A total of 36 groups of sandconcrete interface loading and unloading direct shear tests were used to analyze the mechanical properties of the pile sidesoil interface. The test results show that the interface residual shear stress for the same applied normal stress tends to be constant for the rough sandconcrete interface. The initial shear modulus and peak shear stress of the interface both decrease with the degree of unloading and increase with the interface roughness. The maximum amount of interface shear dilatancy increases with the degree of unloading, and the maximum amount of interface shear shrinkage decreases with unloading for the same interface roughness. A pile side resistancedisplacement model is established using the shear displacement method. The proposed function considers both the radial unloading effect and modulus degradation of soil around the pile. The effect of radial unloading and interface roughness on the degradation of the equivalent shear modulus is analyzed using a single fitting parameter
Piles are generally used to transfer loads from the superstructure to a competent soil or rock layer (
The shear displacement method assumes that the vertical displacement of the soil at any point around the pile is only related to the shear stress at this point, the shear stress transfer causes the settlement of the surrounding soil, and thus the stress and deformation characteristics of the pilesoil system can be obtained (
On one hand, although above scholars considered many factors that affect the pile side resistance developed, the soil radial unloading for the nondisplacement pile during boring stage almost has never been addressed. On other hand, the mechanical properties of soil around a nondisplacement pile are very different compared with those of loading soil (
In this paper, a series of sandconcrete interface loading and unloading direct shear tests are used to analyze the mechanical properties of the pile sidesoil interface. First, the effect of the unloading process and interface roughness on the mechanical properties of the interface are discussed. Then, a pile side resistancedisplacement model is established using the shear displacement method. The proposed
Although the largescale direct shear apparatus has some inherent defects, it is frequently used in interface research due to its simplicity in principle and operation. The test apparatus used in this experiment is the largescale multifunction direct shear test apparatus SJW200, which is independently researched and developed by Tongji University, Shanghai, China. The test apparatus has a large size shear box with net size 600 mm × 400 mm × 200 mm (length × width × height) and wall thickness of 40 mm. The test apparatus in both the normal and tangential directions is equipped with an advanced server and control system; the range of the test displacement and applied load are enough to satisfy the requirements of this paper. Compared with a conventional direct shear device, this test apparatus has more accurate test results because it can effectively reduce the boundary effect (
Schematic of the large direct shear apparatus.
The soil specimen was gray silt, which was obtained from a construction project in Shanghai City. The main properties of the soil are listed in
Parameters of the silt in tests.
Unit weight γ/(kN·m^{–3})  Cohesion 
Internal friction angle φ/(°)  Water content ω/%  Void ratio 
Compression modulus 

19.5  4  31.5  20  0.754  11.23 
Grainsize distribution of gray silt soil (accumulative granulometrical grapher).
Because the bored pile side surface is not smooth in actual engineering, it is necessary to consider the influence of the physical form of the sandconcrete interface. The key is how to simulate and define the roughness of the concrete plate. The quantitative criteria for the interface roughness are as follows.
Dove et al. (
Illustration of the interaction between soil particles and a concrete plate (after (
Zhang et al. (
Illustration of the rough steel plate shape and the definition of roughness (after (
Considering the advantages and disadvantages of the above interface roughness definition and the actual situation of the pile wall, the interface roughness model chosen in this paper is shown in
Illustration of the interface roughness model in this paper.
Three variations of concrete plates are used in this experiment, namely,
A total of 36 groups of sandconcrete interface direct shear tests with three different degrees of interface roughness and initial normal stress were used. The test soil is first consolidated under an initial normal stress
Curves of shear stressshear displacement for loading and unloading conditions: (a), (b) and (c) show the interface roughness at 0 mm, 10 mm and 20 mm, respectively.
The above can be explained by these points. Higher initial normal stress contributes to a higher density of the interface, which results in soil particles around the interface needing a higher shear stress to make them move along the roughness interface and each other. Therefore, interface peak shear stress increases with the initial normal stress at high roughness. If the interface roughness is low, the interface peak shear stress is mainly influenced by the water content of the interface soils rather than the density. Higher initial normal stress lowers the water content of the interface soils, and if the water content is below the optimal water content, the interface peak shear stress under unloading may be less than the loading condition.
The shapes of the curves for loading and unloading are both logarithmic, and the strain softening phenomena of the curves are also consistent between loading and unloading. These phenomena show that the effect of loading and unloading on the sandconcrete interface mechanical properties change the value of interface peak shear stress, but there is no fundamental change in the failure mode of the interface.
Curves of shear stressshear displacement for different unloading degree conditions: (a), (b) and (c) show the interface roughness at 0 mm, 10 mm and 20 mm, respectively.
The interface equivalent frictional angle
Roughness 
Initial normal stress /kPa  

100  200  300  
0  45.7°  46.5°  47.1° 
10  38.4°  44.5°  47.7° 
20  36.5°  43.3°  51.7° 
Fitting curves of peak shear stress and applied normal stress for different roughness conditions: (a), (b) and (c) show the initial normal stress at 100 kPa, 200 kPa and 300 kPa, respectively.
Variation curves of maximum interface shear dilatancy and shrinkage amount for different conditions: (a), (b) and (c) show the interface roughness at 0 mm, 10 mm and 20 mm, respectively.
The proposed pile side resistancedisplacement model curve, as shown in
Schematic of the proposed model.
The vertical displacement of the soil at any point around the pile is only related to the shear stress at this point, according to the shear displacement method assumptions, and can be expressed as [1] (
where
Randolph et al. (
where
The stressstrain behavior of most geomaterials is highly nonlinear at all phases of loading (
Degradation model of the G (
where
By introducing Eq. [3] into Eq. [2] and integrating them, Eq. [2] becomes [4]:
The concept of equivalent shear modulus
The shear modulus
where the coefficient
By introducing Eq. (
There are three methods for determining the peak pile side resistance
The
where
For normal consolidated soil,
The overconsolidation ratio OCR is calculated as [12]
where
Introducing Eq. [11], Eq. [12] and Eq. [13] into Eq. [10] becomes [14]
Eq. [22] is the peak pile side resistance calculation function that considering the unloading effect.
Randolph et al. (
where
From Eq. [15], it is relatively simple to determine the
The downward displacement of the soil at
Eq. [16] shows that the hold condition is
where
Eq. [18] shows that the
By introducing Eq. [14] and Eq. [18] into Eq. [9], the pile side resistancedisplacement model considering the unloading effect and soil modulus degradation is obtained as follows [19]:
The range of the coefficient
The value of parameter
The parameter
Recommended interface friction angle (after (
Pile material  δ 

Rough concrete 

Smooth concrete  0.8 
Steel  0.5 
Timber  0.8 
The initial shear modulus of the soil
where
The algorithm for the analysis of the pile side resistancedisplacement model can be summarized as follows:
The integral relation of τs function is derived by using the shear displacement method, as shown in Eq. [5].
The degradation model of the shear modulus is obtained by using the modified hyperbolic function, as shown in Eq. [8].
Solve the peak pile side resistance
Solve the limiting radius
Obtain the formula of the pile side resistancedisplacement model by introducing Eq. [8], Eq. [14] and Eq. [18] into Eq. [5], thus becoming Eq. [19].
The test results obtained by the largescale direct shear test are used to validate the pile side resistancedisplacement model. The parameter
where
The curves of
Comparison curves of the model calculation and test values for
Comparison curves of the model calculation and test values under
Comparison curves of the model calculation and test values for
Comparison curves of the model calculation and test values for
Degradation curves of the equivalent shear modulus.
The above analysis (section 5.1 to 5.3) shows that the value of the empirical coefficient
In this study, large scale direct shear tests are conducted to analyze the mechanical properties of the pile sidesoil interface. The effects of the unloading process and interface roughness on the mechanical properties of the interface are discussed. A pile side resistancedisplacement model is developed using the shear displacement method. The proposed function considers both the radial unloading effect and modulus degradation of soil around the pile. The main conclusions are drawn as follows:
The shapes of the interface shear stressdisplacement curves for loading and unloading are both logarithmic and the effect of loading and unloading on the sandconcrete interface mechanical properties mainly change the value of interface peak shear stress, but there is no fundamental change in the failure mode of the interface. The interface peak shear stress is mainly influenced by the soil density around the high roughness interface (
The interface peak shear stress, shear displacement corresponding to the peak shear stress and the interface initial shear modulus
The proposed pile side resistance displacement model considers both the radial unloading effect and modulus degradation of soil around the pile has been validated by the direct shear tests of 36 groups; The coefficient
The effect of radial unloading and interface roughness on the interface mechanical properties can be attributed to the degradation of the equivalent shear modulus
This work was supported by the National Key Research and Development Plan [grant number 2017YFC0806000], the National Natural Science Foundation of China under Grant [No. 41672265, No. 41572262, No. 41502275]; and Shanghai RisingStar Program under Grant No. 17QC1400600. The authors are deeply grateful for this support. The anonymous reviewers’ comments have improved the quality of this paper and are also greatly acknowledged.