Mathematical Problems in Engineering

Volume 2016, Article ID 4860143, 15 pages

http://dx.doi.org/10.1155/2016/4860143

## Model Test Research on the End Bearing Behavior of the Large-Diameter Cast-in-Place Concrete Pile for Jointed Rock Mass

^{1}Civil and Engineering School, Harbin Institute of Technology, Harbin 150001, China^{2}Civil and Engineering School, Jilin Jianzhu University, Changchun 130118, China

Received 13 July 2016; Revised 29 September 2016; Accepted 19 October 2016

Academic Editor: Cheng-Tang Wu

Copyright © 2016 Jingwei Cai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

For large-diameter, cast-in-place concrete piles, the end bearing capacity of a single pile is affected by discontinuous surfaces that exist in natural rock masses when the bearing layer of the pile end is located in the rock layer. In order to study the influence of the jointed dip angle on the bearing characteristics of the pile end, the discrete element models are adopted to simulate the mechanical characteristics of the jointed rock masses, and the model tests of the failure mode of the jointed rock masses were also designed. The results of the numerical calculations and modeling tests show that the joints, which have a filtering effect on the internal stress of the bedrock located at the pile end, change the load transferring paths. And the failure mode of the jointed rock foundation also changes as jointed dip angle changes. The rock located at the pile end generally presents a wedge failure mode. In addition, the curves obtained by model tests show that the ultimate end bearing capacity of a single pile is influenced by the jointed dip angle. The above results provide an important theoretical basis for how to correctly calculate end resistance for a cast-in-place concrete pile.

#### 1. Introduction

To improve the end bearing capacity of large-diameter cast-in-place concrete piles, it is best to select rock strata as the bearing stratum at the pile end. Researches by Serrano and Olalla [1, 2], Yang and Yin [3], Saada et al. [4], and Imani et al. [5] focused on the rock mass according to the Hoek-Brown failure criterion, which is applied for intact rocks. However, in practical engineering, the most natural rock masses are made of rock blocks and discontinuous surfaces, and the discontinuity plays an important role in rock deformation and the failure mechanism. However, conducting a destructive test to determine the ultimate bearing capacity of a single pile in a prototype test is cost prohibitive, which limits researchers’ ability to collect sufficient experimental data in order to better understand bearing behavior. This is especially true when the bedrock of the pile end is discontinuous, in which case, even with a large field test, it is very difficult to gather data necessary for a qualitative analysis of the influence of jointed dip angles on bearing capacity. Thus, research needs to focus on how to correctly calculate the end bearing resistance of a single pile in a jointed rock foundation.

At present, some researchers conducted studies on the bearing behavior of jointed rock masses. Reik and Zacas [6] studied the strength and deformation characteristics of jointed media in true triaxial compression. Yang et al. [7] carried out uniaxial compression test of shale rock and found that there are three kinds of failure modes for the jointed rock and that a change in the dip angle caused changes in the failure modes. Yang et al. [8] conducted a uniaxial compression test using marble specimens with prefabricated joints and described the relationship between the dip angle and the failure mode of nonconsecutive jointed rock. Mas Ivars et al. [9] described a new approach they called synthetic rock mass modeling for simulating the mechanical behavior of a jointed rock mass. Zhou et al. [10] fabricated rock-like materials containing multiple fissures under uniaxial compression to further research the effects of preexisting fissures on mechanical properties and crack coalescence of rock. Compared with previous experiments, they found five types of cracks, including wing cracks, quasi-coplanar secondary cracks, oblique secondary cracks, out-of-plane tensile cracks, and out-of-plane shear cracks and ten types of crack coalescence. Gao and Kang [11] demonstrated a numerical analysis using a discrete element method simulation for the jointed rock masses. And the numerical results indicate that fracture intensity has no significant influence on the residual strength of jointed rock masses, independent of confining conditions. Cao et al. [12] combined similar material testing and discrete element numerical method (PFC2D) to study the peak strength and failure characteristics of rock-like materials with multifissures. The failure mode can be classified into four categories: mixed failure, shear failure, stepped path failure, and intact failure. And the results show that the peak strength and failure modes in the numerically simulated and experimental results are in good agreement. Yang et al. [13] studied the relationship between the 3D morphological characteristics and the peak shear strength for jointed rock. And a new peak shear strength criterion for rock joints was proposed using two 3D morphological parameters. Furthermore, the calculated peak strengths using the proposed criterion match well with the observed values. Huang et al. [14] did a series of uniaxial compression tests to research the effects of preexisting fissures on the mechanical properties and crack coalescence process for rock-like material with two unparallel fissures. And the strength and deformability characteristics of rock with preexisting fissures are governed by cracking behavior.

Although the above research results could be applied to a jointed rock mass, the results are different from the jointed rock foundation of a pile end that supports the vertical load from the pile and thus produces different failure modes. Kulhawy and Goodman [15] put forward that the spacing of horizontal and vertical joints is the essential factors in the ultimate pile end resistance. Benmokrane et al. [16] conducted a rock-socketed pile model test and illustrated that when weak intercalated layers exist within the rock mass, the ultimate end bearing capacity is influenced by the different jointed dip angles. Maghous et al. [17] assessed the load bearing capacity of rock foundations resting on a regularly jointed rock and considered the rock matrix and the joints separately. They then compared the obtained results with those derived through considering the jointed rock mass as a homogenized medium. Sutcliffe et al. [18] analyzed the bearing capacity of rock masses containing one to three sets of closely spaced joints. Halakatevakis and Sofianos [19] used a distinct element code to analyze a series of jointed rock samples containing one to three joint sets with various spacing and dip angles and concluded that the strength of the models was independent of the joint spacing. Yu [20] proposed the extended finite element method (XFEM), a numerical method for analyzing discontinuous rock masses that is very convenient for preprocessing. In this model, discontinuities, such as joints, faults, and material interfaces, are contained in the elements, so the mesh can be generated without taking into account the existence of discontinuities. Hossein et al. [21] used distinct element method to build a numerical model to evaluate bearing capacity of strip footing rested on anisotropic discontinuous rock mass. And the results show that the failure mechanism of rock mass depended on both geometrical parameters of joint sets and strength parameters of rock mass.

In order to study the relationship between jointed dip angles and the end bearing characteristics of a single pile, we use discrete element models to simulate the mechanical characteristics of jointed bedrock with different inclination angles. The laboratory model tests are designed to analyze the failure modes, cracking mechanism, and variations in the ultimate end bearing capacity when the jointed dip angles and jointed numbers are changed. The results obtained from the model tests are compared with the numerical analysis results to verify the correctness of the related theory of the failure mechanism of the jointed rock mass.

#### 2. Numerical Analysis of the Failure Mode

##### 2.1. The Theoretical Basis of Discrete Element Method

The failure modes of the jointed rock foundation are simulated with different jointed dip angles according to the discrete element method. Discrete element method (DEM) was firstly proposed by Cundall in 1971. This method is based on the discrete characteristics of material itself to establish numerical model. It shows great superiority in simulating discrete material.

The discrete element program PFC (particle flow code), which can simulate circular particle movement and interaction, is adopted to simulate the failure. The interactional force of particles is calculated according to Newton’s second law and the contact law of force. Discrete element analysis considers the following interactional forces: () the force of gravity; () the contact force between particles and between particles and walls; () the frictional force between particles and between particles and walls. The calculated results are compared to the experimental results in order to verify the correctness of the theoretical analysis.

The basic motion equation of the discrete element is built by dynamic relaxation method as where is the quality of a unit; is the displacement of a unit; is the time; is the viscous damping coefficient; is the stiffness coefficient; is the external load of a unit. Equation (1) can be changed into the following form as equation (2) by using the central difference method.where is the calculating time step and (3) can be obtained by changing (2):

The velocity and acceleration of the particles in the time of can be obtained by bringing into the following two equations:

So it can be seen that the central difference method is used in discrete element method. It is an explicit solution which does not require the solution of a large matrix and saves the computing time. And this method can be used to solve some nonlinear problems.

##### 2.2. Setup Simulation Models and Determination of the Basic Parameters

The model is made up of an end-closed cylindrical container filled with well-compacted round particles and a pipe-shaped model pile. The soil model with a width of (W) and a height of is used, where is the pile diameter and is equal to 50 mm. And the pile length is 20 mm. The roughness of the pile surface can be set up to simulate the friction coefficient.

The relative parameters of particles are shown in Table 1 obtained by general triaxial test of particle flow code. A set of parameters, which can reflect the macroscopic mechanical behavior of rock mass, are obtained by constantly adjusting the microparameters. And this set of parameters could reflect the strength and deformation characteristics of the rock materials. The rock models, which are composed of balls with the diameters uniformly varying between 2 mm and 3 mm, contained intact rock models and the jointed rock models with the dip angles of 0°, 10°, 30°, 45°, 60°, 75° and 90°, respectively.