Evaluation of existing criteria in estimating shear strength of natural rock discontinuities

Highlights

• Direct shear tests were performed on natural discontinuities of granite, quartzite, and sandstone.

• The determined shear strength was compared with the shear strength estimated by eleven shortlisted shear strength criteria.

• Efficiency of these criteria in predicting shear strength of natural rock discontinuities was evaluated.

• Plausible reasons behind all the findings of the study were explained.

Abstract

As evident from the literature, there are a number of shear strength criteria proposed by different researchers. In spite of that, Barton's JRC-JCS model is probably the most widely used criterion in routine engineering environments. Ease of determining the input parameters and efficiency in estimating the shear strength are the two key aspects which make this criterion widespread in rock engineering activities. When the shear strength criteria existing in the literature had been analyzed by the authors, it became apparent that the difficulty levels or eases involved in determining the input parameters of eleven criteria, including Barton's criterion, are broadly comparable. However, the existing criteria do not seem to have been compared in terms of their practicality/applicability while estimating shear strength of ‘real’ natural rock discontinuities. In the present investigation, a total of 196 direct shear tests were performed on natural discontinuities of three distinct rock types (i.e. granite, quartzite, and sandstone) from India at normal stresses within a range of 0.22–2.01 MPa. The estimated shear strengths were compared to the determined shear strengths. The efficacies of the eleven shortlisted criteria in estimating shear strength of ‘real’ natural rock discontinuities were critically evaluated. The criteria emerged to be the most efficient in this regard were highlighted and plausible reasons behind all the findings of this study were also explained.

Introduction

At shallow depth, rock mass failure commonly occurs along weak planes/discontinuities (e.g. joints, faults, bedding planes, foliations, etc.) in shear mode under constant normal load condition because of low stresses (Singh and Rao, 2005, Hoek, 2007). This is controlled by shear behaviors of rock discontinuities. Therefore, an accurate determination of shear strength is crucial for designing safe structures on or within rock masses. With regard to shear strength evaluation through laboratory investigation, the direct shear test has gained significant attention. It should, however, be noted that direct shear test requires a costly shear test apparatus and moreover, it involves a difficult, complex and time-consuming procedure of sample collection and preparation. Therefore, estimation of shear strength empirically by using existing shear strength criteria has got obvious advantages. In the past few decades, many researchers proposed empirical shear strength criteria (Table 1). However, amongst these criteria (Table 1), the JRC-JCS criteria proposed by Barton (1973) and Barton and Choubey (1977) are the most commonly used formulations because of their simplicity and ease to estimate the shear strength. Many researchers (e.g. Zhao, 1997, Geertsema, 2002, Wines and Lilly, 2003, Jiang et al., 2006, Shigui et al., 2011, Sow et al., 2016) also evaluated the reliability of the said criteria which did not always ensure satisfactory estimation of the shear strength of natural rock discontinuities. For example, Kulatilake et al. (1995) indicated that the JRC-JCS model does not have the competence to capture non-stationary profiles. Other researchers like Zhao (1997), Geertsema (2002) and Shigui et al. (2011) mentioned that the said model overestimates the shear strength of natural rock discontinuities. Wines and Lilley (2003) demonstrated that the JRC-JCS model underestimates the shear strength at a low normal stress-range of 300–700 kPa whereas the model overestimates the shear strength at a relatively higher normal stress (i.e. > 700 kPa). Jiang et al. (2006) performed direct shear tests on mated replica joints and compared the determined shear strength values with the ones estimated through the JRC-JCS model. They observed that as normal stress increases, the JRC-JCS model results in overestimation of the shear strength.

Singh and Basu, 2016, Singh and Basu, 2017 indicated that the un-matching discontinuities are frequently observed at shallow depth because of preferential weathering and subsequent erosion of the contact planes of natural rock discontinuities due to movements of various fluids in situ. Sometimes, discontinuity mismatching in situ can also be caused by nearby blasting, excavation or earthquake (Tang et al., 2016a, Tang et al., 2016b). Shigui et al. (2011) concluded that the reliability of shear strength and friction angle estimated through the JRC-JCS model is not always consistent particularly for natural un-matching rock discontinuities.

Some researchers (e.g. Barton, 1973, Barton and Choubey, 1977, Bandis, 1980, Grasselli, 2001, Usefzadeh et al., 2013, Xia et al., 2014, Bahaaddini et al., 2016, Singh and Basu, 2016) indicated that the shear strength is significantly influenced by surface morphology. However, the JRC-JCS model does not have any parameter which can represent surface morphology of a rock discontinuity.

There are other empirical shear strength criteria, proposed by researchers based on their direct shear test investigations in the laboratory, existing in the literature (Table 1). Some researchers suggested that the reliability of shear strength estimation through their proposed criteria needs to be evaluated for natural rock discontinuities (e.g. Ghazvinian et al., 2012, Jang and Jang, 2015, Kumar and Verma, 2016, Zhang et al., 2016). However, it is noticeable that the efficacy of these criteria in estimating the shear strength does not seem to have been assessed by other researchers with reference to natural rock discontinuities. Consequently, it becomes difficult for a practitioner to decide the most appropriate criterion amongst the existing ones (Table 1) to estimate the shear strength in a particular engineering environment. The aim of this study is to shade light on the comparison of measured and estimated shear strength values of natural un-matching rock discontinuities, frequently observed at shallow depth, in order to select the most appropriate shear strength criterion/criteria from the existing ones.

It is apparent from Table 1 that all the indicated shear strength criteria are not easy to be employed for estimating the shear strength because of their formulation-complexity and rigorous nature in estimating the input parameters. In other words, some of the criteria involve assessment of intricate input parameters that are sometimes beyond the scope of determination/estimation in the laboratory (Grasselli, 2001). For example, in the case of Ladanyi and Archmbault (1969)-model, estimation of the input parameter ‘α_s’ (i.e. sheared area of the asperities) is not easy under laboratory conditions (Grasselli, 2001). The Zhao (1997)-model includes ‘Joint Matching Coefficient (JMC)’ (a measure of approximate contact area between lower and upper halves of a direct shear test sample) as an input parameter which is primarily estimated by visual examination. Such estimation is subjective in nature and depends on the assignee. In the case of Tang and Wong (2016)-model, the input parameter ‘k’ (i.e. ratio of imposed dislocation (d) to the length of the sample along the shear direction (l)) is challenging to estimate in situ. Similarly, there are also other input parameters associated with different shear strength criteria which are not easy to estimate either in situ or in the laboratory. In the present investigation, only those criteria are selected which are simple, less time consuming in terms of estimating input parameters both in situ and in the laboratory, and cover almost all parameters that primarily influence the shear strength. Thus, a total of eleven empirical shear strength criteria (i.e. Eqs. (4), (11), (13), (16–21), (24) and (25) in Table 1) are shortlisted to compare their efficacies in predicting the shear strength. It should be noted that the simple criterion proposed by Patton (1966) (Eq. (1) in Table 1) is not considered as this model was developed based on direct shear tests on regular saw-tooth samples which do not resemble shear test samples with natural rock discontinuities.

In this study, direct shear tests are carried out on natural unfilled and un-matching discontinuities of the three distinct rock types (i.e. on joints in granite and quartzite and on bedding planes of sandstone) under constant normal load condition where the applied normal stress range is 0.22–2.01 MPa. Subsequently, the measured shear strength (obtained from the shear stress vs shear displacement plot) is compared with the shear strength estimated using the shortlisted criteria. The influence of normal stress on the prediction efficiency of the shear strength criteria is also studied. Based on the present investigation, applicability of the shear strength criterion/criteria for estimating the shear strength of natural un-matching rock discontinuities is suggested.