PILE SETTLEMENT ZONES ABOVE AND AROUND TUNNELLING OPERATIONS

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1 PILE SETTLEMENT ZONES ABOVE AND AROUND TUNNELLING OPERATIONS H.G. Poulos Coffey Geosciences Pty Ltd. ABSTRACT This paper describes briefly the method of analysis of the response of a pile to tunnelling-induced movements, including estimation of the loss of axial capacity. The various pile settlement zones computed from this analysis are compared with those measured experimentally for tunnels in sand by Jacobsz et al. (21). Some theoretical differences are identified between the cases of tunnels in sand and in clay. Finally, for an example case of a structure over a tunnel, a comparison is made between the performance of three alternative foundation types, a piled foundation, a piled raft foundation and a raft foundation without piles. It is shown that the tunnelling induced movements have less influence on the latter two foundation types than on the fully piled foundation. 1 INTRODUCTION The trend towards increasing urban infrastructure development has resulted in a significant increase in tunnel construction. A side effect of such construction is that existing pile foundations supporting structures in the vicinity of the tunnels will be subjected to both vertical and lateral ground movements and will experience additional vertical and lateral forces and movements. In assessing the possibility of the tunnelling operations causing damage to existing structures, it is important to estimate the foundation movements, particularly the settlements and differential settlements. Various methods of estimating pile foundation settlements have been reported in the literature, including: The use of finite element numerical methods (e.g Mroueh and Sharour, 22; Surjadinata et al., 2); The use of boundary element numerical methods (e.g. Chen et al., 1999; Loganathan and Poulos, 1999); The use of centrifuge model tests (Jacobsz et al., 21). This paper summarizes the approach adopted in the second category, and then compares the computed pile settlement zones with those measured experimentally by Jacobsz et al. (21). Finally, for an example case of a structure over a tunnel, a comparison is made between the performance of three alternative foundation types, a piled foundation, a piled raft foundation and a raft foundation without piles. 2 SUMMARY OF NUMERICAL ANALYSIS METHOD The method of analysis adopted involves two stages: 1. The calculation of the free-field ground movements due to tunnelling; 2. The use of a soil-structure interaction analysis to compute the effects of the free-field ground movements on the response of a pile. The ground movements due to tunnelling have been estimated using the approximate closed-form solutions developed by Loganathan and Poulos (1998). The solutions are for two-dimensional deformations and thus give the ground movements at some distance behind the advancing tunnel face. These solutions, although based on linear elastic theory, have been found to provide good estimates of the surface and subsurface settlements and lateral movements around a bored tunnel (Loganathan and Poulos, 1999, 21; Loganathan et al., 2). They require an estimate of the ground loss due to tunnelling, as well as the geometric characteristics of the tunnel. For the estimation of pile axial response, the computer program PIES (Poulos, 1989) has been used. This program employs the boundary element method to compute the settlement and axial load distribution within a pile subjected to applied axial load and vertical ground movements. Non-linear pile response is modelled via the use of a hyperbolic model for the pile-soil interface and the imposition of limiting shaft and base stresses (ultimate skin friction and end bearing values) at the various elements into which the pile is divided. The applicability of this approach has been demonstrated by Poulos and Davis (198). Australian Geomechanics Vol 41 No 1 March 26 81

2 3 REDUCTION IN PILE CAPACITY DUE TO TUNNEL PROXIMITY An issue which requires consideration is the possible loss of pile capacity due to the presence of the tunnel. Figure 1 defines the generic problem being considered. The volume loss associated with the tunnel construction will lead to, in effect, a reduction in the pressure at the tunnel face and this will in turn lead to reductions in lateral and vertical stress within the soil. The reduction in average pressure, p, around a circular tunnel can be shown to be as follows: where G s = soil modulus around tunnel ε = volume loss due to tunnelling (expressed as a fraction). p = G s [1- (1-ε)] (1) Figure 1: Generic Problem Considered. These stress reductions can be estimated via cavity expansion theory, as described by Poulos and Deng (24). The following expressions are derived for the change of vertical and horizontal stresses due to tunnelling: a 2 1 σ h = 2G( 1 ε 1)( ) r cos 2θ + tg2θ sin 2θ a 2 1 σ v = 2G(1 1 ε )( ) r cos 2θ + tg2θ sin 2θ (2) (3) a 2 tg2θ τ xy = 2G( 1 ε 1)( ) (4) r cos 2θ + tg2θ sin 2θ where, θ is the angle of inclination for the point of interest, as shown on Figure 1; σ x = σ h is the change of horizontal stress and σ y = σ v is the change of vertical stress. In sands, the change of skin friction along the pile, f s, and the change of end bearing, f b can then be calculated by: f = τ + σ tgδ () s f where δ is the pile-soil friction angle; 2 Nφ = tg (4 + φ / 2) is the bearing capacity factor, and φ is the angle of internal friction of the soil. xy h φ πtgφ = σ N = σ e tg 2 b v q v (6) (4 + ) 2 In clays, if an effective stress approach is adopted for the skin friction, the change in skin friction can again be estimated from Equation (). If however a total stress approach is adopted for the end bearing capacity, the change in end bearing can be estimated (approximately) as follows: 82 Australian Geomechanics Vol 41 No 1 March 26

3 where N c is the base bearing capacity factor (typically 9) c u = undrained shear strength, σ v = vertical effective stress. f b = σ v. N c. (c u /σ v ) (7) The stress changes σ n and σ v, and hence the changes in pile capacity, will thus depend on the volume loss, the modulus of the soil surrounding the tunnel and the position of the pile element or point in relation to the tunnel. 4 PROBLEM CONSIDERED Figure 2 shows the specific problem considered, which although somewhat idealized, involves the construction of a circular tunnel of 6 m diameter within a deep soil layer. Two soil profiles are considered: the first, a uniform stiff clay layer, and the second, a medium dense sand layer. The soil parameters assumed for each profile are summarized in Table 1. It is assumed that a bored pile of 8 mm diameter is located in the vicinity of the tunnel and the objective of the analysis is to estimate the settlement of the pile as a function of its position relative to the tunnel. The volume loss is assumed to be 2% (a rather large value, but not atypical of some design values), and the pile modulus is taken to be, MPa, representing a relatively low long-term value for concrete. P Soil Properties: E s = MPa f s = kpa f b = MPa d L D T Pile Properties: d=.8 m X Figure 2: Specific Problem Analysed. For each profile, analyses have been carried out for piles of various lengths, with the pile tip location varying in elevation and in lateral location. The pile is assumed to have an axial load of about one-half of the ultimate axial load capacity acting on it. Table 1: Summary of Assumed Geotechnical Parameters. Parameter Uniform Stiff Clay Profile Medium Dense Sand profile Young s Modulus along shaft (MPa) 3z Young s modulus at tip (MPa) 6L Ultimate skin friction (kpa) 4.6z Ultimate base resistance MPa.72.64z ( 12 MPa) Note: z = depth below surface (m), L = pile length (m). RESULTS.1 PILE CAPACITY LOSS To give some indication of the effect of the tunnel in reducing pile capacity, Figures 3 and 4 plot contours of percentage loss of axial pile capacity, compared to the case of a pile unaffected by the tunnel. The contours relate to the position of the pile tip. The following observations may be made: Australian Geomechanics Vol 41 No 1 March 26 83

4 PILE SETTLEMENT ABOVE TUNNELLING OPERATIONS X COORDINATES OF PILE TIP Z COORDINATES OF PILE TIP CONTOURS OF % LOSS OF ULTIMATE PILE CAPACITY % VOLUME LOSS DUE TO TUNNELLING Figure 3: Effect of Pile Tip Location on Percentage Loss of Ultimate Pile Capacity. Pile in Clay. 1. For the clay profile (Figure 3), the pile tip locations most severely affected are in the immediate vicinity of the tunnel, and also at shallow depths directly above the tunnel. The maximum loss of capacity appears to be of the order of 2%. 2. For the sand profile (Figure 4), the pattern of capacity reduction is rather different to that for the clay profile. Piles whose tips are in the immediate vicinity of the tunnel are affected considerably by the tunnelling process, with axial capacity losses of over 4% being experienced, even for pile tips adjacent to, and below, the tunnel axis. These figures indicate that the effects of tunnelling on load capacity are most severe for piles which derive the majority of their capacity from the pile tip, such as piles in sand..2 ZONES OF SETTLEMENT On the basis of a series of centrifuge tests on piles in sand, Jacobsz et al. (21) have defined three different zones of pile settlement behaviour around a tunnel, as illustrated in Figure : 1. Zone A, within which the pile settlement exceeds the ground surface settlement due to the tunnelling. Zone A lies within the zone bounded by a line drawn at 6 degrees from the horizontal, from the tunnel spring line. 84 Australian Geomechanics Vol 41 No 1 March 26

5 X COORDINATES OF PILE TIP CONTOURS OF % LOSS OF AXIAL CAPACITY Z COORDINATES OF PILE TIP % VOLUME LOSS DUE TO TUNNELLING Figure 4: Effect of Pile Tip Location on Percentage Loss of Ultimate Pile Capacity. Pile in Sand. 2. Zone B, where the pile settlement is approximately equal to the ground surface settlement. This zone is bounded by the 6 degree line and a similar line drawn at 4 degrees from the spring-line; 3. Zone C, where the pile settlement is less than the ground surface settlement. This zone lies outside the area bounded by the 4 degree line from the tunnel spring-line. Figures 6 and 7 show the computed ratios of additional pile settlement due to tunnelling, to the tunnelling-induced ground surface settlement. The additional pile settlements have been computed from the two-stage analysis described previously, in which the computed ground movements due to tunnelling are input into the boundary element program PIES to obtain the settlement and load distribution in a pile. Figure 6 is for the case of a uniform clay layer, while Figure 7 is for the medium dense sand profile. From these figures, the following observations can be made: For piles in clay (Figure 6), there is a zone extending from below the tunnel to the soil surface, in which the pile settlement exceeds that of the soil surface. Outside this zone, which is inclined at about 7 degrees to the horizontal, the pile settlement is less than the soil surface settlement. For the piles in sand (Figure 7), the area in which the pile settlement exceeds the soil surface settlement is wider than that for piles in clay, and is inclined at about 4 degrees to the horizontal. The settlement of piles whose tip is located near the tunnel crown can be considerably larger than the soil surface movement. Australian Geomechanics Vol 41 No 1 March 26 8

6 1. PILE SETTLEMENT ABOVE TUNNELLING OPERATIONS The computed ratios of pile to soil surface settlement for the pile in sand are broadly consistent with the zones defined by Jacobsz et al. (21) and illustrated in Figure. ZONE A ZONE B 4 6 ZONE C ZONE A: ZONE B: ZONE C: PILE SETTLEMENT > GROUND SETTLEMENT PILE SETTLEMENT ~ GROUND SETTLEMENT PILE SETTLEMENT < GROUND SETTLEMENT Figure : Pile Settlement Zones Defined by Jacobz et al (21). X COORDINATES OF PILE TIP 2 2 CONTOURS OF PILE SETTLEMENT SOIL SURFACE SETTLEMENT Z COORDINATES OF PILE TIP % VOLUME LOSS APPLIED LOAD = 1 2 ULTIMATE CAPACITY Figure 6: Effect of Pile Tip Location on Ratio of Pile Settlement to Soil Surface Settlement. Pile in Clay. 86 Australian Geomechanics Vol 41 No 1 March 26

7 X COORDINATES OF PILE TIP 2 2 CONTOURS OF PILE SETTLEMENT SOIL SURFACE SETTLEMENT Z COORDINATES OF PILE TIP % VOLUME LOSS APPLIED LOAD = 1 2 ULTIMATE CAPACITY Figure 7: Effect of Pile Tip Location on Ratio of Pile Settlement to Soil Surface Settlement. Pile in Sand. 6 PRACTICAL IMPLICATIONS FOR VARIOUS FOUNDATION TYPES The settlement response of pile foundations in the vicinity of the tunnel has important practical implications for potential building damage due to tunnelling. The settlements in the region directly above the tunnel will be greater than the surface settlements, while those away from the tunnel will be less. This implies that the differential settlements, and hence the building distortions, will be greater for a building on pile foundations than for the same building supported by piles. As an example, the case in Figure 8 is considered. Three cases have been analysed: A structure supported by a series of surface strip foundations; A structure supported on piles only; A structure supported by a piled strip foundation. The computer program GASP (Geotechnical Analysis of Strip with Piles, Poulos (1991)) has been used to study this problem. This program employs a boundary element analysis for the strip and assumes the piles to be non-linear interacting springs. The soil is assumed to be a linear elastic continuum, but the strip-soil pressures are limited to the bearing capacity of the strip foundation. The soil and pile properties are as shown in Table 1 for the stiff clay profile. The strip is assumed to be 26 m long, 1.6 m wide, and 1. m thick, with a Young s modulus of 3, MPa. Australian Geomechanics Vol 41 No 1 March 26 87

8 ALL LOADS ARE 1. MN 26 A B C D TUNNEL VOLUME LOSS = 1.% Figure 8: Foundation Problem Analysed. Figure 9 shows the profile of computed total settlements, due to both the applied loadings and the tunnelling-induced ground movements, while Figure shows the computed angular rotations for the three foundation types. The following conclusions are drawn from these figures: The largest settlement is experienced by the pile foundation; The strip foundation experiences a smaller maximum settlement than the fully piled foundation, but a smaller minimum settlement. The differential settlement between the centre and outer columns is considerably less for the strip than for the fully piled foundation, and this is reflected in the smaller angular rotations (Figure ). The piled strip foundation experiences a smaller maximum settlement than the other two foundation types, but the differential settlement between the centre and outer columns, and the angular rotations, is still greater than for the strip foundation alone. An interesting result from the GASP analyses is that the proportion of load carried by the piles in the piled strip decreases after the tunnelling-induced settlements has occurred. In the example case considered, the proportion of load carried by the piles reduces from 84% for the applied loads only, to 61% after the tunnelling-induced settlements have occurred. The piles, in effect, pull down the strip footing and so cause it to carry a greater proportion of the applied loading. It may be concluded that, in areas that are likely to be affected by tunnelling-induced ground movements, there may an advantage in using a strip or piled strip foundation (or a raft or piled raft foundation), rather than a floating pile foundation. 88 Australian Geomechanics Vol 41 No 1 March 26

9 Distance From LH End m Settlement mm Strip Only Piles Only Piled Strip 4 4 Figure 9: Computed Total Column Settlements due to Applied Loads and Tunnelling, for various foundation Types..2.2 Angular Rotation rad..1 Strip Only Piles Only Piled Strip. A-B B-C C-D Columns Figure : Computed Angular Rotations for various foundation types (due to Loading & Tunnelling). 7 CONCLUSIONS The analyses described in this note of pile settlement caused by tunnelling operations indicate behaviour which is broadly consistent with the experimental findings of Jacobsz et al. (21). There appear to be three zones, A, B and C, as illustrated in Figure, in which the pile settlement is respectively greater, equal to, and less than the tunnellinginduced ground surface settlements. For piles in clay, the zone in which the pile settlement exceeds the soil surface settlement is more restricted than is the case of piles in sand. The general increase in pile settlement due to tunnelling is also greater for piles in sand than in clay. The presence of the tunnel will also tend to reduce the axial capacity of a pile, due to the reductions in stress around the pile. The capacities reduction are most severe for piles which derive most of their capacity from the pile tip, such as piles in sand. A relatively simple approach can be used to assess the pile axial capacity reduction. In zones close to the pile, the reduction may be sufficiently large so that failure of the pile occurs. If a structure is located above the tunnel, the performance of a fully piled foundation may be inferior to that of a shallow foundation or a piled strip or piled raft foundation, because of the drag-down effect of the tunnelling-induced ground Australian Geomechanics Vol 41 No 1 March 26 89

10 movements. In a piled strip/raft foundation, the drag-down effect of the piles induces a greater proportion of the load to be carried by the strip/raft. 8 REFERENCES Chen, L.T., Poulos, H.G. and Loganathan, N. (1999). Pile responses caused by tunnelling. Jnl. Geotech. & Geoenvir. Eng., ASCE, Vol.12, No.3, Loganathan, N. and Poulos, H.G. (1998). Analytical prediction for tunnelling-induced ground movements in clays. Jnl. Geotech. & Geoenvir. Eng., ASCE, Vol.124, No.9, Loganathan, N. and Poulos, H.G. (1999). Tunnelling induced ground deformations and their effects on adjacent piles. Proc. th Australian Tunnelling Conf., Melbourne, Aus. IMM, Loganathan, N., Poulos, H.G. and Stewart, D.P. (2). Centrifuge model testing of tunnelling-induced ground and pile deformations. Geotechnique, (3): Jacobsz, S. W., Standing, J. R., Mair, R.J., Soga, K. (21). Tunnelling effects on driven piles. Proc. Conference on Response of Buildings to Excavation-Induced Ground Movements, London, UK. Mroueh, H. and Sharour, I. (22). Three-dimensional finite element analysis of the interaction between tunnelling and pile foundations. Int. Jnl. Num. Anal. Methods in Geomechs., 26: Poulos, H.G. (1989). PIES Users Manual. Centre for Geotechnical Research, University of Sydney. Poulos, H.G. and Davis, E.H. (198). Pile foundation analysis and design. John Wiley, New York. Poulos, H.G. and Deng, W. (24). An investigation on tunnelling-induced reduction of pile geotechnical capacity. Proc. 9 th Australia-New Zealand Conf. On Geomechanics, Auckland, Vol. 1, 1: Surjadinata, J., Hull, T.S., Carter, J.P. and Poulos, H.G. (2). Combined finite element and boundary element analysis of the effects of tunnelling on single piles. Int. Symposium on Tunnelling, Amsterdam. 9 Australian Geomechanics Vol 41 No 1 March 26