Direct Approach for Designing an Excavation Support System to Limit Ground Movements L. Sebastian Bryson1 and David G. Zapata-Medina2 1
Department of Civil Engineering, 161 Raymond Bldg, University of Kentucky, Lexington, Kentucky 40506; PH (859) 257-3247; FAX (859) 257-4404; email:
[email protected] 2 Department of Civil and Environmental Engineering; Northwestern University; 2145 Sheridan Road; Evanston, IL 60208 ABSTRACT Traditionally, excavation support systems are designed solely on the basis of satisfying limit equilibrium, using apparent earth pressure diagrams. Using this approach, the support system design becomes a function of the maximum anticipated earth pressure and is governed by overall structural stability as opposed to maximum allowable horizontal or vertical deformation. This approach produces a support system that is adequate with regards to preventing structural failure, but may result in excessive wall deformations and ground movements. This paper presents a design methodology that facilitates the sizing of all components of the excavation support system in such a way that limits the maximum lateral and vertical excavation-induced deformations. Based on the fundamental approach of the presented design methodology, structural and basal stability is guaranteed. INTRODUCTION Conventionally, excavation support systems are designed based on structural limit equilibrium. Although these approaches will prevent structural failure of the support wall, they may result in excessive wall deformations and ground movements. Existing design methods that do consider deformations, relate lateral wall movements to excavation support system stiffness and basal stability. However, these design methods were developed using a limited number of wall types and configurations. These methods do not include considerations for differing excavation support systems, whose performance is highly dependent on construction techniques; the three-dimensional (3D) effects of the wall construction and the excavation process;
the effects of different support types; the influences of the excavation geometry and sequencing; or complex site geology. This paper presents a design methodology that facilitates the sizing of all components of the excavation support system in such a way that limits the maximum lateral and vertical excavation-induced deformations. The design methodology is a semi-empirical approach that was developed from observations of several case histories reported worldwide and a fully 3D finite element analysis that realistically modeled the excavation geometry, the excavation support system, and the excavation activities. Based on the fundamental approach of the presented design methodology, structural and basal stability is automatically achieved. EXCAVATION-INDUCED GROUND MOVEMENTS As was previous mentioned, current design methodologies satisfy structural stability first and then check deformation conditions. This approach does not guarantee that excavation-induced ground movements will not cause damage to the adjacent infrastructure. Thus, the most efficient approach for designing excavation supports systems is to design the systems such that the excavation activities will not cause damage to the adjacent infrastructure. Researchers (Son and Cording, 2005; Kotheimer and Bryson, 2009) have linked damage in buildings adjacent to excavations, to vertical ground movements. These approaches typically relate semiempirical damage criteria to building distortions. These excavation-induced building distortions are then related to changes in ground slope. Changes in ground slope can be predicted via settlement profiles, given the maximum settlement value. Ground movements adjacent to deep excavations occur in response to lateral deflections of the excavation support system. In soft clay, these movements are influenced by the stiffness of the support system, the soil and groundwater conditions, the earth and porewater pressures, and the construction procedures. Clough et al. (1989) presented a design chart for clays that allows the user to estimate lateral 4 movements in terms of effective system stiffness ( EI γ w havg ) and the factor of
safety against basal heave. The EI is the wall flexural stiffness per horizontal unit of length ( E = the modulus of elasticity of the wall element and I = the moment of inertia per length of wall), h = the average vertical spacing between supports, and γ w = the unit weight of water. The factor of safety against basal heave used in the Clough et al. (1989) work is that given by Terzaghi (1943). The Clough et al. (1989) chart was created from parametric studies using plane strain finite element analyses of sheet piles and slurry walls. A link between excavation-induced settlement and lateral wall deformations is made by evaluating case data. Researchers (Clough et al, 1989; Hsieh and Ou, 1998)
have reported that the maximum ground settlement adjacent to deep excavations is directly related to the maximum lateral displacement of the support system. Finno et al. (2002) found that for undrained unloading conditions in saturated soils the lateral deformation envelop closely matched that of the ground settlement. For this study, a definite relationship between maximum settlement and maximum lateral deformation was sought for input into the proposed design methdology. Zapata (2007) investigated the excavation-related ground movements by evaluating data from several case histories. A partial listing of the case history information is given in Table 1. Additional detail of the case history data can be found in Zapata (2007). Table 1. Partial case history database. Soil Type Reference Wall Type H [m] He [m] δH(max) [mm] δV(max) [mm] Stiff Clay Ng (1992) Diaph. 16.3 9.57 18 10 Burland and Hancock (1977) Diaph. 30 18.5 24 20 Hsieh and Ou (1998) Diaph. 33 20 125 78 Whittle et al. (1993) Diaph. 25.6 20.2 54 45 Becker and Haley (1990) Diaph. 26 20 47 102 Medium Ou et al. (1998) Diaph. 35 19.7 107 77 Clay Finno and Roboski (2005) Sheet 19 12.8 63 74 Hsieh and Ou (1998) Diaph. 31 18.4 63 43 Miyoshi (1977) Steel-Conc. 32 17 177 152 Finno et al. (1989) Sheet 19.2 12.2 173 256 NGI (1962) Sheet 16 11 224 200 Wang et al. (2005) Diaph. 38 20.6 48 31 Peck (1969) Sheet 14 8.5 229 210 Soft Clay Finno et al. (2002) Secant 18.3 12.2 38 27 Hu et al. (2003) Diaph. 21 11.5 15 7 Baker et al. (1987) Diaph. 18.3 8.5 37 37 Koutsoftas et al. (2000) Soldier 41 13.1 48 30 H=Height of wall; He=Depth of excavation; δH(max)=maximum lateral deformation; δV(max)=maximum settlement
The case data presented in Table 1 is divided into stiff, medium, and soft clay. These distinctions are made on the basis of undrained shear strength found at the bottom of the excavations. Soft clay is defined as clay deposits with undrained shear strengths between 0 kPa to 25 kPa. Medium clay is defined as undrained shear strengths between 25 kPa and 50 kPa, and stiff clay are deposits with undrained shear strengths greater than 50 kPa. Figure 1 shows the maximum lateral movements as a function of the maximum vertical movements for the case histories. The purpose of Figure 1 is to provide an estimation of the maximum lateral deformation based on an inputted value of the maximum settlement. The maximum lateral deformation can subsequently be used to estimate the required support wall stiffness. This approach is considered appropriate for design of support systems in urban areas because presumably the limiting criteria for design will be the maximum settlement of the ground behind the support wall. In the Figure 1, the maximum lateral deformations are normalized with respect to the depth of wall and the maximum vertical movements are normalized with respect
to the depth of the excavation. This approach follows the implications of data presented by Bryson and Zapata (2007). Their work showed that lateral deformations tended to be more influenced by the physical characteristics of the support system (i.e. length of wall, wall stiffness, etc.), while the vertical deformations tended to be more influenced by the soil behavior. Subsequently, the soil behavior at deep excavations is typically influenced by the depth of excavation. 3 Case History Data
δ H(max)/H (%)
2.5 2
y = 0.5915x + 0.042 R² = 0.9195
1.5 1 0.5 0 0
0.5
1
1.5
2
2.5
3
δ V(max)/He (%) FIGURE 1. CORRELATIONS BETWEEN MAXIMUM HORIZONTAL DEFORMATIONS AND MAXIMUM VERTICAL DEFORMATIONS.
From Figure 1, it is seen that an expression relating the maximum horizontal and vertical deformations can be developed by plotting a linear regression line through the case data. The expression is given by:
δ H (max ) H
δ V (max ) + 0.042 = 0.591 He
(1)
It is noted that both the normalized maximum horizontal deformation and the normalized maximum vertical deformation in Equation 1 are in percent. BASAL STABILITY Basal stability is an important parameter in the analysis and design of excavation support systems in soft soils. Lateral movements of an excavation support system tend to increase dramatically as a result of plastic yielding in the soil beneath and surrounding the excavation. The extent of the plastic yielding can be quantified with the use a factor of safety against basal heave. Basal stability analyses can be carried out using limit equilibrium methods. Limit equilibrium methods assume two-dimensional conditions and are based on bearing capacity (Terzaghi, 1943). The most common bearing capacity methods were
developed before the introduction of stiffer insitu wall systems such as diaphragm walls and secant piles. As a result, these methods ignore the effect of the depth of the wall penetration below the base of excavation, soil anisotropy, and other factors. Ukritchon et al. (2003) presented a modified version of the Terzaghi (1943) factor of safety against basal heave that included the effects of the wall embedment. Figure 2 shows the excavation geometry used in the modification. The expression for the factor of safety is given by: FS ( heave ) =
s u N c + 2 s u (H B ) + 2 s u (D B ) γ sHe
(2)
2 su (H B ) represent the shear capacity and the shear
where the terms su N c and
resistance of the soil mass, respectively and 2 su (D B ) represents the adhesion along the inside faces of the wall assuming a rough surface. s
e
j
B
B B'
He H
g
f
45o
45o
T h
i Failure surface
D 45
o
45
o
Failure surface
(a)
(b)
FIGURE 2. FACTOR OF SAFETY AGAINST BOTTOM HEAVE: (A) WITHOUT WALL EMBEDMENT; AND (B) WITH WALL EMBEDMENT.
Note that Terzaghi (1943) used N c = 5.7 , which originally assumed resistance at the interface of the base of the footing and the soil (i.e., perfectly rough foundation). For basal calculations, this implies some restraint at the base of the excavation. However, it is assumed that the base of the excavation is a restraint-free surface. Thus, N c = 5.14 (i.e., perfectly smooth footing) is more appropriate. RELATIVE STIFFNESS RATIO As was previously discussed, lateral deformation is a performance parameter of the excavation support system and has traditionally been shown to be a function of the factor of safety against basal heave and the effective system stiffness. These relations are shown in the chart developed by Clough et al. (1989). Unfortunately, the chart was developed using a limited number of wall types and configurations. Furthermore, the chart does not include the 3D nature of the excavation.
To address the deficiencies of the Clough et al. (1989) chart, a new relative stiffness ratio is presented. This new ratio was formulated using dimensional analysis of the excavation support system stiffness problem. The relative stiffness ratio is given as
R=
E s sh sv H γ s H e E I su
(3)
where R = relative stiffness ratio; Es = reference secant modulus of the soil at the 50 percent stress level; E = elastic modulus of the wall; I = moment of inertia per unit length of the wall; sh = average horizontal support spacing; sv = average vertical support spacing; H = height of the wall; He = excavation depth; γ s = average unit weight of the soil; and su = undrained shear strength of the soil at the bottom of the excavation. In Equation 3, the terms Es E , S H SV H I , and γ s H e su represent the relative stiffness resistance, the relative bending resistance, and the excavation stability number, respectively. The relative stiffness ratio was compared with data obtained from a 3D finite element parametric study. The parametric study consisted of a 3D system model and 3D ground movements. Figure 3 presents maximum lateral wall displacements obtained from the parametric study versus the relative stiffness ratio, R, for different factors of safety against basal heave. 2.5 FS = 0.5
δH(max) / H (%)
2.0
1.5 FS = 0.75 1.0
FS = 1.0 FS = 1.5
0.5
FS = 2.0 FS = 3.0 0.0 0.01
0.1
Rigid
1
10
Relative Stiffness Ratio, R
100
1000 Flexible
FIGURE 3. RELATIVE STIFFNESS RATIO.
In the figure, the lateral movements are normalized with respect to the height of the wall, and the factors of safety are calculated using Equation 2, which includes the
effects of the wall embedment depth below the base of excavation. For details of the parametric study and the development of Figure 3, the reader is referred to Zapata (2007). Figure 3 allows the designer to predict maximum lateral wall movements for deep excavations in cohesive soils based on simple soil data and excavation geometry. These data can then be used to predict maximum settlement using Equation 1. ELEMENTS OF EXCAVATION SUPPORT SYSTEM DESIGN The proposed direct design methodology is illustrated in the flow chart presented in Figure 4. The proposed methodology allows the designer to size all the elements of the excavation support system, given the maximum allowable settlement of infrastructure adjacent to the excavation. The proposed methodology also allows the designer to predict final ground movements (horizontal and vertical), given data about soil and support system. Start
1
2
Define soil properties and excavation geometry
Calculate the factor of safety against basal heave, FS
Calculate the maximum wall bending moment
Es = reference secant modulus su = undrained shear strength γs = average unit weight φ' = effective friction angle He = excavation depth B = excavation width L = excavation length
Define maximum admissible ground movements [δV(max) and δH(max)] Determine the wall design earth pressure Calculate the required wall embedment depth 1
Check that:
No
Is FS acceptable?
Yes Obtain the required Relative Stiffness Ratio, R Calculate the required wall stiffness and support spacing (EI, SH , SV )req Find sheet pile wall or diaphragm wall thickness which: EIwall ≥ EIreq
2
0.9 ×Mn ≥ Mmax Reinforced Concrete
swall ≥ sreq Sheet pile max sreq = M σ all
σall = allowable flexural stress of the material
Determine the apparent earth pressure envelope Design struts Design wales
End
FIGURE 4. FLOW CHART FOR DESIGNING EXCAVATION SUPPORT SYSTEMS USING THE DIRECT APPROACH.
CONCLUSIONS This paper presents a deformation-based design methodology based on both observation of case histories and fully 3D finite element analyses that realistically model the excavation support system and the excavation activities. This semiempirical approach allows for the design of excavation support systems based on deformation criteria including the influences of the inherent 3D behavior of the
excavation support system and the associated excavation. The proposed approach will also allow the designer to predict final ground movements, given data about soil and support system or size all the elements of the excavation support system, given the allowable soil distortion of adjacent structures. It is important to mention that the new design procedures proposed in this investigation is only applicable to clays similar to those studied and must be verified and validated with real case history data. ACKNOWLEDGEMENTS The material presented in this paper is based upon work supported by the National Science Foundation under grant No. CMS 06-50911, under program director Dr. Rick Fragaszy. This financial support was greatly appreciated. REFERENCES Bryson, L.S. and Zapata-Medina, D.G. (2007). “Physical Modeling of Supported Excavations,” Proceedings of Geo-Denver, Denver, CO, 18-21 February 2007. Clough, G. W., Smith, E. M., and Sweeney, B. P. (1989). “Movement Control of Excavation Support Systems by Iterative Design.” Current Principles and Practices, Foundation Engineering Congress, ASCE, Vol. 2, pp. 869-884. Finno, R. J., Bryson, L. S., and Calvello, M. (2002) “Performance of a Stiff Support System in Soft Clay.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 128(8), pp. 660-671. Hsieh, P-G. and Ou, C-Y. (1998). “Shape of Ground Surface Settlement Profiles Caused by Excavation.” Canadian Geotechnical Journal, Vol. 35(6), pp. 10041017. Kotheimer, M.J. and Bryson, L.S. (2009). “Damage Approximation Method for Excavation-Induced Damage to Adjacent Buildings,” International Foundations Congress and Equipment Expo (IFCEE09), Orlando, FL, 15-19 March, 8 pp. Son, M. and Cording, E. J. (2005). “Estimation of Building Damage Due to Excavation-Induced Ground Movements,” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 131(2), pp. 162-177. Terzaghi, K. (1943). Theoretical Soil Mechanics, John Wiley and Sons, New York. Ukritchon, B., Whittle, A. J., and Sloan, S. W. (2003) “Undrained Stability of Braced Excavations in Clay.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 129(8), pp. 738-755. Zapata. D.G. (2007), “Semi-Empirical Method for Designing Excavation Support Systems Based on Deformation Control.” Master Thesis, University of Kentucky, Lexington, KY.
