Ground movements due to deep excavations in Shanghai: Design charts

Abstract

Recent research has clarified the sequence of ground deformation mechanisms that manifest themselves when excavations are made in soft ground. Furthermore, a new framework to describe the deformability of clays in the working stress range has been devised using a large database of previously published soil tests. This paper aims to capitalize on these advances, by analyzing an expanded database of ground movements associated with braced excavations in Shanghai. It is shown that conventional design charts fail to take account either of the characteristics of soil deformability or the relevant deformation mechanisms, and therefore introduce significant scatter. A new method of presentation is found which provides a set of design charts that clarify the influence of soil deformability, wall stiffness, and the geometry of the excavation in relation to the depth of soft ground.

Graphical abstract

Keywords

Shanghai / excavations / mobilizable strength design / dimensionless groups / design charts

1 Introduction

As the world population continues to increase, the major cities across the globe are increasingly turning to the construction of underground metro systems and subways to relieve congested terrestrial road networks. Shanghai is one of China’s largest municipalities with a population of over 23 million people (National Bureau of Statistics of China, 2012: 2010 data). The rate of construction in Shanghai has allowed the accumulation of considerable field evidence from deep excavation works as exemplified by the comprehensive database presented in the thesis of Xu [1]. Published case studies of monitored excavations in Shanghai include Wang et al. [2], Tan and Li [3] and Ng et al. [4]. Numerical studies back-analyzing excavations in Shanghai include Hou et al. [5]. This paper offers an extension and refinement of some of the ideas presented by Bolton et al. [6] at a keynote lecture to the DFI conference in London in 2010. Further details of some of the main calculation procedures are given in Lam & Bolton [7].

Studies at the University of Cambridge on deep excavations and their influence on nearby buildings have included field monitoring, centrifuge tests and theoretical models (e.g., St John [8]; Powrie [9]; Elshafie [10]; Goh [11]). Although field data are authoritative on the particular sites that are monitored, theory is also significant where it can assist in the comparison of data from different sites, so as to draw more general lessons. This paper presents field data within the Mobilizable Strength Design (MSD) framework developed at the University of Cambridge. This is used to create dimensionless groups of measurable parameters pertinent to the important wall-bulging mechanism, habitually observed in deep excavations below the level of the props. This enables the construction of charts to compare retaining wall deformations and ground movements which have been observed around deep excavations in Shanghai, as reported by Xu [1].

The deterministic use of mechanisms that have been observed to control limit state events is a more reliable route towards good geotechnical design than attempting some statistical inference based on the assumed variation of parameter values but in the absence of any confirmation that the assumed mechanical system is relevant to the case in hand [12]. Early centrifuge tests on model cantilever walls in firm to stiff clay showed the promise of linking the stress-strain states observed in element tests to equivalent states of overall equilibrium and strain mobilized around geotechnical structures: Bolton and Powrie [13]. A central feature of this new approach was the joint use of a simplified equilibrium stress field in conjunction with a simplified but kinematically admissible deformation field that was compatible with structural constraints (rigid body rotation). This was reasonably successful in reproducing the wall rotations observed during simulated excavation in the centrifuge models.

This first application of what has become known as Mobilizable Strength Design (MSD) was quickly adopted into UK practice. BS8002 [14] defined the Mobilization Factor (M) as the ratio between shear strength and the current shear stress, which is equivalent to a factor of safety on undrained shear strength (represented as Eq. (1)).

(1)M＝c_{\mathrm{u}}/{\tau }_{\mathrm{m}\mathrm{o}\mathrm{b}}.

Bolton [15] contended that the partial factors in limit state design calculations for collapse are in reality achieving a high M factor on c_u which limits the deformations under working loads in the field. This is similar to the “stress-reduction factor” discussed in Simpson et al. [16]. MSD seeks to provide a simplified method to design geotechnical structures directly for the serviceability limit state (SLS) which will generally govern the success of the design. The non-linear stress-strain relationship of soil is then seen to be integral to a correct understanding of soil deformations and ground displacements [17,18].

The possible use of MSD for flexible structures was first considered by Osman and Bolton [19] in the context of cantilever walls retaining clay. They compared MSD calculations based on rigid wall rotations with Finite Element Analysis (FEA) that fully accounted for typical soil non-linearity and the flexure of walls with typical stiffnesses. Since displacements within the assumed deformation mechanism are controlled by the average soil stiffness, MSD calculations were based on soil stress-strain data from an undisturbed sample taken at the mid-height of the wall. The objective was to consider the degree to which the mechanisms described in Bolton & Powrie [13,20] could be expected to satisfy serviceability and collapse criteria for a real cantilever retaining structure, through a single calculation procedure. Importantly, a wall designed using MSD earth pressures, calculated assuming wall rigidity, will not collapse if the wall yields, provided that it remains ductile. Furthermore, MSD calculations [19] of wall bending moments and crest deflections showed reasonable agreement with FEA (generally within a factor of 1.5 and 2 respectively). MSD was therefore felt to be an improvement on previous retaining wall design methods based on arbitrary safety factors even though its calculations were, at that stage, based on the assumption of wall rigidity.

MSD was later extended to consider wall flexure explicitly through the use of the principle of conservation of energy applied to an assumed geo-structural deformation mechanism: Osman & Bolton [21], Lam & Bolton [7] and Lam et al. [22]. Both field monitoring and centrifuge model observations were helpful in determining suitable mechanisms.

2 Mechanisms observed in centrifuge tests

The Cambridge Geotechnical Centrifuge [23] has been used to investigate geotechnical mechanisms for 40 years now. Centrifuge testing is a well-established experimental technique to study the geotechnical mechanisms that govern the behavior of deep excavations. At the University of Cambridge, a number of doctoral studies over the past 30 years have focused on the centrifuge modelling of excavations in clay (e.g., Kusakabe [24]; Powrie [9]; and Lam [25]).

To better understand the effects of excavation on the movement of the surrounding ground, centrifuge model tests of deep excavations in lightly over-consolidated soft clay have been carried out using a newly developed testing system, in which the construction sequence of a multi-propped retaining wall for a deep excavation can be simulated in flight.

Recent experimental work at the University of Cambridge has included the development of an in-flight excavator [31] to model staged excavations in the centrifuge. This offers important advantages compared with previous methods, as summarized in Table 1. Figure 1 shows some typical PIV plots from one of the tests. Note the development of the pattern of vectors (drawn at different scales) as the excavation continues.

For the purposes of developing general calculation procedures it is necessary to idealize these deformation mechanisms suitable to the different stages of structural support as the excavation proceeds. Figure 2 shows three such idealizations. Figure 2(a) refers to an initial stage of excavation against a cantilever wall prior to the emplacement of any lateral support, Fig. 2(b) idealizes the succeeding deformations around a stiff wall propped at the top, and Fig. 2(c) characterizes the increment of ground deformations due to the bulging of a well-braced retaining wall below the lowest level of lateral support. In what follows we will focus on the bulging mechanism, which seems to have been associated with the catastrophic failure of a number of braced excavations, for example the Nicoll Highway collapse in Singapore [33]. A sinusoidal curve of wavelength λ is chosen for the shape of the bulge, following a suggestion by O’Rourke [34] based on field observations.

3 Mobilized strength design calculations

O’Rourke [34] defined the wavelength of the deformation at any stage of excavation as the distance from the lowest support level to the point of effective fixity near the base of the wall, where it enters a relatively stiff layer. Lam & Bolton [7] suggested a definition for the wavelength based on assessment of the degree of wall end fixity. In either case, the MSD analysis of a given excavation must proceed incrementally as the wavelength λ reduces stage by stage as new supports are fixed. The average wavelength for the whole construction was shown to be a crucial parameter in the development of dimensionless groups and new design charts for deep excavations [6] and will be shown similarly to contribute to the new design charts developed in this paper.

An incremental plastic deformation mechanism was proposed by Osman and Bolton [21] for wide multi-propped excavations in clay. This was modified by Lam and Bolton [7] to include narrow excavations. Their analysis was based on the conservation of energy in the deforming mechanism, taken stage by stage. In each stage there was assumed to be an incremental wall bulge of amplitude w_max which, according to the mechanism sketched in Fig. 2(c), must also be equal to the amplitude of incremental subsidence. The loss of potential energy ΔP caused by subsidence of the retained soil is equated to the sum of the work done on the soil ΔW and the elastic strain energy ΔU stored in the wall.

(2)\mathrm{\Delta }P=\mathrm{\Delta }W+\mathrm{\Delta }U.

The potential energy loss on the active side of the wall and the potential energy gain of soil on the passive side can be calculated easily. The net change of potential energy (ΔP) in a stage of construction is given by the sum of the potential energy changes within the whole volume:

(3)\mathrm{\Delta }P={\displaystyle {\int }_{\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}}{\gamma }_{\mathrm{s}\mathrm{a}\mathrm{t}}{\delta }_{\mathrm{v}}\mathrm{d}Vol},

where δ_v is the vertical component of displacement of soil; γ_sat is the saturated unit weight of soil.

The total work done in shearing the soil is given by the area under the stress strain curve, integrated over the whole volume of the deformation mechanism:

(4)\mathrm{\Delta }W={\displaystyle {\int }_{\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}}\beta c_{\mathrm{u}}\left|\delta \gamma \right|\mathrm{d}Vol},

Where c_u is the local undrained shear strength of soil; δγ is the shear strain increment of the soil; and the corresponding mobilized strength ratio is given by

(5)\beta ={\displaystyle \frac{\mathrm{1}}{M}}={\displaystyle \frac{{\tau }_{\mathrm{m}\mathrm{o}\mathrm{b}}}{c_{\mathrm{u}}}}.

The total elastic strain energy stored in the wall, ΔU, can be evaluated by repeatedly updating the deflected shape of the wall. It is necessary to do this since U is a quadratic function of displacement:

(6)\mathrm{\Delta }U={\displaystyle \frac{EI}{\mathrm{2}}}{\displaystyle {\int }_{\mathrm{0}}^{\lambda }{\left[{\displaystyle \frac{{\mathrm{d}}^{\mathrm{2}}w}{\mathrm{d}{y}^{\mathrm{2}}}}\right]}^{\mathrm{2}}\mathrm{d}y},

where E is the elastic modulus of wall and I is the second moment of area per unit length of wall.

4 Deformability of fine-grained soil

MSD analysis can be carried out using the raw data from representative stress-strain tests. However, such an approach leaves the user without any clear criterion regarding whether the data conform to the behavior that was expected for soil of that type. It is preferable to fit a mathematical model to the raw data, so that the variation of the parameters of the model can be studied in relation to their statistics in a database.

Vardanega & Bolton [18] presented a simple two-parameter power-law model (Eqs. (7) and (8)) for the undrained shear stress-strain relation of clays at moderate mobilizations (i.e., 0.2c_u<τ_mob<0.8c_u).

(7){\displaystyle \frac{{\tau }_{\mathrm{m}\mathrm{o}\mathrm{b}}}{c_{\mathrm{u}}}}=A{\left(\gamma \right)}^b，

(8)

where γ_M=2 is the shear strain required to mobilize 0.5c_u and b is an experimental exponent. This expression was shown to be capable of representing a large database of tests on natural samples taken from nineteen fine-grained soils. The average b-value was shown to be ~ 0.60 for the 115 tests on nineteen clays, and the use of the average exponent was shown to induce acceptable errors (less than a factor 1.4 for two standard deviations) in the prediction of τ_mob/c_u from Eq. (8), if the mobilization strain (γ_M=2) is known: see Fig. 3.

The influence of soil stress-history on the magnitudes of the two parameters b and γ_M=2 was studied for reconstituted kaolin clay, with the data of eighteen isotropically consolidated triaxial compression tests reported by Vardanega et al. [36]. It is worth noting that the K₀-effect will influence the γ_M=2 values as discussed in Vardanega & Bolton [18] and Vardanega [37]. The curves can simply be shifted (upward) as described in Vardanega & Bolton [18] to roughly account for the in-situ stress condition. Figure 4 implies an order of magnitude increase of mobilization strain (γ_M=2) as the over consolidation ratio (OCR) increases from 1 to 30, giving a regression:

{\log }_{\mathrm{10}}\left({\gamma }_{M=\mathrm{2}}\right)=\mathrm{0.680}{\log }_{\mathrm{10}}\left(OCR\right)-\mathrm{2.395},

(9a)

Or re-arranging, for kaolin:

(9b){\gamma }_{M=\mathrm{2}}=\mathrm{0.0040}{(OCR)}^{\mathrm{0.680}}.

The same suite of tests showed b-values ranging from 0.29 to 0.60, offering a linear correlation for kaolin:

b=\mathrm{0.011}\left(OCR\right)+\mathrm{0.371},

(10)

Data from seventeen high quality triaxial tests on high quality samples of London Clay (conducted at Imperial College London and the University of Cambridge), collected from the literature, showed a power index b ranging from 0.41 to 0.83 with an average of 0.58 [38]. As expected, it is the mobilization strain γ_M=2 that varies most significantly with soil conditions. The same effect of γ_M=2 increasing with OCR, as suggested by Eq. (9b), can be inferred from the trend-line with depth d of samples of heavily over consolidated London clay shown in Fig. 5, offering the regression Eq. (11):

\mathrm{1000}{\gamma }_{{}_{M=\mathrm{2}}}=-\mathrm{2.84}\ln d+\mathrm{15.42},

(11)R^{\mathit{2}}=\mathrm{0.46},n=\mathrm{17},SE=\mathrm{1.79},p=\mathrm{0.003.}

The power law formulation (Eq. (8)) will be central to the development of functional groups for use in the analysis of the database of ground movements around excavations.

5 Field database of Shanghai excavations

Xu [1] and Wang et al. [41] presented a database of over 300 case histories of wall displacements and ground settlements due to deep excavation works in soft Shanghai soil. Full details of this database are provided in the aforementioned thesis and paper.

Of those ~300 case histories, 249 are selected for analysis in this paper. The essential information is given as Appendix A (Table 6) (translated from Chinese into English). Table 2 summarizes the variation and range of the key parameters for case records 1 to 249. A further 59 cases were excluded because they did not quote a value for the wall bending stiffness (EI). The characteristic prop spacing (s) was calculated using Eq. (12):

(12)s={\displaystyle \frac{H-d_{\mathrm{1}}}{n_{\mathrm{p}}}},

where H is the depth of excavation, d₁ is the depth to the first prop and n_p was the number of props. If d₁ was not reported in the database summary of Xu [1] then it was simply taken as being equal to zero.

6 Parameters for Shanghai clay

Shanghai soils are quaternary deposits about 150 – 400 m thick, which can be divided into many layers for classification [41]. Based on the available boreholes (complete analysis shown in Appendix B) a simplified soil profile for Shanghai Clay is shown as Fig. 6. Table 3 summarizes the key features of the upper seven layers as described by Wang et al. [41] following the stated guidance of the Shanghai Construction and Management Commission [46]. Figure 7 shows a summary of geotechnical parameters for a site in Shanghai [47]. MSD analysis of a given excavation can be carried out incrementally, with characteristic soil parameters changing accordingly [7]. The characteristic depth for soil properties is regarded here, however, as the mid-depth of the completed excavation. This simpler characterization enables a comparison to be made between large numbers of excavations with different construction histories.

Figure 7 also shows the data from CPT probing at the Yishan Road station in Shanghai. A lower bound trace of the data is shown and has the formula:

(13)q_{\mathrm{t}}\left(\mathrm{M}\mathrm{P}\mathrm{a}\right)=\mathrm{0.25}+\mathrm{0.044}\left(\mathrm{d}\right).

This can be converted into an undrained strength profile using Eq. (14) with a cone factor N_k = 16 following the suggestion of Robertson & Cabal [48]. Taking an average soil unit weight of 17.5 kN/m³ for the Shanghai deposits, Eq. (15) can be written for the overburden pressure:

(14)c_{\mathrm{u}}={\displaystyle \frac{q_{\mathrm{t}}-{\sigma }_{\mathrm{v}0}}{N_{\mathrm{k}}}},

where (for this site):

(15){\sigma }_{\mathrm{v}0}\sim \mathrm{17.5}d\hspace{0.17em}\mathrm{k}\mathrm{P}\mathrm{a}

Substituting Eqs. (15) and (13) into Eq. (14) we get:

(16)c_{\mathrm{u}}\left(\mathrm{k}\mathrm{P}\mathrm{a}\right)={\displaystyle \frac{\mathrm{1000}\left(\mathrm{0.25}+\mathrm{0.044}d\right)-\mathrm{17.5}d}{\mathrm{16}}},

which gives an approximation for the expected variation of c_u with depth of:

(17a)c_{\mathrm{u}}\left(\mathrm{k}\mathrm{P}\mathrm{a}\right)=\mathrm{16}+\mathrm{1.7}d.

Equation (17a) is plotted on Figure 8 to show that it is also a sensible lower-bound to the vane shear data. While analysis of data from a single site in Shanghai is useful it must be stressed that a variety of design lines could be considered depending on availability of other data, presumably scattered. If sufficient and reliable site-specific data became available for a future site of interest, Eq. (17a) could be modified accordingly. Indeed there is no reason why the line should be straight, or even continuous. For the parametric MSD analysis of generic Shanghai excavations, presented in Section 8, Eq. (17a) will be used as a lower bound, with Eqs. (17b) and (17c) used as middling and upper bound strength profiles in relation to the particular data shown in Fig. 8:

(17b)c_{\mathrm{u}}\left(\mathrm{k}\mathrm{P}\mathrm{a}\right)=\mathrm{22}+\mathrm{2.7}d,

(17c)c_{\mathrm{u}}\left(\mathrm{k}\mathrm{P}\mathrm{a}\right)=\mathrm{28}+\mathrm{3.7}d.

According to Wang et al. [41] soils in the third and fourth layer have c_u values ranging from around 25 to 40 kPa with a representative SPT N-value of 2‒3 in the case of the third layer and 1-2 in the case of the fourth layer. Hara et al. [51] give a correlation for c_u with the SPT blow count for a database of cohesive soils from Japan:

(18)

where N₆₀ is the SPT blowcount. Using equation 18, for N₆₀ varying from 1 to 3 (the range of values for layers 3 and 4), a c_u range of 29 to 64 kPa would be expected. Attributing these values to clays between 4 and 18 m depth, typical for these two layers in Shanghai (see borehole data in Appendix B), it will be seen that this range of c_u values matches the region in Fig. 8 lying between Eqs. (17a) and (17b).

Stroud [52] showed that the c_u/N₆₀ ratio for a collection of British soils (mainly stiff clays) was related to the plasticity index (I_p). Vardanega & Bolton [18] fitted Eq. (19) to Stroud’s database:

(19)c_{\mathrm{u}}=\mathrm{10}\left(N_{\mathrm{60}}\right){\left(I_{\mathrm{p}}\right)}^{-\mathrm{0.22}}\hspace{0.17em}\mathrm{k}\mathrm{P}\mathrm{a}

Figure 9 shows a comparison of Eqs. (18) and (19) demonstrating that Eq. (18) predicts higher strengths than Eq. (19) especially at low N₆₀ values.

A sequence of isotropically consolidated undrained compression and extension tests on samples cored from intact block samples taken from Shanghai clay layers 3 or 4 at 8 m depth was conducted at Hong Kong University of Science and Technology (HKUST). Three samples were cored and mounted in stress-path controlled triaxial cells, and then isotropically consolidated to 100, 200 and 400 kPa. The samples were then sheared to failure at constant volume, at an axial strain rate of 4.5%/hour. Figures 10(a) and (b) show the stress paths and the stress-strain curves, respectively. The tested clay was reported to have a plastic limit of 25%, a liquid limit of 51% and an initial water content of 47% (Li, 2011 pers. comm.). The critical state stress ratio (in compression) is found to be 1.25, which is relatively high for clays but consistent with the relatively low plasticity index of 15% ‒ 27% for layer 3, and 10% to 24% for layer 4 [3] as well as the low range of I_p values for the Yishan Road site (as shown on Fig. 7). Figure 11 shows these data fitted with Eq. (7) for the stress strain behavior of Shanghai clays in the moderate strain range (mobilizing 0.2c_u up to 0.8c_u). The computed values of b and γ_M=2 are given in Table 4; they closely conform to the values reported earlier for normally consolidated kaolin which can be taken from Eqs. (9) and (10) for OCR = 1.

7 Conventional design charts

Figure 12 shows that the use of the excavation depth alone to predict the maximum wall bulge w_max of the selected Shanghai excavations results in a factor 10 scatter. Clough et al. [53] proposed an empirical procedure for estimating the proportional maximum lateral wall movement w_max/H due to excavation in clay in terms of the factor of safety F against base heave (ignoring the wall) and system stiffness η defined (ignoring the soil) by Eq. (20):

(20)\eta ={\displaystyle \frac{EI}{{\gamma }_w{s}^{\mathrm{4}}}},

where EI is the flexural rigidity per unit width of the retaining wall, γ_w is the unit weight of water and s the average spacing of the props. Figure 13 indicates that these additional dimensionless parameters make only a marginal improvement in organizing the data of wall bulge for the Shanghai database.

8 New design charts

A dedicated MSD analysis as described in Lam & Bolton [7] can be used to make site specific predictions of wall bulge. Here, however, MSD concepts will be used simply to derive dimensionless groups for the purposes of charting field monitoring data. The benefits will first be assessed using the Shanghai database described earlier. The new charts can then be used to assist decision-making prior to any detailed analysis that occurs in the later stages of the design process. In this regard, improvements will be demonstrated compared with earlier design charts suggested by Ref. [53–55].

New dimensionless groups

In order to address the size of the assumed MSD deformation mechanism, as shown in Fig. 2, the maximum clay depth C_max is added to the database in Appendix A. These data are obtained by mapping borehole logs in the Shanghai Information Geological System (SIGS) and comparing with the actual locations of the excavations. The statistics of the borehole analysis are given in Appendix B (Table 7). To develop new dimensionless groups, a representative value for the wavelength parameter λ needs to be defined. The maximum clay depth C_max will be used in the estimation of the average wavelength on the basis that walls are effectively fixed below the base of the clay, as indicated by Eq. (21):

(21){\lambda }_{\mathrm{a}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}}=C_{\max }-\mathrm{0.5}H.

Inspection of the database records shows that the mid-depth of most excavations (where the soil stress-strain properties are taken for MSD analysis) generally coincides with the third and fourth layers (as described in Ref. [1,41]), in Shanghai Clay. New dimensionless groups will thereby be derived, as follows.

According to Lam & Bolton [7] the wall bulging deflection (w_max) can be related to the average shear strain (γ_average) in the adjacent soil mass by Eq. (22):

(22)w_{\max }\approx {\displaystyle \frac{\lambda {\gamma }_{\mathrm{a}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}}}{\mathrm{2}}}.

Lam & Bolton [7] define a displacement factor ψ which is modified in this paper to ψ* using γM=2 as the deformation parameter. Rearranging Eq. (8) we get:

(23){\left({\displaystyle \frac{\mathrm{2}}{M}}\right)}^{\frac{\mathrm{1}}{b}}={\displaystyle \frac{\gamma }{{\gamma }_{{}_{M=\mathrm{2}}}}}={\psi }^{*}.

Rearranging Eq. (22) and substituting into Eq. (23), using γ_average = γ:

(24){\psi }^{*}={\displaystyle \frac{\mathrm{2}{w}_{\max }}{{\lambda }_{\mathrm{a}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}}{\gamma }_{{}_{M=\mathrm{2}}}}}={\left({\displaystyle \frac{\mathrm{2}}{M}}\right)}^{\frac{\mathrm{1}}{b}}.

The virtue of Eq. (24) is that it relates the maximum extent w_max of both wall bulging and ground subsidence to the average ground strains γ_average in the zone of interest, and in relation to the characteristic γ_M=2. For a given value of w_max, in a less compliant soil with a small value of γ_M=2, or in the case of a smaller depth of excavation so that λ_average is smaller, the displacement parameter ψ^* returned by Eq. (24) is larger: Small ground movements must be taken more seriously, because the mobilization factor M will be smaller. And, correspondingly, around deep excavations in soils that have a larger strain to failure, more ground movements can be tolerated before the soil will approach failure. The values chosen for the soil parameters should reflect the averages expected in the deformation mechanism. The depths of excavation in the database typically fall in the range 10 to 20 m, so the mid-points of the mechanisms will be taken to lie in clay layers 3 and 4, and to have an initial vertical effective stress in the range of 100 to 200 kPa. Accordingly, values of γ_M=2= 0.5% and b= 0.4 are chosen from Table 4 to characterize the soft clay. Given these assigned parameters and using Eq. (24) and the simple soil model (Eq. (8)), the limits of ψ^* values that can be sensibly computed using MSD range from 0.10 (at M = 5) to 3.24 (at M = 1.25) because equation 8 is validated by Vardanega & Bolton [18] in the range 1.25<M<5.

The virtue of Eq. (24) is that it relates the maximum extent w_max of both wall bulging and ground subsidence to the average ground strains γ_average in the zone of interest, and in relation to the characteristic γ_M=2. For a given value of w_max, in a less compliant soil with a small value of γ_M=2, or in the case of a smaller depth of excavation so that λ_average is smaller, the displacement parameter ψ^* returned by Eq. (24) is larger: Small ground movements must be taken more seriously, because the mobilization factor M will be smaller. And, correspondingly, around deep excavations in soils that have a larger strain to failure, more ground movements can be tolerated before the soil will approach failure. The values chosen for the soil parameters should reflect the averages expected in the deformation mechanism. The depths of excavation in the database typically fall in the range 10 to 20 m, so the mid-points of the mechanisms will be taken to lie in clay layers 3 and 4, and to have an initial vertical effective stress in the range of 100 to 200 kPa. Accordingly, values of γ_M=2= 0.5% and b= 0.4 are chosen from Table 4 to characterize the soft clay. Given these assigned parameters and using Eq. (24) and the simple soil model (Eq. (8)), the limits of ψ^* values that can be sensibly computed using MSD range from 0.10 (at M = 5) to 3.24 (at M = 1.25) because equation 8 is validated by Vardanega & Bolton [18] in the range 1.25<M<5.

Figure 14 shows the modified displacement factor ψ^* plotted against system stiffness η as defined in Eq. (20). Recalling that the present analysis concerns the bulging of an earth retaining wall below the level of its lowest support (Fig. 2(c)) the use of prop spacing s to define a non-dimensional parameter η for system stiffness is open to criticism. It is the structural span, here taken to be wavelength λ, that should be taken to determine the flexural stiffness of the unsupported section of the wall. Accordingly we define a new system stiffness parameter η^* as given by Eq. (25):

(25){\eta }^{*}={\displaystyle \frac{EI}{{\gamma }_{{}_w}{\lambda }^{\mathrm{4}}}}.

Figure 15 shows ψ^* plotted against η^*. Comparing Fig. 13 to Fig. 14 and then Fig. 15 we can see a steady improvement in the separation between the subsets of the data representing shallow (H/C_max<0.33) and deep(0.33<H/C_max<0.67) excavations. In the preferred representation of Fig. 15 it is made evident both that designers tend to specify stiffer wall systems for deeper excavations and that, for a given system stiffness η^*, deeper excavations result in greater displacement factors ψ^*. Figure 16 shows the same field data re-plotted with ψ^* converted through Eq. (24) to an estimated M factor. This suggests that none of the retaining walls have fully mobilized the undrained soil strength of the soil; indeed, most are performing at quite low levels of strength mobilization. There is co-variance on Fig. 16 in the sense that the wavelength appears on both axes but since correlation analysis is not attempted between M and η^* this remains a valid normalization of the dataset.

8.1 MSD Analysis

Lam & Bolton [7] compared a sequential MSD calculation with a set of Finite Element Analyses (FEA) described in Jen [56] that used corresponding non-linear shear stress-strain relations for the soil. The magnitude of wall bulging was underestimated by a factor of about 1.2, but the maximum curvature was actually overestimated albeit by only a factor of 1.1. MSD also overestimated the magnitude of maximum subsidence by a factor of about 1.3, and overestimated green-field ground curvature by an even larger margin of factor of two. It seems, therefore, that MSD analyses might offer a promising basis for conservative design and quick decision-making.

The MSD bulge appeared significantly deeper than the FEA bulge, however, which must mainly be due to the assumption of a deep point of fixity from which the sinusoidal wavelength λ is later determined. This presents a particular problem in relatively deep soft ground. It would be desirable to characterize the deformed shape of the retaining wall in terms of its flexibility relative to the soil, and its length relative to the depth of the excavation. Further work could be undertaken to improve the matching of flexible wall deformation profiles in MSD by comparison to detailed FEA studies. In the mean time, caution is advised in allocating vertical steel reinforcement following an MSD analysis of wall bending moments.

Of course, the objectivity and usefulness of new design tools can only be assessed properly in relation to real field data. Lam & Bolton [7] compared MSD predictions of maximum wall movement with observations of excavations in soft clays beneath nine cities world-wide, reported by different groups of authors. For each soft clay, these original authors had published a shear stress-strain curve, and these were idealized as parabolas in the moderate strain region (up to 80% mobilization of undrained shear strength) for use in MSD analyses. By using this very minimal amount of soil data, and by estimating the depth of wall base fixity appropriate to each of the 110 sites, together with the published information about wall stiffness and supports, site-specific MSD analyses were shown to match maximum wall bulging within a factor of 1.3 in 90% of the cases. This seemed to confirm the usefulness of the method. An improved understanding of the significance of soil variability would follow an extended parametric analysis with variations in the vertical profiles of undrained strength c_u and mobilization strain γ_M=2, and site-specific analyses should ideally be furnished with soil test data accordingly.

Although sixty-seven sites in Shanghai were included in the study by Lam & Bolton [7], the larger database of Xu [1] reported in Wang et al. [41] is used in this paper. This was felt to be particularly important because of the initial difficulty of objectively assigning an elevation of base fixity in such a deep alluvial deposit. Clear rules are now established.

A site-specific MSD analysis (or FEA) should ideally include a soil profile obtained by borings, a strength profile such as by cone penetration testing, and the results of relevant tests conducted on good-quality cores so that representative stress-strain soil behavior can be assessed. Both compression and extension tests should ideally be carried out from K_o conditions on samples from a variety of horizons. It is recognized, however, that this ideal may not be available to design engineers in practice. It therefore becomes of interest to explore the potential consequences of adopting a simpler approach, albeit one that will inevitably lead to additional prediction errors and to some scatter in field data when case studies are amalgamated.

Parametric analyses are therefore conducted by MSD to study the influences of key parameters on an excavation that is broadly representative of the works in Shanghai listed in Appendix A: a “wide” excavation is considered and the ultimate proportional depth H/C_max is taken to vary between 0.1 and 0.8. Stages of excavation and propping were taken at intervals of ∆H = 3 m. Flexural stiffnesses were selected for the retaining walls within the range EI = 10⁴ to 10⁷ kNm²/m. Previous MSD analyses accompanying the field data published by Lam & Bolton [7] focused on the influence of the relative depth of excavation (H/C), the strain to mobilize peak strength, and the system stiffness η. In the current work we refined the soil strength mobilization model in Eq. (8) following Vardanega & Bolton [18], and use representative values from Table 4 to select shear strain γ_M=2 = 0.5% required for 50% strength mobilization, and a power curve with an index b = 0.4 to replace the previous parabola with b = 0.5 that was assumed in Bolton et al. [6] and Lam & Bolton [7]. The system stiffness η^* from equation 25 is used to relate better to wall bulging below the lowest level of propping by non-dimensionalizing with the average wavelength given by Eq. (21). Finally, three soil strength profiles are used following Eqs. (17a), (17b) and (17c), as given in Fig. 8. The soil unit weight is regarded as constant in this parametric survey at 17.5 kN/m³.The results of sequential MSD analyses using the inputs and assumptions outlined above are shown on Fig. 17 as design curves. From the simulation results, it can be seen that the choice of the c_u-profile has a major effect on the computed modified displacement factor, an insight that goes beyond the findings of Lam & Bolton [7] in relation to the effects of soil deformability for a given soil strength profile. The lower bound strength envelope used in the production of Fig. 17(a) results in ground movements around relatively modest excavations (H/C_max≥0.35) being extremely sensitive to system stiffness. The strength of this rather weak ground is almost fully mobilized in such cases and ground displacements are restrained principally by the wall retention system. However, for the upper bound strength profile in Fig. 17(c) the sensitivity of ground and wall bulging displacements to the wall system stiffness is much reduced except for the deepest excavations (H/C_max≥0.8). Excavation-induced movements are then limited not so much by soil strength as by soil stiffness. Figure 17 publishes in a design chart, for the first time, the relative influences on wall and ground displacements w_max of the profile of soil strength c_u, the non-linear soil deformability normalized by mobilization strain γ_M=2, the depth of the excavation H in relation to the depth of soft clay C_max, and the wall stiffness EI.

Figure 18 shows that the central soil profile line from the published strength data offers an adequate upper bound to the datasets of field observations. However, it is also evident that many of the icons representing more flexible retaining walls fall below the MSD design curves. This may be due to the assumption in the current MSD analyses of a full-depth mechanism, with λ defined in Fig. 2(c) as the distance from the bottom prop to the base of clay, no matter how deep the wall, or how flexible. It is known, however, that more flexible retaining walls display larger localized deformations: see Fig. 19 which is taken from Potts and Day [57]. If, by having ignored this flexibility effect, λ has effectively been overestimated by a factor of 2 for example, η^* should increase by a factor of 16 and ψ^* should double. Such a correction would tend to shift the data of more flexible walls into the region described by the MSD analyses.

8.2 Link to structural performance

Having established simplified predictions of ground movement, it is possible to produce outline designs of earth retention schemes so as to satisfy structural criteria of distortion and damage. For example, consider the requirement to avoid the creation of plastic hinges in the retaining wall itself, due to bulging beneath the lowest level of lateral bracing. It can be shown that the maximum bending strain induced in a wall of thickness t bulging w_max over sinusoidal wavelength λ is:

(26){ϵ}_{\max }={\mathrm{\pi }}^{\mathrm{2}}{\displaystyle \frac{w_{\max }t}{{\lambda }^{\mathrm{2}}}},

on the simplifying assumption that the neutral axis of bending remains at the middle of the wall. This maximum strain is notionally attained at three locations: just below the bottom prop, just above the hard layer which fixes the bottom of the wall, and half-way between these two elevations.

Structural engineers must assure themselves that such a bulge could not lead to the formation of plastic hinges. Two strain criteria might be considered in relation to Eq. (26). The longitudinal reinforcing steel will yield in tension at about ε_steel≈ 1.5 × 10^-3, while concrete may crush in compression at about ε_concrete≈ 4.0 × 10^-3: see, for example, Park & Gamble [58].The first of these might be regarded as a serviceability criterion, after which unacceptable tensile cracking may occur, threatening water ingress which could compromise the long-term integrity of the reinforcement. Equation (27) then permits the designer to specify a just-tolerable degree of bulging:

(27){\left({\displaystyle \frac{w_{\max }}{\lambda }}\right)}_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}={\displaystyle \frac{\lambda {ϵ}_{\max }}{{\mathrm{\pi }}^{\mathrm{2}}t}}.

If, for example, it were decided to restrict steel strains to 1.5 × 10^-3 in a 0.8 m thick diaphragm wall that is free to bulge over an average wavelength of 20 m, the critical distortion w_max/λ would be about 3.75 × 10^-3, corresponding to a bulge of w_max= 75 mm. If the designer was able to guarantee both the short-term and long-term performance of the retaining wall with larger strains in the concrete, a correspondingly larger permitted bulge could equally be deduced using Eq. (27).

Damage due to soil subsidence must also be controlled in any structures and services neighbouring the excavation, of course. The theoretical models invoked to cover such deformations are the bending of load-bearing walls treated as beams, and the shearing of framed wall panels, elaborated initially by Burland & Wroth [59]. Building damage due to excavation was subsequently examined by Boscardin & Cording [60]. Boone [61] created a convenient bibliography with a summary of the various parameters that control damage, and he makes the case for determining structural damage in relation to the relative settlement ∆/L defined as the deviation ∆ from an initially straight chord-line of length L drawn through the structure. The key damage criterion in most structures is the tensile strain and cracking induced in plaster panels or, more seriously, in masonry and concrete walls. Hogging deviations are generally found to be more significant than sagging, because walls are relatively free to crack at the roof-line compared with the base which is generally restrained by the friction created by its self-weight (except for those walls that are free to slide over a damp-proof course). The worst case for design is reflected in a bending analysis that permits the neutral axis to shift fully to the compressive side, to the base of a wall in hogging, or to the top of a wall in sagging, so that tensile strains are generated by the full wall height.

Boscardin & Cording [60] went on to study the additional influence of lateral ground movements, but here we will restrict ourselves to vertical subsidence effects, considering that the bracing system will have restricted the lateral movements of the retained ground and shallow foundations resting on it. Table 5 sets out distortion limits accordingly, following Boscardin & Cording [60], and relating them to the sinusoidal subsidence profile assumed in Fig. 2 through the sketch given in Fig. 20. If the subsidence were truly sinusoidal, two side zones of width λ/4 would subject a building to hogging, whereas a central zone of width λ/2 would create sagging. Furthermore, it can be seen that the equivalent values of ∆/L would be about (0.105 w_max)/(0.25λ) = 0.42 w_max/λ in the hogging zone but w_max/λ in the sagging zone. Although the sagging zone notionally suffers 2.4 times more relative settlement, therefore, the hogging zone is regarded as converting relative settlement into damage by cracking at twice the rate, because of the supposed shift in neutral axis. Within the margin of uncertainty afforded by current literature, therefore, the excavation-induced damage deduced in Table 5 in relation to the hogging of load-bearing walls will also apply to the wider region of sagging.

9 Discussion

9.1 Role of numerical analysis

Caution must be exercised in applying the results of Table 5 in relation to the assumed settlement trough of Fig. 20. As discussed above, a full stage-by-stage analysis would produce a more realistic settlement trough. Nevertheless, the study by Lam & Bolton [7] suggested that MSD using the mechanism of Fig. 2 may conservatively overestimate the distortion of structures on the retained ground, by underestimating the width of the zone affected. The prime objective of this paper is to present a dimensionally consistent account of ground movements due to excavation in relation to structural damage that might occur, either to the earth retaining wall itself or to buildings nearby. This enables a design engineer to estimate, at a glance, the ground movements that may occur and the damage that may result to structures that are flexible compared to the ground, so that they do not alter the green field subsidence trough. Furthermore, it links these projected ground movements with a strength-reduction factor M consistent with the magnitude of soil strains.

If greater accuracy were required for design purposes, the engineer is advised to apply MSD stage by stage to the projected construction sequence. As indicated by Lam & Bolton [7], the progressive reduction in wavelength λ stage by stage, as props are fixed at lower levels, results in a succession of sinusoidal displacement increments which accumulate to create a wall profile with its maximum bulge below the average mid-depth, and a cumulative subsidence trough with its maximum closer to the wall. These more realistic non-sinusoidal subsidence profiles can then be re-analyzed for sagging and hogging following Section 8.3. However, if the degree of structural distortion and damage were required with greater accuracy, a full finite element analysis should be conducted with appropriate non-linear stiffnesses applied both to elements of the structure and to the soils. Some old masonry structures, and some modern multi-story framed structures, will be sufficiently stiff that they respond to subsidence almost as rigid bodies, engendering tilt rather than distortion: see, for example, Goh & Mair [62].

9.2 Advances on previous construction charts

There is a much clearer segregation of field data when presented as normalized displacement ratio ψ^* versus modified system stiffness η^* in Fig. 15, compared with the well-known charts of Clough et al. [53]. Confirming the earlier work of Lam & Bolton [7], it is clear that proportional excavation depth H/C_max is a very significant determinant of ground movements. The influence of variations in the soil strength profile is also significant and this re-emphasizes the need for a thorough ground investigation prior to the use of the MSD method. Finally, larger values of the modified system stiffness are seen to lead to reduced ground movements, but a more economical approach to ground movement control may be to conduct deep soil stabilization, such as by cement soil-mixing, to provide “propping” between the diaphragm walls. Therefore, studies into the various construction options to limit excessive ground movements should be investigated further along with the influence of ground improvement on the values of λ.

9.3 Uses of the new construction charts

The new charts enable an engineer to plot inclinometer data from an active construction site and compare it immediately with previous ground movements from other sites in Shanghai. It allows a design authority, a project insurer, or an engineer acting for a neighboring facility, to press for achievable limits to be placed on ground movements due to a new excavation. But it also allows the designer of the excavation to argue quantitatively for reasonable ground movements to be permitted, which may ultimately reduce the common tendency for over-conservatism in the design of some earth retention systems. It is notable that Figs. 15 and 16 suggest that many retention schemes in Shanghai have been constructed with a large safety factor on soil strength, especially those relating to shallower excavations. Now this may be perfectly in keeping with the necessity to keep neighboring ground subsidence to a small enough magnitude, considering the damage criteria set out in Table 5. But it also suggests that where such excavation is to be undertaken in less congested areas where sensitive facilities are absent from the zone of influence, fewer propping levels, or thinner walls, may be acceptable.

9.4 Proposed changes in the approach to design and construction of deep excavations

Boone [63] advocated three strands of Research & Development effort so that decision-making could be improved:

1) Sufficient testing of specific soil deposits to characterize uncertainty in their properties.

2) Sufficient predictions compared to field case studies to define uncertainty in analysis.

3) Sufficient case histories with construction details to characterize uncertainty in workmanship.

This paper has shown that case records and site data can be the key to developing well-calibrated design guidance for major construction areas in cities around the world. A lot of construction is currently taking place in the Shanghai Clay deposit, and further characterization studies need to be conducted so that both numerical modelling and MSD-style analyses can be performed by design engineers. A larger database with appropriate site specific soil data will allow the scatter on design charts (Figs. 14‒16) to be reduced. As this occurs then more objective and economical design rules for construction in Shanghai can be developed based on actual data and parameter sensitivity studies.

In other parts of the world, geotechnical engineers have attempted to codify design by applying partial factors, such as in Eurocode 7 [64], but without reference either to the deformation mechanisms involved or to any database of soil deformability or field monitoring data. Eurocode 7 [64] also requires some validation of serviceability, but no framework is suggested within which ground displacements could be assessed. The authors suggest that the performance-based approach taken in this paper offers a useful basis for future development.

Tan and Shirlaw [65] made the following comment in their review, summarised as follows:

In view of the uncertainties in ground conditions, analytical methods, and construction procedures, engineers generally follow a wise course; they build a retaining and bracing structure so strong that the stiffness of soil contributes little to the overall stiffness of the soil-structure system.

The analysis presented in this paper has offered a quite different perspective. The strength and stiffness of the soil has been shown to have a significant impact on the observed wall bulging. And extraordinary stiffness is required of a retention system for deep excavations in soft clay if that system alone is to be relied upon to limit the magnitude of associated structural displacements to values consistent with serviceability.

10 Summary

This paper has explained the development of improved charts that are intended to provide guidance for engineers involved in the design and construction of deep excavations in Shanghai Clay. The new charts make use of the principles of MSD and the power curve characterization of shear stress-strain curves for clays. In addition to the previously reported data of monitoring from numerous sites in Shanghai, curved relationships are given for “typical” excavations in “typical” ground conditions, with normalized ground displacements plotted versus normalized system stiffness for different depths of excavation and different soil strength profiles. The methodology and references given in this development give the reader the ability to extend the method to any desired situation by running sequential MSD analyses with appropriate sets of parameters.

In addition, the mechanisms of structural damage arising from excavations are reviewed and damage criteria are established in relation to the new definitions of normalized ground displacement. The assessment is based on the wall bulging observed below the lowest level of structural support, and the corresponding subsidence trough which is found at the retained soil surface. Proper limitations are accordingly derived for permissible ground movements.

The aforementioned analyses and design charts cannot take the place of a site-specific MSD analysis which is required if the influence of construction sequence is to be approximately allowed for, or of an FEA which is required if structural stiffness is to be fully included in an assessment of damage due to excavation. However, FEA is time consuming and expensive, more so if the engineer has not got a clear understanding of the potential problems that must be solved. It is the Authors’ intention that the paper will prove useful in that respect also. The new design charts give immediate guidance on sizing in relation to performance criteria, prior to any subsequent refinement.

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