A simplified method for the determination of vertically loaded pile-soil interface parameters in layered soil based on FLAC^3D

Abstract

The numerical analysis of pile-soil interaction commonly requires a lot of trial works to determine the interface parameters and the accuracy cannot be ensured normally. Considering this, this paper first conducts a sensitivity analysis to figure out the influence of interface parameters on the bearing behavior of a single pile in sand. Then, a simplified method for the determination of pile-soil interface parameters in layered soil is proposed based on the parameter studies. Finally, a filed loading test is used for the validation of the simplified method, and the calculated results agree well with the monitoring data. In general, the simplified method proposed in this paper works with higher accuracy and consumes less time compared with the traditional trial works, especially on the determinations of interfacial cohesive and interfacial friction angle.

Keywords

determination of interface parameters / pile-soil interaction / FLAC^3D / sensitivity analysis / layered soil

Introduction

Mechanical properties of soil-structure interface, one of the core issues for soil-structure interaction studies [ 1], is the prerequisite for solving soil and structure interaction problems [ 2]. For a long time, on the researches of soil-structure interface, many scholars have proposed a variety of constitutive models and element types to facilitate the analysis of pile-soil interaction [ 3− 6].

Generally, the determination of interface parameters is based on the indoor shearing tests. Acer et al. [ 7] and Potyondy [ 8] used the indoor shearing test to investigate the behavior of structure and soil interface for the first time. Vogelsang et al. [ 9] developed a large-scale testing device for the experimental investigation of soil-structure interactions, and the device can observe the evolution of deformations and measure the stress in the contact zone. Taha et al. [ 10] presented the results of an experimental study on Leda clay-concrete interface shear behavior. Although the indoor testing techniques for the behavior of pile-soil interface are fully developed, there are still some certain difference between the test results and the in situ pile-soil interface, and many relevant research works tend to use numerical analysis [ 1, 3, 4] to figure out the behavior of pile-soil interface.

The numerical methods have achieved great developments in the past decades as they provide complementary guidance and predictive information that cannot be achieved by the traditional empirical ways [ 11, 12]. In a numerical analysis, the interface element can be used to simulate the slip and the failure behavior of pile-soil contact surface [ 13]. As one of the general geotechnical numerical analysis software, FLAC^3D, which adopts the no-thickness-joint interface element, has been widely used in the pile-soil interaction research. The most common parameters of the interface element in FLAC^3D consist of normal stiffness k_n, shear stiffness k_s, interfacial cohesion c_c, and interfacial friction angle φ_c. Apparently, a rational selection of these four parameters can directly affect the accuracy of calculated results. By now, many researchers have different opinions on the chosen criteria of these four parameters and have not yet obtained a unified understanding, and the determination of these four parameters is still based on experience with certain randomness [ 14, 15]. Therefore, the numerical analysis of pile-soil interaction often requires a lot of trial works and it is difficult to achieve the required accuracy.

For the above, this paper first conducted a sensitivity analysis, namely SA method [ 16, 17], to figure out the influence of interface parameters on the bearing behavior of a single pile in sand. Then, a simple and practical method for the determination of pile-soil interface parameters in layered soil is proposed based on the sensitivity analysis. Finally, a filed loading test is used for validation based on the method proposed in this paper.

Sensitivity analysis of pile-soil interface parameters

Basic example

Generally, the pile-soil interaction is extremely complex for piles located in site with layered strata, and the exertion of skin friction at different soil depth is usually not synchronous. In addition, the relevant studies have shown that the soil strength around pile tip have a greater impact on the development of skin friction [ 18]. Therefore, the sensitivity analysis of parameters for pile-soil interface should ensure that the skin friction and the tip resistance are developed independently.

To simplify the calculation, a single pile under tension in sand is chosen to be as the basic example. During the loading process, the pile tip moves upward and breaks away from the underlying soil gradually. During this process, the tip resistance remains zero which ensures that the development of skin friction is not influenced by the tip resistance. The initial value of interface parameters (k_n0, k_s0, c_c0, and φ_c0) in the basic numerical example is specified as follows: k_n0 is 100 times of the shear modulus of sand, k_s0 is one time of the shear modulus of the sand, c_c0 and φ_c0 is the value of cohesion and internal friction angle of sand. The numerical model and the interface element for the basic example are shown in Fig. 1, and the parameters are listed in Table 1.

In it, ρ represents density; E is elasticity modulus, K is bulk modulus and G is shear modulus; c is cohesion and φ is inner frictional angle, μ is Poisson's ratio.

Normal stiffness

To investigate the influence of different interfacial parameters on the skin friction of the pile in basic example, a series of parameter studies are carried out. Figure 2 illustrates the curves of the average skin friction at 2 and 7-m depth of the pile body changing with the pile-soil relative displacement (namely, f-Δs curves) under different k_n. It can be seen that:

1) The slope of all the f-Δs curves are basically the same at the locations of 2-m depth and 7-m depth. The f-Δs curves with different k_n almost changed at the same line before the ultimate skin friction is attached. Therefore, the skin friction is not related to k_n when its ultimate value has not been reached.

2) It can be found that the ultimate skin friction is closely related to k_n; the larger of k_n and the greater of the ultimate skin friction as can be seen in Fig. 2. Take the f-Δs at 7-m depth with different k_n as an example, the ultimate skin friction under 1 k_n0 is about 15 kPa, and it goes to 28 kPa when k_n is 10k_n0. The skin friction almost remains the same value, 30 kPa, when k_n exceeds 100 k_n0.

Fan et al. [ 14] considered that the normal stiffness k_n is relevant to the normal deformation and suggested that k_n should be a relatively large value to avoid the normal penetration and detachment on pile-soil interface. Yuan et al. [ 19] found that the normal stiffness of pile-soil interface should take a relatively large value, on the order of 10⁸ N/m³ in general. The studies about the selection of k_n have shown that a large value of k_n can simulate the actual situation of pile-soil interface well. Therefore, k_n will be set to a large value (100 times of the shear modulus of the soil adjacent) in the following studies.

Shear stiffness

Figure 3 illustrates the curves of the average skin friction at 2 and 7-m depth of pile body changing with the pile-soil relative displacement (namely, f-Δs curves) under different k_s. It can be seen that:

1) The ultimate skin friction of pile at different depth keeps a constant value basically with the changing of k_s. Take the 2-m f-Δs curves (see Fig. 3(a)) as an example, the ultimate skin friction remains at almost 18 kPa regardless of the variation of k_s.

2) It can be found that the k_s is mainly related to the slope of f-Δs curve. All the curves at different position show that the slope of f-Δs curve increases with the increment of k_s nonlinearly. The slope increases significantly when k_s is less than 10k_s0 and develops slowly when k_s is larger than 10k_s0. Take the 7-m f-Δs curves (see Fig. 3(b)) as an example, the slopes with 0.1, 1, 10, 50k_s0 are 0.93, 3.83, 5.81, 5.96, and the pile-soil relative displacement where ultimate skin friction locates are 21.8, 8.48, 5.06, 4.6 mm, respectively. The changing rate of the slope slows down when k_s amounts to a relative large value.

Interfacial cohesion

As can be seen from the varying curves of f-Δs with different c_c (Fig. 3), the slope of all f-Δs curves remains unchanged under different c_c and the ultimate value of skin friction is directly proportional to the value of c_c.

The ultimate skin friction increases with the increment of c_c and the incremental quantity of the ultimate skin friction is approximately the changing value of c_c. See Fig. 4 (a), the ultimate skin friction with 0, 0.5, 1, and 10c_c0 are 15.7, 16.3, 17.9, and 18 kPa, respectively. The incremental quantity of the ultimate skin friction from 0c_c0 to 10c_c0 is 0, 0.3, 1.1, and 1.5 times of c_c0 (2 kPa), respectively. The influence of c_c on the skin friction can be explained by the Mohr-Coulomb shear theory [ 13] based on Eq. (1).

(1) F_{s\max }=c_{\mathrm{i}\mathrm{f}}A+\tan {\phi }_{\mathrm{i}\mathrm{f}}(F_{\mathrm{n}}-uA)

In it, F_smax is the maximum force when failure is generated on the pile-soil interface, namely the ultimate skin friction; F_n is the normal force, namely the normal soil pressure around pile body; A is the pile-soil contact area; c_if is the interfacial cohesion and φ_if is the interfacial friction angle; u is the pore water pressure which is will be not considered in this paper for simplification.

Based on the Mohr-Coulomb shear theory, the relationship between the ultimate skin friction and the soil pressure under different c_c can be illustrated in Fig. 5. It can be found that the value of ultimate skin friction under the same soil pressure increases with the increment of interfacial cohesion (c₁ is larger than c₂). Meanwhile, the differential value of the ultimate skin friction between piles elements under c₁ and c₂ should be c₁-c₂ whether it is under σ₁ or σ₂. Those can explain the phenomena mentioned about Fig. 4 above.

Interfacial friction angle

As can be seen from the varying curves of f-Δs with different φ_c (Fig. 6), the slope of all f-Δs curves remains consistence at different positions of pile body and the ultimate skin friction is directly proportional to the value of φ_c. The increment of ultimate skin friction is relatively small when φ_c is larger than 1φ_c0 due to the interfacial friction angle cannot beyond the inner friction angle of the soil adjacent [ 9] generally. Unlike the influence of c_c on pile-soil interaction, the incremental quantity of ultimate skin friction under different φ_c is not a certain value.

The influence of φ_c on pile-soil interaction can also be explained by equitation (1). Figure 7 illustrate the relationship of the ultimate skin friction and the soil pressure under different φ_c based on the Mohr-Coulomb shear theory. It can be seen that under a small soil pressure σ₁ (namely, at a shallow position of pile body), both of the ultimate skin friction and the differential value between the ultimate skin fiction under φ₁ and φ₂ (φ₁ is larger than φ₂) are relatively small, and vice versa. Compared with the interfacial cohesion, the interfacial friction angle has a greater influence on the development of skin friction; and the impact will be more obvious when soil pressure around pile body hits to a relatively large value.

A simplified method for the determination of pile-soil interface parameters

The proposal of the method

As mentioned before, for pile under tension, the following rules can be drawn on the selection of interface parameters:

1) The shear stiffness k_s is related to the slope of the f-Δs curve, and the larger of k_s, the greater of the slope. At the same position of the pile body, the pile-soil relative displacement where the ultimate skin friction generated will be reached fast if a small value of k_s is selected. Therefore, a rational value of k_s is important to the development of skin friction.

2) Both of the interfacial cohesive c_c and the interfacial friction angle φ_c are directly proportional to the ultimate skin friction. Compared with the interfacial cohesion, the interfacial friction angle has a greater influence on the skin friction; and the impact will be more obvious when soil pressure around pile body hits to a relatively large value.

Based on the analysis above and taking into account the other circumstances that may exist in a practical project, a simplified method for the determination of pile-soil interface parameters in layered soil are summarized as shown in Fig. 8. It is worth noting that some factors in practical site are considered in the proposed method shown in Fig. 8, so that the method can be applicable to different situations. First, if there are some recommend values of c_c and φ_c that measured by indoor or field tests, the interface parameters can be determined directly and small adjustment may be needed for k_s. Secondly, if there are some measured data like Q-s or f-Δs curves in field site, the interface parameters (c_c and φ_c) can be determined according to the Mohr-Coulomb criteria by reverse calculating the layout of the soil pressure around the foundation. Thirdly, if there are no suggested data, the interface parameters can be deduced by the trial calculation which is described in the flow chart of Fig. 8. In all, the simplified method proposed in this paper can facilitate the determine process of interface parameters and it is suitable for different situations.

Verification example

To verify the reasonableness of the method proposed above, the SYZB01 pile in field loading tests on large-diameter and super-long bored piles of Shanghai Center Towers reported by literature [ 20] is simulated by FLAC^3D.

Since the formation of the site strata is relatively complex, the soil layers in this numerical simulation is simplified which is illustrated in Fig. 9. The test pile, with 1-m diameter and 63-m effective length, can be treated as a super-long pile. The pile is surrounded by double-layered-steel-casing pipe at depth from 0 to 20.7 m to be isolated from soil. The parameters of pile material and soil profile are listed in Table 2.

According to the method proposed in Fig. 8, set the values of k_n and k_s to be some times of the relevant parameters of soil adjacent, first. Due to the field data are in detail, the soil pressure can be derived as shown in Fig. 10. According to the distribution of soil pressure, the initial values of c_c and φ_c of each soil layer can be evaluated according to the Mohr-Coulomb shear theory as shown in Table 3.

After the initial determination of interface parameters mentioned above, trial calculations will be carried out according to the process shown in Fig. 8. After several times of adjustments and trials, the eventual results can be determined, as listed in Table 4. Compared to Table 3, the initial and the determinate values of c_c and φ_c are basically the same which indicate that by using the method proposed in this paper to determine c_c and φ_c based on soil pressure distribution is reasonable.

The final calculation results of Q-s curves and f-Δs curves are compared with the field data, as shown in Figs. 11 and 12. The results show that the calculated results are basically conform to the measured data on both settlement and bearing behavior, which indicate that the selection of pile-soil interface parameters are reasonable and can be used to simulate the behavior of the in situ pile-soil interaction. The simplified and practical method for the determination of pile-soil interface parameters in layered soil needs less time and works with higher accuracy.

Conclusion

From above investigation, the main conclusions can be summarized as follows:

1) The shear stiffness k_s is related to the slope of the f-Δs curve, and the larger of k_s, the greater of the slope. At the same position of the pile body, the pile-soil relative displacement where the ultimate skin friction generated will be reached fast if a small value of k_s is selected. Therefore, a rational value of k_s is important to the development of skin friction.

2) Both of the interfacial cohesive c_c and the interfacial friction angle φ_c are directly proportional to the ultimate skin friction. Compared with the interfacial cohesion, the interfacial friction angle has a greater influence on the skin friction; and the impact will be more obvious when soil pressure around pile body hits to a relatively large value.

3) This paper put forward a simple, practical method for the determination of pile-soil interface parameters in layered soil based on the sensitivity analysis of interface parameter, and the method needs less time and works with higher accuracy.

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