Civil Engineering March 2021 | Vol 29 No 2

Civil Engineering March 2021 63 occurs prior to reaching soil failure when using HS. Additionally, stiffness remains unchanged when using Mohr-Coulomb over the embedded portion of the wall while HS and HS-small exhibit strong stress-stiffness dependency. According to literature, the HS-small constitutive model typically matches in-situ displacement measurements quite well. DEFLECTION AND ASSOCIATED LATERAL AND VERTICAL MOVEMENT The following question was asked: How do you estimate the expected deflections/displacements of a lateral support system? All respondents indicated that they use FE or BOE Winkler spring analyses to predict displacements. Three respondents stated that they accompanied these numerical modelling checks with empirical checks. In the past, codes of practice included displacements measured during construc- tion of various excavations. Although these case studies are extremely valuable in back analyses to establish how effective FE analyses are in predicting displacement, the prestress force, prestress distribution, stiffness of the ground profile, and wall stiffness have the greatest influence on the displacements. These properties are typically not reported in these tables and are therefore considered of little value as various designers use different design methods and different pre- stress distributions. Typically, displacements ranging from 0.05% to 0.15% of the retained height are measured in South Africa on Franki projects (Chang and Byrne, 2019). Other studies state that displacement equal to 0.2% of the height can be expected. The use of FE modelling is considered the best method to predict displacements of embedded multi-anchored pile walls. It is, however, important to get sufficient Table 2 Results from analyses using different constitutive models Solution 2.5 m c/c with anchors 2.5 m c/c with anchors prestressed to 80% FHWA 2.5 m c/c with anchors prestressed to 80% FHWA 2.5 m c/c with anchors prestressed to 80% FHWA Analysis type FHWA pressure/ Caltrans beam – DeepEx Mohr- Coulomb – RS2 Hardening Soil – RS2 Hardening Soil with small strain stiffness – RS2 A1 (kN) 520 453 439 437 A2 (kN) 280 333 340 325 A3 (kN) 387.5 353 358 349 BM per pile (kN.m) 312.5 237.5 240 192.5 Horizontal displacement (mm), maximum all stages 27 36 36 20 Figure 5 Comparison of bending moment with depth using various constitutive models Depth (m) Bending moment (kN.m) –200 –100 0 100 200 300 16 14 12 10 8 6 4 2 0 HS MC HSSmall Figure 4 Output from elastoplastic Winkler Spring analysis with 80% FHWA prestress applied 2.7 m Wall 1 Reinforced concrete piles (lag.) Pile diameter: 60 cm, 6 rebars Φ25, @ 2.5 m O.C. FykRebars = 413.8 MPa, Fck = 35 MPa Supports beam analysis Wall δ = 50% Φ Wall δ.drive = 66% Φ 2.7 m 2.7 m 2.9 m 11 m 4 m El. –11 m Moment (kN-m/m) Pressures (kPa) –100 0 100 200 –150 –50 50 150 122.6 kN-m/m 167.03 kN/m 105.28 kN/m 131.3 kN/m 52.5 kPa 146.8 kPa 62.6 kPa 133.9 kPa 8.4 kPa 10° 10° 10° El. 0 m F γt = 19.625 kN/m 3 φ’ = 30 ° E = 45 000 kPa rEur = 3 e =0.4 Effective horizontal soil pressures Wall bending Seismic pressures