using shear stiffness (k s ) and normal stiffness (k n ) on the interface. These values are difficult to determine and the effect should always be checked using a sensitivity parametric study. If a liner element is used without a zero thickness interface element, full friction will develop, which often re- sults in non-conservative structural forces. In Winkler spring BOE software packages, the driving friction is normally assumed to be δ = 0.66φ’ and δ = 0.5φ’ in resisting. GEOTECHNICAL CONSTITUTIVE MODELS The following question was asked: Which constitutive models do you use to model soil and rock? How do you think these constitutive models affect the structural forces? This question was asked to assess how familiar respondents are with the stress- dependency of stiffness (i.e. the associated increase in stiffness with increased confinement pressure) and the occurrence of plastic strain before reaching failure. Soldier pile wall CL Retained soil Restraining soil Spacing wider than 3× pile diameter P active P water P water P passive Figure 2 Passive resistance and active pressure below embedded portion of wall for cohesionless materials