Civil Engineering March 2021 | Vol 29 No 2

62 March 2021 Civil Engineering Additionally, deep excavation design relies on loading, unloading, and reloading of soils and the stiffness behaviour is de- pendent on the stress conditions of a spe- cific excavation stage under consideration. Five of the respondents indicated that they only use the linear-elastic perfectly plastic Mohr-Coulomb constitutive model with a single stiffness value, while two others indicated that they use hardening soil, hardening soil small strain stiffness or softening-hardening (RS2) to model soils. For rock, the Hoek-Brown constitutive model is normally used. Continuum (joint does not govern behaviour) or discon- tinuum (joint plays a major role) modelling can be used depending on the role of discontinuities on behaviour. Over the past few years significant progress has been made and constitutive models have been refined to better imitate actual soil behaviour. The Mohr-Coulomb constitutive model requires limited input from the user and is therefore commonly preferred due to its simplicity. The Mohr- Coulomb model however does not incor- porate stiffness for unloading and relies on a single stiffness value that does also not increase with increasing confinement pres- sure (i.e. increase in depth below surface) and demonstrates only isotropic elastic behaviour before reaching failure. The Hardening Soil (HS) and Hardening Soil Small Strain (HS-small) constitutive models are better defined to model embedded wall staged excava- tion and should result in more accurate displacement predictions as shear displace- ments and unloading-reloading behaviour is modelled. Table 1, from Bowles (1997), provides constant elastic moduli and shear parameters for granular soils of various consistencies. Input parameters for hardening soil can be obtained from Recommendations of the Committee for Waterfront Structures: Harbours and Waterways (2004), using SPT-N density correlations. It is highly recommended that these correlations be accompanied by interpretation from actual triaxial test results with an unload- reload cycle. Small-strain stiffness can be determined in the triaxial test if it has been modified by including bender elements (to the authors’ knowledge not available in South Africa) or continuous surface wave (CSW) testing. Pressuremeter testing (PMT) also provides valuable information on soil stiffness. The example used in this article to demonstrate various principles is for an 11 m high soldier pile wall in a Berea Red silty sand profile with grouted anchors of vertical and horizontal spacing of 2.7 m and 2.5 m respectively (Figure 3). The soldier pile wall consists of 600 mm continuous flight auger (CFA) soldier piles spaced at 2.5 m c/c horizontally. The wall was first assessed using a limit equilibrium analysis with Federal Highway Administration (FHWA) pressure and a Caltrans beammodel (20% negative mo- ment) and then analysed using the three different constitutive models with 80% FHWA applied grouted anchor prestress load to three strand anchors. The results of these analyses are summarised in Table 2 and Figure 5, which compare the moments that develop down the length of the piles using the different constitutive models. The following soil properties were as- sumed for different constitutive models: Q Q Mohr-Coulomb: ф’ = 30°, c’ = 1 kPa, E = 55 MPa, ν = 0.35, γ = 19.6 kN/m 3 Q Q Hardening Soil: ф’ = 30°, c’ = 1 kPa, R f =0.9, m = 0.5, e 0 = 0.55, e max = 1, E ref,50 = 45 MPa, E ref,oed = 45 MPa, E ref,ur = 105 MPa, P ref = 100 kPa, ν = 0.35, γ = 19.6 kN/m 3 Q Q Hardening Soil Small Strain: ф’ = 30°, c’ = 1kPa, R f =0.9, m = 0.5, e 0 = 0.55, e max = 1, E ref,50 = 45 MPa, E ref,oed = 45 MPa, E ref,ur = 105 MPa, P ref = 100 kPa, G 0,ref = 158 MPa, γ 0.7 = 0.0001, ν = 0.35, γ = 19.6 kN/m 3 The installation of CFA piles can only be done up to a depth of 16 m to 18 m in South Africa (rigs available) to prevent splicing of auger stems and associated interrupted grout placement. This implies that the maximum excavation depth, using CFA piles, is roughly 12 m to 15 m, depending on the rig. These maximum excavation depths are typically seen in Durban and Cape Town where the CFA installation method is commonly used in soft soils to prevent collapse. Typically, a maximum of five basement levels can be achieved using CFA piles unless cased auger solutions are used. In Gauteng, much deeper basements are exca- vated due to drier conditions and the use of open bore auger piles to great depths. From the above it can be seen that considerably more input parameters are required for the HS and HS-small constitutive model compared to the simple Mohr-Coulomb constitutive model. These enhanced models also consider unloading and reloading stiffness of soils. Based on the above analyses it can be interpreted that the bending moment is similar for the Mohr-Coulomb and HS constitutive models, while lower using the HS-small model. Bending moments could either be higher or lower when using HS and HS-small when compared to the Mohr-Coulomb constitutive model. This is due to the fact that plastic deformation Table 1 Typical values of elastic modulus, cohesion and friction for gravelly soils of different consistency Material γ (kN/m 3 ) Elastic modulus (MPa) Cohesion (kPa) Friction angle (°) Very loose 17 5.5 2 24 Loose 17 19 3 29 Medium dense 18 55 3 33 Dense 18 110 3 38 Very dense 19 137 3 43 2.7 m 2.7 m 2.9 m 11 m 4 m El. –11 m Resist KaH = 0.333 KpH = 4.964 Drive KaH = 0.333 KpH = 4.964 10° 10° 10° Figure 3 DeepEx analysis for 11 m high embedded multi-anchored soldier pile wall 2.7 m