Advances in Materials Science and Engineering

Volume 2017 (2017), Article ID 6241479, 15 pages

https://doi.org/10.1155/2017/6241479

## Permanent Deformation Characteristics of Coarse Grained Subgrade Soils under Train-Induced Repeated Load

^{1}School of Civil Engineering, Harbin Institute of Technology, Heilongjiang, Harbin 150090, China^{2}School of Transportation Science and Engineering, Harbin Institute of Technology, Heilongjiang, Harbin 150090, China

Correspondence should be addressed to Peng Li

Received 30 August 2016; Revised 12 December 2016; Accepted 26 December 2016; Published 6 February 2017

Academic Editor: Donato Sorgente

Copyright © 2017 Xianzhang Ling 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

This paper presents the results of a laboratory experiment that aimed to characterize the permanent deformation behavior of coarse grained soils. To evaluate the effects of the cyclic stress amplitude, initial mean stress, and initial stress ratio on the permanent axial deformation, six series of repeated load triaxial tests were performed. The results indicate that permanent deformation of coarse grained soils increased with increasing cyclic stress amplitude. In particular, for relative low cyclic stress levels, accumulation rate of permanent deformation decreased progressively with number of cycles and eventually reached an equilibrium state. The initial stress ratio was also found to obviously facilitate the buildup of axial deformation since it means higher deviatoric stress as the mean pressure kept constant. As the initial stress ratio was less than the slope of static failure line, the experimental results indicated that the increase of initial mean stress enhanced the capability of resisting deformation. A simplified mechanistic empirical prediction model was proposed, which predicted the permanent deformation as product of four independent functions about cyclic stress amplitude, initial mean stress, initial stress ratio, and number of load cycles. Satisfactory predictions of the permanent deformation behavior of coarse grained soils were obtained with the proposed model.

#### 1. Introduction

Increased wheel loads and speeds of freight rail traffic are accelerating the track deterioration of railway lines. In general, a dominant factor of the deterioration in ballasted tracks is uneven subsidence of ballast and subgrade layer due to the cumulative plastic deformation. So as the foundation of track structure, a properly compacted good quality subgrade will effectively absorb and dissipate train vibration loads and further provide strong underneath supports to the upper components through high shearing resistance. In real project, the guidelines for deformation control during track subgrade construction are generally based on the method of setting a reserved settlement amount. Thus, detailed understanding and characterization of the deformation behavior of subgrade soils are a prerequisite for both the construction and subsequent maintenance of railway substructure.

Coarse grained soils, which are generally the main construction materials of subgrade layer in railway system, usually present two types of deformation behavior when subjected to repeated traffic-type dynamic load: (a) resilient or recoverable deformation, which is related to the load-carrying ability of track structure, reflects stiffness properties of the material and (b) residual or irreversible deformation, which contributes to most of the subgrade settlement, determines long-term performance of railway line [1–4]. Although small compared to the resilient deformation, the residual deformation accumulates in each load cycle and may eventually reach a significantly large value that causes subgrade failure.

Over the years, considerable investigations have been devoted to characterizing the resilient behavior of soils using laboratory techniques, and lots of mathematical models have been developed to predict resilient response considering the effects of stress levels, void ratio, and some other factors [5–8]. For instance, in view of the material nonlinearity, Seed [9] introduced the concept of resilient modulus first, which was defined as the ratio of cyclic stress level to recoverable axial strain, and some similar definitions were widely used by later researchers. In contrast, the permanent deformation behavior of coarse grained soils is still less clearly known in practice. Although it is easy to measure the settlement in railway subgrade, exact prediction of the permanent deformation development is an extremely difficult matter. The most possible reason is that the deformation accumulation under repeated loading is a time-consuming process affected by too many factors, and the obtained test results are much more scattered than resilient modulus tests [10, 11].

The permanent deformation investigations are mostly based on repeated load triaxial tests, and stress state unquestionably is the most important factor affecting the development of permanent deformation for coarse grained soils. In early stage, some investigations based on repeated load triaxial tests found that, to a certain physical condition, the permanent axial strain clearly increased with increasing cyclic stress and decreasing confining pressure [12]. In this sense, it is principally some forms of stress ratio that governed the permanent deformation behavior in the tests, and more research attention was paid to the deformation prediction model based on that stress ratio. Afterwards, several research workers also attempted to correlate the results under repeated loading with the failure deviator stress from monotonic tests [13–15]. In such an approach, the failure line was considered as the boundary of equilibrium state and incremental collapse, and the amount of permanent deformation could be determined by how close the applied stress path to the material failure line. Raymond and Williams [16] introduced a stress ratio of the maximum deviator stress divided by monotonic failure stress to characterize the test results and reported good correlation with laboratory observations. It is important to note that the anisotropic consolidation cases are not considered in this method; that is to say, the same permanent strain will be obtained as long as identical maximum deviator stresses are applied. Pappin [17] observed this problem and alternatively described the permanent strain with ratio of deviator stress amplitude to mean normal stress. Good performances of this model were reported without other verification found in the literatures. However, several researchers [18] have investigated and questioned the approach of predicting the permanent deformation of coarse grained soils under repeated loading based on monotonic failure stress, since unreasonable results were obtained for describing their experimental data. They argued that the failure of specimen under monotonic loading presented as sudden collapse, but it was a gradual process when subjected to cyclic loading, so the structural response of the materials may not be the same in these two kinds of tests.

Generally, most of the experimental results show that permanent deformation buildup of coarse grained soils under repeated loading is actually a ceaseless gradual process, which means that in each load repetition a small strain increment will be accumulated to the total deformation. Morgan [19] conducted a series of repeated load triaxial tests with up to load cycles and found that the increase of permanent strain did not cease even at the end of the tests. Based on this deformation behavior, lots of prediction models without asymptotic values were proposed [20, 21]. In the meantime, still some researchers believed that the deformation at relative low stress levels will eventually reach an equilibrium state, during which no further permanent strain increase occurred with increasing number of load cycles [18, 22–24]. So it can be seen that, maybe due to the material nonlinearity caused by large particles, the permanent deformation behavior of coarse grained soils varies significantly under the same loading conditions.

The major objective of this research is to examine the influence rules of the factors such as cyclic stress amplitude, initial mean stress, and stress ratio and to develop an improved empirical model for capturing the permanent deformation behavior of coarse grained soils under train-induced repeated loading. The model is developed based on repeated load triaxial tests where it is possible to analyze the deformation behavior for a wide range of stress conditions, especially for the isotropic consolidation cases common in subgrade layer. Some widely used existing prediction models will also be compared with the present model to verify its performance.

#### 2. Existing Permanent Deformation Models

Permanent deformation prediction models are generally divided into two categories: incremental models based on elastoplastic theory and mechanistic-empirical models from plentiful test data [26]. Incremental models can accurately quantify the effects of stress amplitudes and paths on the permanent deformation, but the complex and time-consuming nature also makes them hard to implement. In contrast, mechanistic-empirical models can generally produce prediction results in acceptable accuracy with less parameter and computing time, so they are more widely used in practical subgrade design. Although plenty of empirical models have been proposed by different researchers, only some famous and widely used ones are summarized in this section.

The first well-known prediction model is that proposed by Barksdale [20], who performed repeated load triaxial tests on various base coarse materials, and proposed a linear relationship between permanent axial strain and the logarithm of number of load cycles as

Later, Monismith et al. [27] and Sweere [21] found that the semi-log model did not well fit the experimental data for larger numbers of load cycles, so a power law model or log-log model was suggested as follows:

Wolff and Visser [28] performed a series of full-scale heavy vehicle simulator tests on granular materials with millions of load cycles but observed that both the logarithm model and log-log model tended to underestimate the permanent strain at small number of load cycles and in reverse overestimate it for larger cycles. Based on test results, they described the buildup of permanent strain with a model consisting of two phases likewhere and are, respectively, the slope and intercept of the asymptote and is a parameter controlling the curvature. Pérez et al. [29, 30] verified reliability of the above-mentioned models by fitting models with measured results of repeated load triaxial tests but found that (3) also overestimated the results for large load cycles.

To take into account the stress dependency nature of prediction models, Li and Selig [14] investigated the influence factors of parameters in (2a) and obtained the following improved model:in which is soil static strength. For the same soil type, exponent was concluded independent of soil deviator stress and physical state. However, Korkiala-Tanttu [31] performed similar research and proposed the model as (5):where is the shear failure ratio; is the failure line in - space; and are material parameters. It can be seen that the accumulation rate (curvature) of this model depends on the stress level and physical state, conflicting with the conclusions of Li and Selig.

On the other hand, in addition to those growth-type prediction models, a representative model with a stabilization prediction value may be the one proposed by Paute et al. [32] as (7), which simultaneously depicted the effects of both stress levels and number of load cycles on the buildup of permanent strain:in which is the accumulated permanent axial strain during the first 100 cycles; and are regression parameters. In reality, we can see that as load cycle increases toward infinity, the limit value represents additional permanent strain for . Thus, the authors expressed with stress states by another equation as follows:where and are the maximum deviator stress and maximum mean normal stress and is a stress parameter defined by intersection of the failure line and the -axis. Lekarp et al. [18] and Pérez et al. [30] used this model to fit their experimental data, but they all believed that the (8) did not well represent the limit value of permanent deformation.

#### 3. Cyclic Load Triaxial Test Program

##### 3.1. Test Equipment

In present research, all tests were carried out with the repeated load triaxial apparatus MTS-810 at State Key Laboratory of Frozen Soil Engineering of Chinese Academy of Science. Figure 1 shows the configuration of the test equipment. Both the axial load and confining pressure are applied through two sets of independent servohydraulic actuators, which can provide a maximum axial force up to 250.0 kN and a maximum confining pressure of 20.0 MPa on normal specimens of 61.8 mm in diameter and 125.0 mm in height. During each test, the cyclic load can be applied with a frequency range of 1~50 Hz employing built-in sine, triangular, and square waveforms or any other user-defined ones by means of external input. The axial deformation of specimen is measured through one linear variable differential transformer equipped on load piston of the apparatus, and the maximum scale range is 85.0 mm with an accuracy of 0.001 mm. Data points sampling intervals can be set through the data acquisition and control system which is connected to the central computer. More detailed information about the apparatus can be found in [1].