Comparison of Analysis Specifications and Practices for Diaphragm Wall Retaining System

Calculations are done under plain strain conditions. Diaphragm wall sections are simulated using elastic plate element defined by normal stiffness, bending stiffness and Poisson’s ratio. Soil masses are modelled as elastic plastic material with Mohr-Coulomb failure criterion, while struts are modelled by the fixed end anchor element facility in Plaxis. The analysis includes the following construction stages.

Activation of Diaphragm walls and loads

A significant issue regarding excavation modelling is the way in which partial factors are applied. Partial factors should be applied on material properties and loads. Coefficients to be imposed on loads and material properties according to the various codes are listed in Table 1 and Table 2.

Table 1

Partial factors of safety applied on loads.

Table 2

Partial factors of safety applied on material parameters.

Factored values of loads, resistances and material properties should be used for calculations and modelling. For the modification of material properties, factored values can be directly entered into the material sets of Mohr-Coulomb model. The material parameters on which partial coefficients are applied are cohesion, angle of internal friction and wall specific weight (unit weight of wall material multiplied by wall thickness). Table 3 gives the ultimate values included in the material set.

Table 3

Factored values of material properties.

Safety factors on loads and resistances need to be carefully applied since they should take into account the load variations during the excavation process. To incorporate the load variations, factoring must be done on such parameters that the factored loads at each construction stage will be revised automatically. Here, the partial coefficients are applied on saturated and unsaturated unit weights of soil (γ_sat, γ_unsat), uniformly distributed load representing surcharge loads and unit weight of ground water (γ_gw). The modified values of these parameters, after the application of partial factors, are entered into the material sets of input file. Separate soil profiles are created in the material set for active and passive soil mass. The reduction factors for resistances are applied on passive soil profile set and the corresponding load increment factors are entered into the active soil profile set. In this manner, factored loads and resistances can be calculated accurately for every construction stage. The final factored values are given in Table 4.

Table 4

Factored values applied for calculating loads and resistances.

European standards of foundations and earth and retaining structures used for the study are EN 1997-1 Geotechnical design - Part 1: General rules [15] and EN 1997–2 Geotechnical design- part 2: Ground investigation and testing [16]. Eurocode 7 offers three design approaches namely DA 1, DA 2 and DA 3. They define the way in which partial safety factors are distributed. The design values (S_d) [15] should be calculated as stated in Eq. (1):

Sd=Sk/γ<!-- ? -->M$$\begin{array}{} \displaystyle S_{d}\,=\,S_{k}/\gamma_{M} \end{array}$$(1)

where, S_k is the characteristic value of material properties and γ_M is the corresponding partial safety factor. Partial factors are provided for actions/effect of actions (A1, A2), material properties (M1, M2) and ground resistances (R1, R2, R3).

The design approaches are defined as:

DA1- A: A1 + M1+ R1

Partial coefficients applicable for the analysis are given in Table 1 and Table 2. The third design approach is omitted from calculations due to its similarity with DA1.The maximum values of lateral deflection (H_max), bending moment (B.M_max) and shear force (S.F_max) acting on the wall and the axial force developed on the strut (T) are given in Table 5. Examples of results are demonstrated in Figs. 2–4.

Table 5

Results of analysis with EC7.

Figure 2

Figure 3

Figure 4

Australian standards chosen for the analysis of diaphragm walls are AS 4678: Earth retaining structures [22], AS 1170.1 Part 1: Dead and live loads and load combinations [23] and AS 5100.3: Bridge Design-Part 3: Foundations and soil supporting structures [24]. Condition specified in Eq. (2) must be satisfied for all load combinations [22,23].

R≥<!-- = -->S$$\begin{array}{} \displaystyle R\,\ge\,S \end{array}$$(2)

where R is the factored design resistance and S is the factored design action. Partial coefficients for design are described in AS 4678 [22]. These factors are given in three groups; reduction factors φ_R, uncertainty factors φ_u, and structure classification factors φ_N Safety factors on material strength are applied on cohesion (c) and tangent of angle of internal friction (φ) as stated in Eq. (3) and Eq. (4).

c★<!-- ? -->=Φ<!-- F -->ucc$$\begin{array}{} \displaystyle c^{\bigstar}\,=\,\it\Phi_{uc}c \end{array}$$(3)

ϕ<!-- ? -->★<!-- ? -->=tan−<!-- - -->1(Φ<!-- F -->uϕ<!-- ? -->(tanϕ<!-- ? -->))$$\begin{array}{} \displaystyle \phi\,\,^{\bigstar}\,=tan^{-1}\,\,(\it\Phi_{u\phi}\,(tan\phi)) \end{array}$$(4)

where, φ_uc and φ_uφ represent the reduction factors for c and φ respectively. The code recommends a minimum surcharge load of 5 kPa. The partial coefficients to be applied according to the Australian standards are listed in Table 1 and Table 2. The factored values entered into the model are given in Table 3 and Table 4. The results of analysis are given in Table 6.

Table 6

Results of analysis using Australian codes.

The partial factors applied as per the limit states of strength and stability resulted in excavation failure indicating the need for introduction of extra support. The values shown merely represent those obtained from the analysis.

The Indian codes of practice referred for the study are IS 9556: Code of practice for design and construction of diaphragm walls [9], IS 4651-Part 4: Planning and design of port and harbours-Earth pressures [10] and IS 4651-Part 2: Planning and design of port and harbours – General design considerations [ 11]. IS 9556 illustrates the requirements of slurry wall construction procedures, material characteristics, equipment and accessories. IS 4651 (Part 2) explains the methods for estimating lateral loads and IS 4651 (Part 4) gives the partial coefficients to be applied on lateral pressures. The design values of material strengths (M_d) and loads (F_d) as per Indian standards [11] are given in Eq. (5) and Eq. (6).

Md=Fmγ<!-- ? -->m$$\begin{array}{} \displaystyle M_{d}\,=\,\frac{F_{m}}{\gamma_{m}} \end{array}$$(5)

Fd=Flγ<!-- ? -->f$$\begin{array}{} \displaystyle F_{d}\,=\,F_{l}\gamma_{f} \end{array}$$(6)

where F_m and F_l are the characteristic strengths of materials and loads. γ_m and γ_f represent corresponding safety factors. The partial coefficients for limit states of serviceability and collapse are given in Table 1 and Table 2.The final values are given in Table 3 and Table 4.Table 7 shows the results of analysis according to the Indian standards.

Table 7

Results of analysis with Indian codes.

The American standard used for the analysis is AASHTO LRFD bridge design specifications [1,2]. The code implements the use of limit states on geotechnical requirements and hence can be applied for foundation design [17]. For the calculation of geotechnical parameters, LRFD (Load and Resistance Factor Design) method is followed. AASHTO specifications assign safety factors on actions and resistances. For each limit state, an overall factor is applied on the ground resistances calculated from unfactored parameters. The final factored load as per AASHTO should be computed using Eq. (7):

Q=Σ<!-- S -->niγ<!-- ? -->iQi$$\begin{array}{} \displaystyle Q\,=\,\Sigma n_{i}\gamma_{i}Q_{i} \end{array}$$(7)

where n_iγ_i and Q_i represent load modifier, load factor and load effect respectively. Load modifier is a factor related to ductility, redundancy and operational classification [2]. Load factors are multipliers assigned to the load effects. The load factors applicable for the analysis of diaphragm walls are listed in Table 1 and Table 2. The results are shown in Table 8.

Table 8

Results of analysis with American code.

The standards that can be used for the analysis of diaphragm walls are the Canadian Foundation Engineering Manual [12] and the Canadian Highway Bridge Design Code (CHBDC)[13,14]. Canadian codes apply the total resistance factor approach. In this method, the parameters are not individually factored. According to CHBDC, the designs of embedded walls are to be regulated by the overall stability of the wall, overturning and horizontal resistances. The design values[12] are given by Eq. (8).

ϕ<!-- ? -->Rn≥<!-- = -->Σ<!-- S -->α<!-- a -->iSni$$\begin{array}{} \displaystyle {\rm\phi}R_{n}\,\ge\,\Sigma\alpha_{i}S_{ni} \end{array}$$(8)

where φR_n represents factored geotechnical resistance. R_n is the ultimate ground resistance and φ is the geotechnical resistance factor. Σα_iS_ni denotes the total factored load with α_i being the load factor. The load factors and resistance factors can be obtained from standards like the National building code of Canada and Canadian highway bridge design code. The numerical values of partial factors to be applied and their factored values are given in Tables 1–4. Table 9 shows the results of analysis.

Table 9

Results of analysis with Canadian codes.

The British standards considered for the analysis are BS 8002: Earth retaining structures [6], BS 8004: Foundations [7], BS NA EN 1997-1: British National Annex to Eurocode [5] and BS EN 1538: Execution of special geotechnical works – Diaphragm walls [4]. BS EN 1538 give guidance for the design, construction and execution of diaphragm walls. The earlier versions of BS 8002 and BS 8004 were temporarily withdrawn in 2010 and deemed by Eurocodes. Partial safety coefficients are provided in the British National Annex to Eurocode. The recent codes provide guidance for implementing the conditions of Eurocode 7. National Annex adopts DA 1 for the analysis of earth retaining structures. The partial factors and their ultimate values are given in Tables 1–4. These are same as that of the first design approach in Eurocode 7. The results are shown in Table 10.

Table 10

Results of analysis with British standards.