Evaluation of Tunneling-induced Downdrag on End-bearing Piles
Professor of Civil Engineering, Changsha Communications University, Hunan, China. Presently, Visiting Scholar in the Department of Civil & Environmental Engineering, The Pennsylvania State University - University Park, PA, USA
Professor of Civil Engineering, Department of Civil & Environmental Engineering The Pennsylvania State University - University Park, PA, USA
Ground loss induced by soft-ground tunneling may result in considerable down-drag loading on nearby piles. This paper presents a method for estimating the tunneling-induced down-drag loads on end-bearing piles. The method of analysis involved determinations of ground settlement profile and distribution of negative skin friction followed by integration of the negative skin friction over the entire pile length. In the analysis, the negative skin friction was assumed to increase linearly with soil settlement along pile shaft to a constant maximum value. The total down-drag load was determined using the Euler’s integration method. The computed down-drag loads were non-dimensionalized by expressing in terms of total positive shaft resistance. The dimensionless ratios were related graphically with the ratios of tunnel depth to pile length as well as horizontal distance between tunnel and pile to tunnel diameter. The relations were developed for three levels of ground loss with a broad range of soil properties. These graphical relations are useful for estimating the tunneling-induced down-drag loading on end-bearing piles nearby tunnel constructions.
KEYWORDS:Downdrag, End-Bearing Pile, Soft Ground Tunnel, Negative Skin Friction, Shaft Resistance, Ground Loss, Analysis
Tunneling in soft grounds inevitably will result in a loss of ground due to soil deformation and displacement into the opening. The tunneling-induced soil displacement may influence the performance of piles adjacent to the tunnel. Specifically, the downward displacement of soil along the pile may induce negative skin friction resulting in considerable down-drag loads. Another possible effect of tunneling on adjacent piles is the decrease in lateral support on one side of the pile possibly causing lateral deformation/bending of the pile toward the tunnel.
The condition of soft ground tunneling near existing piles occurs more often in urban and suburban areas. In the densely populated areas with growing demand of sewer, utility, and transportation tunnels, the construction of new tunnels can take place very close to existing pile foundations, causing excessively large down-drag loads on the piles. Such a high down-drag loading may adversely affect the stability of the existing pile foundation.
The analysis of tunneling-induced down-drag loading on piles is a difficult task. Although there are studies related to this problem, a method of predicting the tunneling-induced down-drag loading is yet to be developed. Examples of related studies include Mair et al. (1993), Verruijt and Booker (1996), Loganathan and Poulos (1998), Chen et al. (1999), and Loganathan et al. (2001). Of these studies, Mair et al. (1993) and Verruijt and Booker (1996) analyzed the ground settlement profile induced by tunneling. Loganathan and Poulos (1998) presented an analytical method for predicting tunneling-induced soil movement in both vertical and horizontal directions. Chen et al. (1999) investigated the lateral and axial responses of piles to tunneling. Loganathan et al. (2001) reported an analytical method for pile-group response to tunneling. These available studies provide useful information for analysis of tunneling-induced down-drag loading on piles. This paper presents a method for evaluating the tunneling-induced down-drag loading on end-bearing piles.
The down-drag loading on piles is computed from integration of downward shear stress (or negative skin friction) induced by soil settlement relative to the pile. The relative soil settlement (or slip) due to tunneling is estimated based on available empirical methods. The analysis of down-drag loads is performed for tunnels at different depths and at various locations from the pile together with different soil conditions. The analyzed down-drag loads are non-dimensionalized by expressing as ratios of positive skin friction. The non-dimensional down-drag loads are then related graphically with tunnel depths and locations for ease in applications. Details of each step of analysis follow.
The tunneling-induced soil settlement is estimated based on the methods proposed by Peck (1969) and Mair et al. (1993). According to their methods, the shape of settlement profiles at ground surface and subsurface can be characterized as the Gaussian distribution, as illustrated in Figure 1. The equation of settlement profile is given below (Mair et al. 1993):
s = settlement at horizontal distance x from tunnel center
smax = maximum settlement above tunnel center
i = horizontal distance between tunnel center and the reflection point of settlement profile (or trough)
H = depth to tunnel center
z = depth of interest
K = Coefficient determined by the method proposed by Mair et al. (1993)
Figure 1. Ground movements induced by tunneling
The maximum settlement can be determined from tunnel diameter (D), ground loss (VL), and i using the following equation. Ground loss (VL) is defined as the volume ratio between surface settlement profile and the tunnel opening.
Equation (1) is used to estimate the vertical settlement of soil along the pile shaft at any depth and pile location from tunnel center. The magnitude of soil settlement thus obtained is used in the following step of analysis to determine the negative skin friction.
NEGATIVE SKIN FRICTION
The negative skin friction at a depth induced by soil slip along the pile shaft is determined from vertical force equilibrium of a pile segment involving the axial load, pile weight, and friction force. For a pile segment of dz in length at a depth of z, the force equilibrium yields the following equation
Ep = elastic modulus of pile
A = cross section area of pile
p = perimeter length of pile cross section
w = vertical displacement of a pile cross section
τ = shear stress at pile-soil interface
The shear stress (τ) at pile-soil interface is computed from the sum of adhesion and friction. It is assumed that the shear stress increases linearly with increasing relative soil-pile displacement to a maximum value then remains constant. According to Alonso et al. (1984), the relative soil-pile displacement at maximum shear stress ranges between 2 and 3 mm for most cases. In this study, the average of 2.5 mm is used. Thus
s = soil settlement or vertical displacement
(s-w)ult = relative pile-soil displacement at maximum τ ≈2.5 mm
ca = adhesion at pile-soil interface
δ = friction angle at pile-soil interface
σn = normal stress on pile-soil interface
γ = unit weight of soil
Ks= lateral earth pressure coefficient
φ’ = effective internal friction angle of soil
Incorporating Equations (4) and (5) into Equation (3) yields the following governing differential equations:
in which r = radius of pile cross section.
To determine the variations of negative skin friction as well as axial pile load with depth, the governing differential equations (6) and (7) are solved numerically by following the approach adopted by Vaziri and Xie (1990) in their analysis of axially loaded piles. Their approach essentially is the Euler’s integration method. In the analysis, the pile is divided into n segments of equal length and is integrated through the n integration points along the pile length. The boundary conditions include the tunneling-induced axial pile load at pile top equal to zero and also zero pile tip displacement for end-bearing piles. The solution is obtained through iterations by adjusting successively the initial conditions at pile top until pile tip displacement is equal to zero or within a tolerant limit. Specifically, the error resulted from each iteration is obtained. Then, the errors of two consecutive iterations together with the assumed initial pile top displacements are used to determine the pile top displacement for the next iteration as shown below:
w0, wn = pile top and tip displacements, respectively
i = ith cycle of iteration
The iteration process continues until the calculated pile tip displacement is less than 0.001 mm.
Analyses were conducted for conditions including 6 m tunnel diameter, 20 m tunnel depth, 4 m horizontal distance from a pile, 1.2 m pile diameter, 25 m pile length, 30 GPa pile modulus, 17.0 kN/m3 soil unit weight, zero cohesion, 25˚ internal friction angle, and three levels of ground loss (0.5%, 1.0%, and 5.0%). The analyzed soil settlements along the pile are illustrated in Figure 2. It is seen from Figure 2 that soil settlements increase with increasing ground loss as would be expected. For a given level of ground loss, soil settlements along the pile increase with increasing depth to a maximum, which takes place at an elevation considerably higher than the tunnel crown. At crown elevation, soil settlement decreases to a very small value.
Figure 2. Soil settlement along the pile shaft
The tunneling-induced down-drag loading is determined through integration of negative skin friction over the entire pile length. In addition to down-drag loading, upward positive skin friction is also computed for no-tunneling condition. The analysis is made for a wide range of soil conditions including a range of cohesion (c) between 0 and 50 kPa, and a range of internal friction angle (φ) between 15˚ and 35˚. In the analysis of positive skin friction, possible soil arching effect is not considered. Meanwhile, the value of adhesion (ca) is taken at 0.7c and the pile-soil friction angle (δ) at 0.7φ. The various geometric conditions analyzed include the depth to tunnel (H) of 10 to 40 m, horizontal distance to pile (Xp) of 6 m to 30 m, a tunnel diameter (D) of 6 m, and a pile length (Hp) of 45 m. Other parameters include pile radius (r) of 0.6 m, modulus of elasticity of pile (Ep) of 30 GPa, and soil unit weight (γ) of 17 kN/m3. Furthermore, three levels of ground loss (VL), i.e. 0.5%, 1.0% and 5.0% are considered. These values correspond, approximately, to the conditions of good, average, and poor workmanship of tunnel constructions.
The analyzed down-drag loads are expressed non-dimensionally as a ratio of positive pile shaft resistance in order to consider, at least partly, the effect of soil properties. The dimensionless ratios are related with depth to tunnel and horizontal distance to pile. Both tunnel depth and distance to pile are also expressed in dimensionless ratios in terms of pile length and tunnel diameter, respectively. The graphical relations are presented for three values of ground loss in Figures 3 and 4. Specifically, Figure 3 presents the relation between down-drag load and tunnel depth, whereas, Figure 4 shows the relation of down-drag load vs. tunnel distance to pile.
Figure 3 (a). Relationship between M and Xp/D for VL = 0.5%
Figure 3 (b). Relationship between M and Xp/D for VL = 1%
Figure 3 (c). Relationship between M and Xp/D for VL = 5%
Both Figures 3 and 4 show that increasing ground loss increases down-drag loads due to greater soil settlements as would be expected. According to Figure 3, for a given level of ground loss and distance to pile, down-drag loads increase with increasing tunnel depth within the range of tunnel depth investigated. This can be attributed to the increased extent of settlement trough with deeper tunnels. For a given tunnel depth and ground loss, down-drag loads decrease as the tunnel is located farther from the pile as illustrated in Figure 4. This is as would be expected primarily because the pile is farther away from the tunneling-induced settlement trough.
The graphical relations presented in Figures 3 and 4 are for a broad range of soil properties. The results for different soil properties spread within a narrow range along the relation curves as shown in the figures. The numerical data of analysis, which are not presented here, show that, for a constant cohesion (c), the down-drag load to pile shaft resistance ratio (M) decreases with increasing internal friction angle (φ), and that, for a constant φ, M increases with increasing c. However, the maximum range of variation is roughly about ±10% of the value indicated by the relation curve. With such a narrow range of variation, these graphical relations can become a useful tool for estimating possible down-drag loads on end-bearing piles induced by nearby tunneling.
Figure 4 (a). Relationship between M and H/Hp for VL = 0.5%
Figure 4 (b). Relationship between M and H/Hp for VL = 0.5%
Figure 4 (c). Relationship between M and H/Hp for VL = 5%
SUMMARY AND CONCLUSIONS
With the growing demand in utility, sewer, and transportation tunnels in the densely populated urban and suburban areas, the construction of new tunnels can take place near existing pile foundations. Soft ground tunneling always causes varying degrees of ground loss. As ground settles, the nearby existing pile foundations may be subjected to considerable down-drag loading that may adversely affect the stability of the pile foundation. The analysis of tunnel-induced down-drag loading is a difficult task. This paper presents a method for evaluating the tunnel-induced down-drag loading on end-bearing piles.
In the analysis, the tunneling-induced ground settlement was characterized as a Gaussian distribution. From the pile location in the settlement trough, the magnitude of soil settlement (or slip) along pile shaft was estimated. The estimated soil slip was then used to compute the downward shear stress (or negative skin friction). In the computation, the shear stress was assumed to increase linearly with soil slip to a constant maximum value. The total down-drag load on the pile was computed by integrating the negative skin friction over the entire pile length.
Based on the results of the analysis, the computed down-drag loading was related graphically with tunnel size, tunnel location and soil properties. In the graphical relations, the down-drag loads were non-dimensionalized by expressing in terms of positive pile shaft resistance. Also, both tunnel depth and horizontal distance to pile were expressed in dimensionless ratios in terms of pile length and tunnel diameter, respectively. The relations were developed for three levels of ground loss with a broad range of soil properties. For different soil properties, the relations vary within a narrow range of roughly ±10%. It is concluded that the developed graphical relations can be useful for estimating the tunneling-induced down-drag loads on end-bearing piles for various tunnel sizes and locations as well as different soil properties.
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