A modified model of a single rock joint shear behavior in limestone specimens

📝 Abstract

The shear behavior of a single rock joint in limestone specimens, under a constant normal load (CNL), was analyzed in this study. Test specimens with different asperity roughness were prepared and tested. The Goodman model of a rock joint shear behavior, under CNL, was modified to render a better representation of the data obtained. The model applicability was validated. The proposed model shows better correlation with experimental data. It also, requires fewer variables. The steps to calculate all the necessary variables for the model are discussed.

💡 Analysis

The shear behavior of a single rock joint in limestone specimens, under a constant normal load (CNL), was analyzed in this study. Test specimens with different asperity roughness were prepared and tested. The Goodman model of a rock joint shear behavior, under CNL, was modified to render a better representation of the data obtained. The model applicability was validated. The proposed model shows better correlation with experimental data. It also, requires fewer variables. The steps to calculate all the necessary variables for the model are discussed.

📄 Content

1    This paper is accepted for publication in the International Journal of Mining Science and Technology

A modified model of a single rock joint’s shear behavior in limestone specimens Dindarloo Saeid R a*, Siami-Irdemoosa Elnaz b

a Department of Mining & Nuclear Engineering, Missouri University of Science &Technology, Rolla, MO, USA b Department of Geosciences & Geological & Petroleum Engineering, Missouri University of Science &Technology, Rolla, MO, USA

ARTICLE INFO

ABSTRACT Article history: Received
Accepted
Available

The shear behavior of a single rock joint in limestone specimens, under a constant normal load (CNL), was analyzed in this study. Test specimens with different asperity roughness were prepared and tested. Goodman’s model of a rock joint’s shear behavior, under CNL, was modified to render a better representation of the data obtained. The model’s applicability was validated. The proposed model showed better correlation with experimental data. It also, requires fewer variables. The steps to calculate all the necessary variables for the model are discussed. Keywords: limestone rock joints Constant normal load Direct shear test

Nomenclature τ ൌShear Stress τp ൌPeak Shear Strength τr ൌResidual Shear Strength u ൌShear Displacement up ൌShear Displacement at Peak Shear Strength ur ൌResidual Displacement σn ൌNormal Stress σT ൌ Transitional stress in Ladanyi െArchambault
φ ൌInternal Friction Angle as ൌ Proportion of Total Joint Area Sheared Through Asperities
sr ൌ Shear strength of asperities k1 , k2 ൌ Empirical Constants in Ladanyi Archambault C1, C ൌFirst and Second Constants of the Experiment
in the Proposed Model vሶൌSecant Rate of Dilatancy at Peak Shear Strength i= Arctan ሺvሶሻ im ൌTriangular Asperity Angle Z ൌShear Strength Factor in the Proposed Model

• Corresponding author: Email: srd5zb@mst.edu, Tel: (+1) 573- 201-0737     2   

1. Introduction Rock joints are mechanical discontinuities that have geological origins. In general, the strength and deformability properties of these discontinuities are quite different from those of intact rock. In many cases, the discontinuities completely dominate both the shear and the deformation behavior of the in situ rock mass in given stress conditions [1- 2]. Engineers in the mining, civil, and petroleum industries often face problems that are associated with jointed rock masses. Rock joint’s shear behavior must be examined comprehensively to understand the jointed rock mass mechanical behavior. Many applications could benefit from the study of joints at a smaller scale, such as petroleum and energy recovery applications [3]. A number of researchers have tried to model the shear behavior of a single rock joint under laboratory conditions-most use the direct shear test. The test is conducted under two major boundary conditions. A direct shear test under constant normal load (CNL) and a direct shear test under constant normal stiffness (CNS). A CNL is used when the rock can dilate freely i.e. with constant normal load under shear displacement. This situation is typically encountered in surface rock structures such as rock slopes. In case, the joint is constrained with surroundings materials and cannot dilate freely upon shearing, the normal load will increase. This load’s curve is controlled by the stiffness of surrounding rocks. The CNS condition is typically encountered in deep underground cavitations. The shear behavior of rock joints is not simply controlled by boundary conditions (i.e., either CNL or CNS). It is also controlled by a number of other important factors, including the intact rock properties, joint roughness, shear rate, and filling materials [4- 5]. A comprehensive mathematical model that considers all of these effective variables has not been developed. The application of experimental methods and models is necessary to addressing the difficulties of modeling this complex behavior analytically [6]. Experimental results are useful both in modeling and calibrating several of the model’s parameters. They are also useful in validating the results.
   Direct shear tests under the CNL condition were conducted on natural rock joints in this study. The results were used to render an experimental equation for the shear behavior. Tests specifications, specimens, and materials are introduced in Sec.
2. The Goodman’s model under the CNL condition and the proposed model are discussed in Secs. 3-4. Finally, Sec. 5 concludes the paper.
3. Specimens and tests specifications Fourteen limestone specimens were collected and prepared for the purpose of understanding the shear behavior of joints in limestone rocks. These specimens were collected from a dam site located inside a limestone zone. The direct shear test procedure conducted by Bandis et al [7] was used in this study. The material’s basic properties wer

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