Civil Engineering March 2021 | Vol 29 No 2

64 March 2021 Civil Engineering information on the stiffness profile with depth of a particular site and use the cor- rect constitutive models. Stiffness of the soil profile is however seldom measured during subsurface investigations in South Africa for deep excavations. These tests could include CSW or multi-channel surface wave (MSAW), Pressuremeter test and at a most basic level SPT-N test results which can be used to derive stiffness from correlations. Various constitutive models will predict different displacements as discussed in this article. Displacements must typically be measured in urban areas using surveying methods to confirm that any excessive displacements are noted, systems are strengthened (need be), and no damage is caused to adjacent properties. PROBABILISTIC DESIGN Probabilistic analysis of embedded pile walls is complicated to assess holistically, as various elements come into play, namely soil-structure interaction, pile and grouted anchor structural strength, and anchor grout-bond strength. Assuming that the structural sections and grout bond capacity are adequately designed to have a higher reliability index (RI) than that of global stability, the probability of the wall can be analysed using limit equilibrium methods. FHWA (1999) states that current state-of-the-practice limit equilibrium methods do not include generally accepted approaches of modelling the restraint force provided by prestressed grouted anchors. One could typically apply a pressure, on a vertical cut face in limit equilibrium slope stability software, equivalent to the sum of the per meter lock-off grouted anchor loads divided by the exposed depth of the wall, as shown in Figure 6. All slope failures that result through the vertical cut in such analyses should be ignored and only failures below the excavation line should be considered (wall structural resistance not considered in LE). Most reliability solutions incorporate c’ and φ ’ and it is fairly well known that c’ is log-normally distributed with a coefficient of variation (COV) of 40% with φ ’ following a normal distribution with a COV of some 10%. This causes the FoS to follow a hybrid distribution. The hybrid is however much more log-normal and the authors typically use a log-normal distribution of FoS. The same wall in the example above was modelled in limit equilibrium software using an applied stress that is equivalent to the anchor forces calculated using the FHWA method. The method of estimating the probability of failure (PoF) as detailed in Duncan &Wright (2005) was used. The reliability index (RI) was found to be 2.26 with a PoF of 1% when assuming the same applied stress over the face (Figure 7) in all analyses. However, this is not considered entirely correct as the force in the anchors and associated pressure at the face will increase if the internal friction angle is lower than that assumed in the baseline analysis. To illustrate this point, if grouted anchors are locked off at 80% to 100% of FHWA pressures, and the actual internal friction angle of the retained soils is lower, the red arrow in Figure 8 indicates the ad- ditional strain and resulting increased stress (K a γH with higher K a ) will develop at the face. This is similar, but maybe less severe if locked off at 1.5 T required from a simple wedge analysis (green arrow in Figure 8). This is due to the fact that grouted anchors are designed to be stronger than that re- quired to achieve an FoS = 1 in the baseline analysis. Therefore, if the internal friction angle is lower than that assumed, the tensile force in the anchors and the pressure at the face would accordingly increase. This in- crease in anchor loads is clearly noted when modelling using EN1997-1 DA1/2 approach, Figure 7 Reliability Index versus PoF for example (blue dot RI using LN distribution of FoS) Extremely short term temporary structures Hazardous Unsatisfactory Poor Below average Good Probability of failure 1.E+00 1.E–01 1.E–02 1.E–03 1.E–04 1.E–05 1.E–06 1.E–07 Reliability index 5 4 3 2 1 0 Above average Most short term conditions Most geotechnical structures in RSA Nice to have Probably not used for most RSA Conditions Only used for unclear or high-life-loss structures Parrock recommended values Phoon (2008) recommended values Over the top Figure 6 Modelling grouted anchor forces as an applied stress at wall facing in limit equilibrium analysis Safety factor 0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000 5.500 6.000+ 0.29 34.00 kN/m 2 Only FoS’ below vertical cut considered