Pile-Soil Interaction and Settlement Effects Induced by Deep Excavations

The axial deformation of the pile head, $p$, is determined by the following effects:

For end-bearing piles, $p_s$ is expected to be significant only if the pile bases are very close to the excavation, as shown similarly for tunnels by Kaalberg et al. (2005) and Lee and Ng (2005). Stress relief around the pile base can lead to additional mobilization of positive shaft friction. The settlement under the pile base, $p_b$, may be calculated without interaction with the piles, for example, with a finite-element (FE) analysis or by using the Aye et al. (2006) method for deeper soil displacements caused by excavations. The interaction component, $p_i$, is different for friction piles and end-bearing piles. If the soil displaces an equal amount over the whole length of the pile, the pile settles with this amount of soil settlement. Any other shape of soil settlement (either larger at the top as expected for excavations or larger near the pile base as expected for tunneling) will cause additional negative and positive shaft friction. For a piled building with certain stiffness, redistribution of loads takes place. If this happens, the external load on the pile changes, leading to a new equilibrium. This effect, $p_r$, should be determined by a coupled analysis for a pile group, such as with a boundary element method as described by Xu and Poulos (2001) or with the D-Pile Group model with a cap over the piles as described in Bijnagte and Luger (2000).

For many cases, the effect of stress relief $p_S$ can be assumed small. The effect of load redistribution $p_r$ or settlement below the base $p_b$ can be determined on the basis of the methods previously described. The interaction effect $p_i$ depends largely on existing conditions and is studied in this paper in more detail.

The interaction effect $p_i$ along the pile caused by excavation-induced settlements is similar to the concept of negative skin friction development. Negative skin friction can be determined by a total stress approach ($\alpha$-method), an effective stress approach ($\beta$-method) or empirically from in situ test results such as cone penetration test (CPT). The neutral level is commonly described as the level at which the interface shear stress changes from negative to positive. The maximum force in the pile is found at this level. For single piles, the negative skin friction is primarily controlled by the free-field subsoil settlement profile and the mobilization of the pile shaft resistance. If ground settlements along the pile occur, negative skin friction will develop. This will lead to three possible situations, shown in Fig. 2:

In the following section, the general model will be explained first, after which specific situations are given in subsequent paragraphs.

In this section, the effect of positive and negative shaft friction is discussed on the basis of a nonlinear analytical spring model that was developed to study the difference in behavior between friction piles and end-bearing piles ($p_i$, based on axial interaction for single piles). The effect of the initial loading condition of the piles is shown for pile loads varying from 0 to 100% of the maximum bearing capacity $Q_{\text{max}}$. The pile deformation can be determined relative to the greenfield settlement of the soil by finding the depth $z$ at which the pile deformation equals the soil settlement. This depth $z$, relative to the length of the pile $L$ ($z/L$), is in this paper called the interaction level. This is close to but not the same as the neutral level, which is defined as the depth at which the shaft friction changes from negative to positive (Fig. 2). The greenfield settlement is defined as the settlement at the location of the pile as if no pile or building were present. All soil displacements referred to in this paper are greenfield values.

The deformation of the pile ($p_i$) related to the displacement of the soil ($S_z$) can be determined from the basic pile equilibrium equationwhere $\tau$ = shaft friction along the pile with diameter $D$; $z$ = vertical axis (positive down along the pile); and $q_b$ = average foundation pressure around the base in ($\mathrm{kN}/{\mathrm{m}}^2$) with cross section $A({\mathrm{m}}^2)$. The pile is positioned from $z=0$ to $z=L_p$, with $L_p$ as the length of the pile (Fig. 3). The actual working load $W$ on the pile is assumed constant (no redistribution between piles). The shaft friction ${\tau }_z$ is the function of the relative displacement between soil and pile and the relative displacement $D_z$, at which ${\tau }_{\max }$, the maximum shaft friction, is reached in a bilinear approach (Fig. 4). This function can be derived either from field tests or existing codes.

For friction piles, the base resistance plays only a very minor role and is neglected in this paper. Working toward a dimensionless representation, all variables are transformed by relating them to a characteristic dimension and are further denoted bywhere ${\tau }_{av;\max }$ = average shaft friction over the pile length.

Other dimensionless variables used areEq. (1) transforms for friction piles in dimensionless form to

The general shaft friction formula (Fig. 4)becomes in dimensionless form

The initial stiffness $k_s$ is the gradient of shaft friction $\tau$ at

During the initial loading of the pile (called Step 1), the shaft friction along the length of the pile can be found by solving Eq. (2) in combination with Eq. (4). The pile deformation $p_{i1}$ will be found as a result, with the corresponding ${\tau }_1$, when the initial soil displacement $S_z=0$.

The next step is the occurrence of an external soil displacement initiated by the excavation (called Step 2). For Step 2, the formula of the shaft friction is given in three parts, represented by the striped line in Fig. 4. The unloading-reloading stiffness is the same as the initial stiffness $k_s$, and the original tangent hyperbolic function applies for positive and negative loading.

The dimensionless pile deformation after this step ($p_{i2}^{\prime }$) can be found from Eq. (6)

The solution of the pile deformation for Step 2 depends on the shape of the soil displacement and the shaft friction with depth, which are described in the following two sections. The pile deformation caused by the greenfield soil displacement can be found by subtracting the pile deformation from Steps 1 and 2.

The shape of the soil displacement with depth along the pile is an important parameter for the interaction between pile and soil. The settlement can be derived from monitoring data, or if monitoring data are not available, settlements can be assessed by either FE analysis or by simplified charts, such as presented by Clough and O’Rourke (1990) or Aye et al. (2006). For excavations, the settlement at the surface is usually larger than at the pile base. For this analytical model, at first a linear shape of the soil displacement is assumedwhere $S_0^{\prime }=S_0/D_z$, the dimensionless factor of the soil displacement at $z=0$; $S_{lp}^{\prime }=S_{lp}/D_z$, the dimensionless factor of the soil displacement at $z=L_p$; $\mathrm{\Delta }S=S_{L_p}-S_0$.

$S_0^{\prime }$ may be taken out of the equation, because any overall settlement of the soil along the pile can be added to the pile settlement after the interaction calculation. A different interaction settlement $p_i$ will be found for the same surface settlement and settlement of the foundation layer, when the shape of the settlement with depth is not linear, for example, because of the nature of the settlement origin, such as dewatering, tunneling, or excavation. Because of the $p_i$ settlement, a small amount of extra shaft resistance could be obtained for the extra embedment in the bearing layer. When the cone resistance in the bearing layer is not constant, also the tip resistance might be affected. Both these effects are considered to be second order and should be neglected in normal conditions.

The analytical solution of Eq. (8) can be extended for a linearly increasing ${\tau }_{\max }$ with depth (Fig. 8)where ${\tau }_{\max ;0}$ = maximum shaft friction at $z=0$; ${\tau }_{\max ;L_p}$ = maximum shaft friction at $z=L_p$; and $D_z$ = assumed to be constant for the different depths.

Combining Eq. (12) with Eq. (13) leads to

For the initial condition with $S_{z1}=0$, this leads to the same solution of $p_{i1}^{\prime }$ as for the constant shaft friction with depth, as shown in Eq. (10). Eq. (11) should now include the shaft friction function with depth with the following loading and unloading branches:

To obtain the pile deformation $p_i$ Eq. (12) can be used after solving $p_{i2}^{\prime }$ from the aforementioned branches.

For a linearly increasing maximum shaft friction with depth, the pile deformation problem includes the following dimensionless parameters: $z/L_p$; $W/Q_{\max }$; $\mathrm{\Delta }S/D_z$; and ${\tau }_{\max ;L_p}/{\tau }_{\max ;0}$. The result for different variations of these parameters is shown in Fig. 9.

For increasing maximum shaft friction with depth, the interaction level at low initial loads (small $W/Q_{\text{max}}$ indicating large factor of safety) is found deeper along the pile. This leads, for excavations, to a smaller pile deformation compared with the situation with constant shaft friction.

Lateral pile response to horizontal soil deformations can be determined by FEM analysis or more simplified methods based on $p-y$ curves. For piles subjected to lateral loads from deep excavations, the green field soil displacements are determined first in an uncoupled approach. The springs are next subjected to these displacements, which determine the response of the piles. In this paper, the $p-y$ curves from API (1984) have been used for sand and clay, which both are nonlinear. The springs are not coupled, so no transfer of load takes place between the springs. In this model, the piles are connected to the pile cap, but there is no pile-soil-pile interaction. The soil resistance for each pile is considered according to API (1984) for static loads. The API continuous $p-y$ curve is approximated by five parallel elastoplastic springs (Bijnagte and Luger 2000).

The combination of axial and lateral displacements is in reality more complex than can be modeled by noncoupled springs because a combination of loading in several directions will lead to soil failure at a lower stress level than for each direction separately and also pile group effects need to be considered for a more advanced approach. Both can be modeled using FEM. In many cases, however, the different loadings are considered consecutive. The D-Pile Group cap model does allow for interaction between the piles through the pile cap, as is shown in the comparison with field data presented in the following section.

Field data from the construction of the 9.5-km-long North South Metro line under construction in Amsterdam are compared with the model results. The project consists of two bored tunnels with three large cut and cover stations in the historic center of the Dutch capital. The stations are built to a maximum depth of approximately 30–33 m below surface level. A detailed description of the construction works is given in Korff (2013). Historic buildings found on timber piles are present at close distance from the excavations. Some of the oldest buildings (before 1925) typically are built with masonry walls, wooden floors, and a pairs of timber piles, founded approximately 12 m deep in a sand layer overlain by Holocene soft clay and peat deposits (Fig. 12).

Most of the piles under the buildings along the North South Line are approximately 100-year-old timber piles. On the basis of several pile load tests in the historic centre, it is known that the timber pile foundations have low factors of safety because of subsequent raising of the street level over the last 100 years, which caused negative skin friction to develop. Usually, some positive skin friction has developed above the pile tip to balance the negative skin friction. To obtain realistic values for the shaft friction behavior of the piles, the results of pile load tests on tapered timber piles (the diameter is 220 mm at the top and 130 mm at the tip; in calculations, an average $D$ of 180 mm is used) were analyzed in more detail to obtain separate shaft friction curves for the soft layers and the foundation layer. The resulting curves are shown in Fig. 13.

In the Holocene clay, the maximum shaft friction develops at approximately 25 mm and in sand at approximately 15 mm of relative displacement, which is derived from tests by Hoekstra and Bokhoven (1974). This gives $D_z$ values of 5.5 and 4 mm, respectively. In the calculations hereafter, the derived nonlinear curves of Fig. 13 have been used directly. The corresponding ${\tau }_{\max }$ is 5.3 and $35\mathrm{kN}/{\mathrm{m}}^2$, respectively, and the pile’s Youngs’ modulus is set to $8\times {10}^6\mathrm{kN}/{\mathrm{m}}^2$. The maximum base capacity for piles with a diameter of 130 mm is reached at approximately 10% of the diameter, as can be found in common design methods. The old piles find in failure 60% of their capacity at the base, 10% as friction in the sand layer, and 30% as friction in the Holocene layers.

The measured ground settlements caused by the excavation are presented in Fig. 14, showing that the surface settlements (approximately 10 mm, in green) are larger than at the level of the base of the piles [Nieuw Amsterdams Peil (NAP)-12 m, in blue]. The settlements at deeper levels are even smaller. The settlement also decreases with the distance to the excavation, reducing to negligible values at approximately 2–2.5 times the excavated depth.

The excavation-induced settlements influenced the buildings along the length of the deep excavation and were used to analyze the soil-pile interaction at Ceintuurbaan Station. Buildings were selected according to the availability and the quality of the monitoring and historical data of the structure. Fig. 15 shows a top view of Ceintuurbaan Station with the locations of the buildings and the monitoring instruments. Fig. 16 shows the measurement points along the façade of Govert Flinckstraat 124. The piles are located under the walls and façade of the building.

On the basis of the soil and building displacements presented in Fig. 17, the average interaction level $z/L$ is determined in Table 1. The resulting $z/L$ for these buildings is 0.3–0.5. When $z/L=0$, the pile settlement is equal to the surface settlement. For $z/L$ values between 0 and 1, a linear soil settlement profile between the surface settlement and the settlement at the sand layer (foundation level, depth $L$) is assumed.

With the generally available information and some typical values for Amsterdam conditions, an estimate is made for the building’s initial interaction level based on the pile load and pile capacity. At Govert Flinckstraat 124, a typical Amsterdam timber pile foundation is present, and the pile load and capacity can be estimated. The 5.9-m-wide building has two piles beneath each wall section and 1.1 m between the piles along the wall. The average line working load along the wall is determined at $200\mathrm{kN}/{\mathrm{m}}^2$ for a building with floor floors, height of 12 m, width of 6 m, wall thickness of 0.22 m, a live load, and a roof load. The resulting working load per pile is

The pile capacity in failure is estimated to be approximately $170\mathrm{kN}/\mathrm{pile}$ based on the characteristics of the Dapperbuurt piles Hoekstra and Bokhoven (1974). The $W/Q_{\text{max}}$ thus becomes 65%, leading with Fig. 18 to $z/L=0.55$, which is slightly higher than the measured values in Table 1 for Govert Flinckstraat 124. If the pile load is somewhat higher at 120–125 kN, $W/Q_{\text{max}}=70–75\%$, and $z/L$ fits the value taken from the measurements best.

In cross section 13110WN, Ferdinand Bolstraat 118 is analyzed. The foundation of this building has been renewed by placing additional steel piles. The location of the buildings and monitoring data and the deep excavation are shown in Fig. 19, and the corresponding displacements in Fig. 20. Ferdinand Bolstraat 118 is constructed in 1893, has four regular stories, a top floor, and no basement. The top of the original foundation is found at NAP -1 m, and the designed pile load is 65 kN (the façade is perpendicular to the station) to 80 kN (walls are shared with neighboring buildings). The new piles have the same length as the original piles (base at NAP-12 m in the first sand layer) and are placed under the walls and façades at a minimum distance of 4 m from the deep excavation wall.

The building settlements in the period 2001–2009 are shown in Fig. 20, and the combined ground and building settlements with corresponding interaction level $z/L$ in Table 2. The observed average $z/L$ value is between 0.8 and 1.0 for this building. This is consistent with what is expected for a new, end-bearing foundation. According to Fig. 18, $z/L=0.9$ for $W/Q_{\text{max}}=0.4$, which is representative for a new foundation with an overall safety factor of 2.5.

For the two buildings described, the axial interaction between soil and pile has been determined in detail according to an estimate of the foundation capacity and working load of the piles. For these buildings, the calculated interaction level $z/L$ is in good agreement with the measured values. In most cases in practice, no detailed information is present about the foundation, but it would be practical to estimate the amount of interaction according to generally known building characteristics. For a large number of buildings along the three stations, the interaction level has been determined on the basis of the monitoring data and compared with known building characteristics. The main factor of influence appeared to be the working load $W/Q_{\text{max}}$ because this factor determines the initial neutral level and the interaction level $z/L$ during excavation works. The old timber pile foundations in Amsterdam generally have interaction levels $z/L$ of approximately 0.5 for the original foundations and 0.8–1.0 for the renewed foundations. Modern pile foundations have interaction levels $z/L$ of close to 1.0. This indicates that the building deformation will be close to the free-field displacement of the foundation layer ($p_b$).

The lateral deformations are assumed from Fig. 14 and show a maximum displacement of about 8 mm at the level of the pile tip and almost zero deflection at the top of the wall. The detailed shape over the depth of the pile is shown in Fig. 21. The lateral interaction with the soil is considered separately from the axial response, by using the nonlinear spring model of D-Pile Group with $p-y$ curves from API (1984). The springs used are presented in Fig. 22; for clay, there was an increasing stiffness with depth for the upper 4 m along the pile and constant thereafter. By assuming a maximum bending stress of $9\mathrm{N}/{\mathrm{mm}}^2$, the maximum allowable moment is 8 kNm for the piles. The soil displacements from Fig. 14 are imposed upon the $p-y$ springs. If the maximum possible soil displacement (equal to the wall deflection) is transferred to the pile closest to the excavation (which is a very conservative upper limit for piles more than 10 m away from the wall), this will cause bending moments in the pile in the order of 1.6 $\mathrm{kN}·\mathrm{m}$ (Fig. 21). For an upper limit of the pile stiffness (five times the original value) or five times the increase of the soil deformation, the maximum moment is still acceptable for the measured wall deflection shape. For group effects, a row of six piles is considered, spaced 1.2 m and with free-head conditions. The lateral displacement is assumed to decrease linearly between the first pile (100%) and the sixth pile (0%). The introduced moment is 2.4 $\mathrm{kN}·\mathrm{m}$, which is still acceptable. From this it is concluded that for the relatively short (compared with the excavation), very flexible old timber piles, the lateral response is not governing. For longer or stiffer piles or substantially larger soil displacements, the bending moments could become more significant.