Assessment of deformation modulus of weak rock masses from pressuremeter tests and seismic surveys

The deformation modulus of intact rock can be determined through standardized laboratory tests for heavily jointed rock masses but this is very difficult, while in situ tests are time-consuming and expensive. In this study, the deformation modulus of selected heavily jointed, sheared and/or blocky, weathered, weak greywacke, andesite and claystone were assessed, based on pressuremeter tests, geo-engineering characterization and seismic surveys. Empirical equations based on GSI and RMR values are proposed to indirectly estimate the deformation modulus of the greywackes. For the andesites, the spacing of the discontinuities is greater than the length of the pressuremeter probe hence the intact rather than rock mass deformation modulus is obtained. The pressuremeter test results from the claystones could not be correlated with the field data; the relationship between the ratio of rock mass modulus to intact rock modulus and RQD appears to give a better estimation of the deformation modulus.      

Empirical methods for determining shaft bearing capacity of semi-deep foundations socketed in rocks

Semi-deep foundations socketed in rocks are considered to be a viable option for the foundations in the presence of heavy load imposed by high-rise structures, due to the low settlement and high bearing capacity. In the optimum design of semi-deep foundations, prediction of the shaft bearing capacity, rs, of foundations socketed in rocks is thus critically important. In this study, the unconfined compressive strength(UCS), qu, has been applied in order to investigate the shaft bearing capacity. For this, a database of 106 full-scale load tests is compiled with UCS values of surrounding rocks, in which 34 tests with rock quality designation(RQD), and 5 tests with rock mass rating(RMR). The bearing rocks for semi-deep foundations include limestone, mudstone, siltstone, shale, granite, tuff, granodiorite, claystone, sandstone, phyllite, schist, and greywacke. Using the database, the applicability and accuracy of the existing empirical methods are evaluated and new relations are derived between the shaft bearing capacity and UCS based on the types of rocks. Moreover, a general equation in case of unknown rock types is proposed and it is verified by another set of data. Since rock-socketed shafts are supported by rock mass(not intact rock), a reduction factor for the compressive strength is suggested and verified in which the effect of discontinuities is considered using the modified UCS, qu(modified), based upon RMR and RQD in order to take into account the effect of the rock mass properties.     

A geo-engineering classification for rocks and rock masses

In this article, an attempt is made to assess the reliability of predicting the uniaxial compressive strength and the corresponding modulus of a rock mass by current approaches. These two basic engineering properties, when estimated from rock mass rating (RMR), Q and geological strength index (GSI), indicate hardly any change in the modulus ratio with the change in the quality of the rock mass from very good to very poor. However, the modulus ratio obtained from the relations involving the joint factor, J_f, indicate a definite decrease in the modulus ratio with a decrease in the quality of the rock mass. The strength and modulus in the unconfined and confined states, the modulus ratio and failure strain in the unconfined case were linked to J_f in earlier publications based on a large experimental database. Some of these relations were adopted to verify the response of jointed test specimens, the response of the rock mass during excavations for mining and civil underground chambers, in establishing ground reaction curves including the extent of the broken zone, and the bearing capacity of shallow foundations.The joint factor is now linked to RMR, Q and GSI. The prediction of compressive strength and modulus of the rock mass appears to be more suitable. For classifying the rock, based on these properties, the Deere and Miller engineering classification, applicable to intact rocks, has been suitably modified and adopted. The results of different modes of failure of jointed specimens establish definite trends of changes in the modulus ratio originating from the intact rock value on the modified Deere and Miller plot. A geo-engineering classification is evolved by considering strength, modulus, quantifiable weathering index and lithological aspects of the rock.     

基于V.RQD值与Hoek-Brown准则的破碎岩体强度研究

被多组贯通结构面切割后产生的大体积破碎岩体在不同围压下仍具有一定的强度,但通过Hoek-Brown准则对其进行强度评价时,因对岩体结构划分缺乏定量描述,使得参数m与s的取值很难准确确定。在传统RQD值不足的基础上,引入不同阈值下的三维体积V.RQD值概念,建立破碎岩体质量指标V.RQD值计算机模拟方法,结合RMR评分标准和Hoek-Brown强度准则,通过探讨三维体积V.RQD值的取值范围,得到不同阈值时岩体质量参数m,s值与Hoek-Brown强度包络线以及岩体变形模量E0等之间的一些变化规律,定量化表述V.RQD值对破碎岩体强度的影响。结果表明,V.RQD值作为岩体质量指标之一,可为破碎岩体的强度估计提供新的实用途径。     

Post-failure behavior of two mine pillars confined with backfill

Researchers from the National Institute for Occupational Safety and Health used a series of instruments (borehole extensometers, earth pressure cells, and embedment strain gauges) to study the post-failure behavior of two pillars confined by backfill in a test section at the Buick Mine near Boss, MO, USA. Evaluation of these pillars was part of a research project to assess the safety of the test section when high-grade support pillars were mined.Data from borehole extensometers installed in several backfill-confined pillars and numerical modeling indicated that these pillars failed during extraction of the support pillars. Failure was corroborated by the post-yield pillar strain response in which the immediate elastic strain was negligible compared to the time-dependent strain component measured between blasting rounds.A three-dimensional, finite-element program with an elastic perfectly plastic material model was calibrated using extensometer data to estimate rock mass modulus and unconfined compressive strength. The resulting rock mass modulus was 45–60% of the average deformation modulus obtained from laboratory tests, and the calibrated compressive strength was 40% of average laboratory values. A rock mass modulus equal to 52% of the average laboratory deformation modulus was calculated using the rock mass rating (RMR) system. Rock mass strength was calculated with the generalized Hoek–Brown failure criterion for jointed rock and indicated that in situ strength was 33% of laboratory strength. Post-failure stresses calculated by the finite-element model were larger for confined pillars than post-failure stresses in unconfined pillars calculated using empirical plots. Data from the calibrated model provided a strain-hardening stress-versus-strain relationship. This knowledge is critical for the design of mines that use partially failed pillars to carry overburden load.     

基于GSI系统的岩体变形模量取值及应用

 在分析岩体的变形特性时,岩体变形模量是一个非常重要的参数,一般要通过现场试验来确定。但利用现场试验直接确定岩体变形模量时,具有时间长、代价高以及试验结果可靠性差等缺点。E. Hoek利用地质强度指标GSI,通过大量现场试验数据的分析研究,建立一种新的估算岩体变形模量的公式。分析这种最新计算岩体变形模量的方法,并通过对岩体结构特征和结构面表面特征的定量描述,对GSI系统进行量化取值,特别对岩体体积节理数Jv的取值进行深入分析。最后通过实际工程的运用,研究应用这一方法的具体过程。最后通过与现场试验结果进行对比,分析这一方法的合理性。     

Reply to Discussion on “Empirical methods for determining shaft bearing capacity of semi-deep foundations socketed in rocks”

Semi-deep foundations socketed in rocks are considered to be a viable option for the foundations in the presence of heavy loads imposed by high-rise buildings and special structures, due to the low settlement and high bearing capacity. In this study, the unconfined compressive strength (UCS) and rock mass cuttability index (RMCI) have been applied to investigating the shaft bearing capacity. For this purpose, a comprehensive database of 178 full-scale load tests is compiled by adding a data set (n = 72) collected by Arioglu et al. (2007) to the data set (n = 106) presented in Rezazadeh and Eslami (2017). Using the database, the applicability and accuracy of the existing empirical methods are evaluated and new relations are derived between the shaft bearing capacity and UCS/RMCI. Moreover, a general equation in case of unknown rock types is proposed and it is verified by another set of data (series 3 in Rezazadeh and Eslami (2017)). Since rock-socketed shafts are supported by rock mass (not intact rock), a reduction factor for the compressive strength is suggested and verified in which the effect of discontinuities is considered using the modified UCS, based upon RMR and RQD to consider the effect of the rock mass properties.     

Estimation of limestone rock mass deformation modulus using empirical equations

Determining the geomechanical parameters of rock masses at dam sites is a very important task. Different methods of determining these parameters have been proposed, depending on various factors such as the study phase, facilities, budget, and the time available. The deformation modulus is an important input parameter in any analysis of rock mass behavior. In the present study, the deformation modulus of the rock mass at the site of the Khersan II double-arch concrete dam was investigated using different field and experimental methods. The Khersan II Dam is located in the southwest of Lordegan, Chaharmahal Bakhtiary Province, Iran. The predominant formation at the site of the dam is the Upper Asmari limestone. The results of in situ tests such as plate load tests (PLTs) were analyzed to determine the deformation modulus, using the ASTM standard, Unal, and ISRM methods. These results were then compared to one another and interpreted. After that, engineering classification parameters such as RMR, GSI, and Q were evaluated at the same site that the PLTs were performed. Finally, the correlations between these classification ratings and the in situ deformation modulus of the rock mass were assessed, and some formulae for determining the deformation modulus of the rock mass at the Khersan II Dam site were derived. The accuracy and credibility of every formula was evaluated. These formulae for estimating the deformation modulus of the rock mass at the Khersan II Dam site were found to be highly accurate compared to other similar formulae.     

Modification of the BQ system based on the Lugeon value and RQD: a case study from the Maerdang hydropower station,China

Bulletin of Engineering Geology and the Environment - Current rock mass quality classification methods include the rock mass rating (RMR), the Q system, the geological strength index (GSI) and the...     

Numerical simulations of rock mass damage induced by underground explosion

The damage prediction of rock mass under blast loads induced by accidental explosions, rock bursts or weapon attacks is crucial in rock engineering. In this paper, parametric studies are conducted to evaluate the effect of loading density, rock mass rating (RMR) and weight of charge on the rock mass damage induced by underground explosions. The numerical simulations are carried out based on the transient dynamic finite element program ANSYS-LSDYNA. The numerical model was calibrated against the data obtained from a field blast test. A fully coupled numerical analysis, incorporating the explosion process, has been performed, where the large deformation zone near the charge is solved by the Arbitrary Lagrange–Euler (ALE) method. The deformable modulus and compressive strength of rock mass of granite are estimated by the RMR system. The peak particle velocity (PPV) damage criterion and the plastic strain criterion were adopted to study the damage zone around the charge hole, and an empirical formula considering the effects of loading density, RMR and weight of charge was obtained to estimate the damage zone in granite based on the numerical results.     

Strength of massive to moderately jointed hard rock masses

The Hoek-Brown(HB) failure criterion and the geological strength index(GSI) were developed for the estimation of rock mass strength in jointed and blocky ground where rock mass failure is dominated by sliding along open joints and rotation of rock blocks. In massive, veined and moderately jointed rock in which rock blocks cannot form without failure of intact rock, the approach to obtain HB parameters must be modified. Typical situations when these modifications are required include the design of pillars,excavation and cavern stability, strainburst potential assessment, and tunnel support in deep underground conditions(around s1/s ci 0.15, where s1 is the major principal compressive stress and s ciis the unconfined compressive strength of the homogeneous rock) in hard brittle rocks with GSI ! 65. In this article, the strength of massive to moderately jointed hard rock masses is investigated, and an approach is presented to estimate the rock mass strength envelope using laboratory data from uniaxial and triaxial compressive strength tests without reliance on the HB-GSI equations. The data from tests on specimens obtained from massive to moderately jointed heterogeneous(veined) rock masses are used to obtain the rock and rock mass strengths at confining stress ranges that are relevant for deep tunnelling and mining;and a methodology is presented for this purpose from laboratory data alone. By directly obtaining the equivalent HB rock mass strength envelope for massive to moderately jointed rock from laboratory tests,the HB-GSI rock mass strength estimation approach is complemented for conditions where the GSIequations are not applicable. Guidance is also provided on how to apply the proposed approach when laboratory test data are not or not yet available.     

Estimation of rock mass deformation modulus using variations in transmissivity and RQD with depth

Discontinuity normal stiffness and deformation modulus of large scale rock masses are very difficult to determine. A method for estimation of discontinuity normal stiffness based on the decrease in transmissivity with depth has been proposed by the authors in a former paper. In the current study, the method is further developed by accounting for the changes in both discontinuity aperture and frequency with depth, which are key factors that cause the transmissivity to decrease with depth. The discontinuity frequency can be estimated from RQD measurements, which are readily available in most geotechnical investigations. The transmissivity data from packer tests are usually available in geotechnical investigations for hydropower plants. For a rock mass in a dam site mainly controlled by lithostatic stress, based on transmissivity and RQD data at different depths, the change in discontinuity aperture with depth can be linked to the change in aperture with stress, which defines the normal stiffness of discontinuities. In the case study, the discontinuity normal stiffness is successfully estimated by using transmissivity and RQD data, and the result shows that the normal stiffness increases with stress (depth) and the rate of normal stiffness versus stress (depth) decreases with stress (depth), which is consistent with experimental studies. The estimated normal stiffness has been utilized to calculate the rock mass deformation modulus using an equivalent model. The result of deformation modulus by the proposed method is close to that obtained by using in situ measurements, as well as by using empirical models relating RQD to deformation modulus.     

A comparative review in regards to estimating bearing capacity in jointed rock masses in northeast Jordan

There are a number of different methods used for estimating the bearing capacity in jointed rock masses. In this paper, the geological strength index (GSI) introduced by Hoek et al. (1995) was used to estimate the bearing capacity of the rock mass via rock mass rating (RMR). An empirical relationship is proposed to estimate the bearing capacity of the rock mass using the GSI-dependent toughness factor (TF). The proposed formula was correlated with bearing capacity equations used in the literature. The regression analyses showed exponential relationships with a high correlation coefficient.     

Advances in statistical mechanics of rock masses and its engineering applications

To efficiently link the continuum mechanics for rocks with the structural statistics of rock masses,a theoretical and methodological system called the statistical mechanics of rock masses(SMRM)was developed in the past three decades.In SMRM,equivalent continuum models of stressestrain relationship,strength and failure probability for jointed rock masses were established,which were based on the geometric probability models characterising the rock mass structure.This follows the statistical physics,the continuum mechanics,the fracture mechanics and the weakest link hypothesis.A general constitutive model and complete stressestrain models under compressive and shear conditions were also developed as the derivatives of the SMRM theory.An SMRM calculation system was then developed to provide fast and precise solutions for parameter estimations of rock masses,such as full-direction rock quality designation(RQD),elastic modulus,Coulomb compressive strength,rock mass quality rating,and Poisson’s ratio and shear strength.The constitutive equations involved in SMRM were integrated into a FLAC3D based numerical module to apply for engineering rock masses.It is also capable of analysing the complete deformation of rock masses and active reinforcement of engineering rock masses.Examples of engineering applications of SMRM were presented,including a rock mass at QBT hydropower station in northwestern China,a dam slope of Zongo II hydropower station in D.R.Congo,an open-pit mine in Dexing,China,an underground powerhouse of Jinping I hydropower station in southwestern China,and a typical circular tunnel in Lanzhou-Chongqing railway,China.These applications verified the reliability of the SMRM and demonstrated its applicability to broad engineering issues associated with jointed rock masses.     

Effects of confinement on rock mass modulus: A synthetic rock mass modelling (SRM) study

The main objective of this paper is to examine the influence of the applied confining stress on the rock mass modulus of moderately jointed rocks (well interlocked undisturbed rock mass with blocks formed by three or less intersecting joints). A synthetic rock mass modelling (SRM) approach is employed to determine the mechanical properties of the rock mass. In this approach, the intact body of rock is represented by the discrete element method (DEM)-Voronoi grains with the ability of simulating the initiation and propagation of microcracks within the intact part of the model. The geometry of the pre-existing joints is generated by employing discrete fracture network (DFN) modelling based on field joint data collected from the Brockville Tunnel using LiDAR scanning. The geometrical characteristics of the simulated joints at a representative sample size are first validated against the field data, and then used to measure the rock quality designation (RQD), joint spacing, areal fracture intensity (P₂₁), and block volumes. These geometrical quantities are used to quantitatively determine a representative range of the geological strength index (GSI). The results show that estimating the GSI using the RQD tends to make a closer estimate of the degree of blockiness that leads to GSI values corresponding to those obtained from direct visual observations of the rock mass conditions in the field. The use of joint spacing and block volume in order to quantify the GSI value range for the studied rock mass suggests a lower range compared to that evaluated in situ. Based on numerical modelling results and laboratory data of rock testing reported in the literature, a semi-empirical equation is proposed that relates the rock mass modulus to confinement as a function of the areal fracture intensity and joint stiffness.     

Variability of intact rock mechanical properties for some metamorphic rock types and its implications on the number of test specimens

Intact rock strength and stiffness properties are commonly used in rock mass mechanical characterization, and their evaluation is usually based on laboratory tests. Due to the variability that affects strength and stiffness parameters, the determination of the number of laboratory-tested specimens required to obtain a reliable reference value is very useful. However, many studies reported in apposite literature focused only on the variability of strength parameters. This study investigates the variability of some of the most important strength and stiffness properties (unconfined compressive strength, indirect tensile strength, tangent and secant Young’s moduli, Poisson’s ratio) by applying statistical methods (statistical decision theory and statistical inference theory). A data set of 451 laboratory tests was used, performed on three rock types. The statistical analyses were applied with the aim of assessing how closely intact rock laboratory data follow a normal distribution and determining the minimum number of specimens required to obtain a reliable average value of the parameters in relation to a targeted precision index for a confidence level of 95 %. The results indicate that the minimum number of samples needed varies depending on rock and test types. Among the stiffness properties, tangent Young’s modulus has a lower variability than both the secant modulus and the Poisson’s ratio, whereas in terms of strength parameters, unconfined compressive strength is subject to greater variability than indirect tensile strength.     

Genetic programming approach for estimating the deformation modulus of rock mass using sensitivity analysis by neural network

We use genetic programming (GP) to determine the deformation modulus of rock masses. A database of 150 data sets, including modulus of elasticity of intact rock (Ei), uniaxial compressive strength (UCS), rock mass quality designation (RQD), the number of joint per meter (J/m), porosity, and dry density for possible input parameters, and the modulus deformation of the rock mass determined by a plate loading test for output, was established. The values of geological strength index (GSI) system were also determined for all sites and considered as another input parameter. Sensitivity analyses are considered to find out the important parameters for predicting of the deformation modulus of rock mass. Two approaches of sensitivity analyses, based on “statistical analysis of RSE values” and “sensitivity analysis about the mean”, are performed. Evolution of the sensitivity analyses results establish the fact that variable of UCS, GSI, and RQD play more prominent roles for predicting modulus of the rock mass, and so those are considered as the predictors to design the GP model. Finally, two equations were achieved by GP. The statistical measures of root mean square error (RMSE) and variance account for (VAF) have been used to compare GP models with the well-known existing empirical equations proposed for predicting the deformation modulus. These performance criteria proved that the GP models give higher predictions over existing empirical models.     

Determination of instantaneous breaking rate by Geological Strength Index, Block Punch Index and power of impact hammer for various rock mass conditions

In mining and construction industries, selection of appropriate excavation method and equipment significantly affects the project feasibility. In the selection, the most important parameters are the geomechanical properties of the rock mass in the excavation route as extensively reviewed in literature. The most widely used geomechanical parameter is uniaxial compressive strength (UCS). However, UCS laboratory test requires time consuming and expensive sampling and core sample preparation processes, which can be quite difficult or sometimes impossible for a weak rock material taken from foliated, laminated or thinly bedded rock masses of low Rock Quality Designation (RQD) values (0-20%). For these reasons, Block Punch Index (BPI) test, which has thus gained an importance for the last decade because of its simplicity, has become applicable to determine rock strength for highly-jointed and weak rocks of low RQD. BPI provides significant convenience particularly for laminated-foliated-anisotropic rocks. In this study, the excavability of various rocks with impact hammer was investigated using Geological Strength Index (GSI), power of impact hammer (P), BPI. Valuable results from which the users could benefit were obtained.     

Estimation of bearing capacity of basalts at the Atasu dam site,Turkey

This paper describes the results of the engineering geological investigations and bearing capacity studies carried out at the proposed site of the rock fill Atasu Dam, to be constructed on basalts and pyroclastics. Rock mass strength and modulus of elasticity of the rock mass were determined using the Hoek–Brown empirical strength criterion. Rock mass classifications for the dam rock foundation were undertaken following the RMR, Q and GSI systems and the stress distributions using the finite element technique. To estimate the bearing capacity of the basalts, different empirical equations were used and compared.