Predicting the shear characteristics of rock joints with asperity degradation and debris backfilling under cyclic loading conditions

doi:10.1016/j.ijrmms.2019.06.001

International Journal of Rock Mechanics and Mining Sciences

Volume 120, August 2019, Pages 108-118

https://doi.org/10.1016/j.ijrmms.2019.06.001 Get rights and content

Abstract

This study presents a constitutive model to predict the shear behavior of rock joints under cyclic loading. The model focuses on asperity degradation and debris backfilling during a complete shear cycle. The degradation of two-order asperity is associated with the evolution of waviness and unevenness based on the classic wear theory. The produced debris significantly influences the joint shear behavior in the subsequent shear processes, and its thickness is dependent on shear displacement, joint length, as well as worn area and wavelength of asperities. The model particularly considers the dilation angles of waviness, unevenness, and backfilled debris at different processes during the shear cycle. The validation results show that the model can well predict the shear behavior of regularly shaped joints, but the accurate prediction for irregularly shaped joints depends on the quantitative description of joint surface roughness. The proposed model uses the quantitative description of joint profiles to evaluate the shear behavior of rock joints, which is more practical than previous models relying on empirical judgement or data back analysis.

Introduction

Joints significantly influence the shear resistance of rock masses, which is a key issue in the design and construction of underground structures. The shear behavior of rock joints is difficult to predict, as it is associated with several geometrical and mechanical properties, such as surface roughness and asperity strength. When rock joints are subjected to cyclic shear loading due to earthquakes and blasting operations, the progressive degradation of two-order asperities and the mechanical response of backfilled debris may result in the shear behavior more complicated. Understanding the evolutionary process of rock joints under cyclic shear loading is crucial to predict the dynamic response of jointed rock masses.

Most existing studies focus on the shear behavior of rock joints under direct shear conditions, which is commonly encountered after perturbing an initial equilibrium state of rock masses.1, 2, 3, 4, 5, 6, 7, 8 The mechanical behavior of rock joints under cyclic shear loading has received increasing attention, as the joint behavior may evolve with asperity degradation and debris backfilling. On the one hand, Barton⁹ developed the JRC (joint roughness coefficient)-JCS (joint wall compressive strength) model to simulate the shear behavior of rock joints under cyclic loading. The development of the JRC-JCS model stems from the statistical analysis of experimental data,¹⁰^,¹¹ which is difficult to accurately predict asperity degradation and joint dilation.12, 13, 14 Asadollahi and Tonon¹¹ used JRC to study the shear behavior of rock joints under cyclic loading, and showed that JRC is a good option but not very satisfactory in some cases. On the other hand, Plesha¹⁵ proposed a constitutive model based on the classic plasticity theory, by which the asperity degrades exponentially accompanied by plastic deformation. This model focuses on the shear behavior of regular shaped rock joints, and motivates several studies on the shear behavior of irregular shaped joints.¹³^,16, 17, 18, 19 However, the model is limited to predict joint dilation using empirical coefficients. Moreover, previous studies rarely consider the generation and backfilling of debris during cyclic shear loading.20, 21, 22, 23, 24, 25, 26

This paper introduces a constitutive model to predict the shear behavior of rock joints with asperity degradation and debris backfilling under cyclic loading. We particularly consider the evolution of waviness and unevenness and the dilation angle of backfilled debris. The mechanical involvements of waviness and unevenness in the shear process are respectively represented by the critical waviness and the critical unevenness.¹⁴^,²⁷ All the parameters required by the model are obtainable from laboratory experiments. The constitutive model is validated with existing experimental results on both regularly and irregularly shaped joints.

Section snippets

Problem description

Fig. 1 depicts a rock block containing a naturally matched joint subjected to a cyclic shear stress ( $τ$ ) and a constant normal stress ( $σ_{n}$ ). The upper block can move horizontally and dilate vertically. The lower block is fixed in both directions. The joint profile inherently possesses waviness and unevenness.¹⁴^,²⁸ The geometrical properties of waviness include the initial angle ( $i_{0}$ ), wavelength ( $λ_{w}$ ), and amplitude ( $A_{w}$ ). The geometrical properties of unevenness are the initial angle ( $α_{0}$ ),

Model validation

In the implementation of the proposed model, we use a shear stiffness reduction factor R, which is defined as the ratio between the actual and the mobilisable shear stresses³³: $R = 1 - \frac{τ}{τ_{m}}$

The slope of the shear stress-shear displacement curve, $R k_{s}$ , is able to smoothly transit from the elastic stage to the plastic stage (Fig. 2a).

We separately consider the shear stiffness in the forward ( $k_{s}^{F}$ ) and backward ( $k_{s}^{B}$ ) shear processes, which can be estimated from the slopes of corresponding shear

Prediction errors

We appraise the performance of the proposed model by comparing the analytical predictions to the experimental data obtained from the cyclic shear tests on regularly and irregularly shaped rock joints under varying normal stresses. To examine the accuracy of the analytical predictions, the average percent error ( $δ_{a v e}$ ) is used as a precision index. The average percent errors of shear stress ( $δ_{a v e} (τ)$ ) and dilation ( $δ_{a v e} (δ_{n})$ ) are respectively: $δ_{a v e} (τ) = \frac{1}{n} \sum_{i = 1}^{n} | \frac{τ^{exp} - τ^{a n a}}{τ^{exp}} | \times 100 %, δ_{a v e} (δ_{n}) = \frac{1}{n} \sum_{i = 1}^{n} | δ_{n}^{}$

Conclusions

In this paper, we proposed a constitutive model to predict the shear characteristics of tightly mated rock joints subjected to cyclic loading. This model evaluates the shear stress and dilation as a function of shear displacement during a complete shear cycle, and particularly considers asperity degradation and debris backfilling. Based on the classic wear theory, the degradation of two-order asperity develops during the shear process, and changes initial waviness and unevenness into worn

Acknowledgements

This study was supported by the Ministry of Education - Singapore (Grant No. RG169/16). Yingchun Li thanks the financial supports from the National Natural Science Foundation of China (Grant No.51809033), the China Postdoctoral Science Foundation (Grant No.2018M631789), the National Key Research and Development Plan (Grant No.2018YFC1505301), and the Fundamental Research Funds for the Central Universities, China (Grant No. DUT19RC(4)022). Bo Liu thanks the support from the National Natural

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Predicting the shear characteristics of rock joints with asperity degradation and debris backfilling under cyclic loading conditions

Abstract

Introduction

Section snippets

Problem description

Model validation

Prediction errors

Conclusions

Acknowledgements

Int J Rock Mech Min Sci

Int J Rock Mech Min Sci

Eng Geol

Int J Rock Mech Min Sci

Eng Geol

Int J Rock Mech Min Sci

Comput Geotech

Comput Geotech

Int J Rock Mech Min Sci

Int J Rock Mech Min Sci

Int J Rock Mech Min Sci

Int J Rock Mech Min Sci

Soil Dynam Earthq Eng

Int J Rock Mech Min Sci

Eng Geol

Int J Rock Mech Min Sci

Int J Rock Mech Min Sci

Int J Rock Mech Min Sci

Int J Rock Mech Min Sci

J Struct Geol

Eng Geol

Int J Rock Mech Min Sci

Int J Rock Mech Min Sci

Simulation of shear behavior of a jointed rock mass

The shear strength of rock joints in theory and practice

Rock Mech