The deformation modulus of rock masses — comparisons between in situ tests and indirect estimates

Three methods of in situ deformation modulus (Em) measurements of rock masses have been described, analysed and compared. The plate jacking (PJT) test, where the deformations are measured by extensometers in drill holes, gives generally the best results. A factor of 2.5 has been found between PJT and the Goodman jack test, and the plate loading test. From analyses of the results it has been pointed out that the damage from blasting of the test adit reduces the magnitude of test results with a factor between 2 and 4. The existing equations for indirect estimates of the rock mass deformation modulus from classification systems have been analysed and adjustment suggested. Taking into consideration the uncertainties connected to in situ deformation measurements caused by blast damage, test procedure and test method, a good characterization of the ground may give comparable, or possibly better Em values, using the RMi or the RMR system than the in situ tests. The RMR system gives, however, values that are too high for Em in massive rock.     

Performance analysis of empirical models for predicting rock mass deformation modulus using regression and Bayesian methods

Deformation modulus of rock mass is one of the input parameters to most rock engineering designs and constructions. The field tests for determination of deformation modulus are cumbersome, expensive and time-consuming. This has prompted the development of various regression equations to estimate deformation modulus from results of rock mass classifications, with rock mass rating (RMR) being one of the frequently used classifications. The regression equations are of different types ranging from linear to nonlinear functions like power and exponential. Bayesian method has recently been developed to incorporate regression equations into a Bayesian framework to provide better estimates of geotechnical properties. The question of whether Bayesian method improves the estimation of geotechnical properties in all circumstances remains open. Therefore, a comparative study was conducted to assess the performances of regression and Bayesian methods when they are used to characterize deformation modulus from the same set of RMR data obtained from two project sites. The study also investigated the performance of different types of regression equations in estimation of the deformation modulus. Statistics, probability distributions and prediction indicators were used to assess the performances of regression and Bayesian methods and different types of regression equations. It was found that power and exponential types of regression equations provide a better estimate than linear regression equations. In addition, it was discovered that the ability of the Bayesian method to provide better estimates of deformation modulus than regression method depends on the quality and quantity of input data as well as the type of the regression equation.     

Estimation of deformation modulus of rock masses by using fuzzy clustering-based modeling

The paper describes a method which incorporates Takagi–Sugeno (TS) fuzzy modeling with two data clustering approaches including fuzzy-c-means (FCM) clustering and subtractive clustering to estimate the rock mass modulus of deformation. For this aim, a database including 120 cases collected from several galleries of dam sites locations was established. The information returned by fuzzy clustering was initially used to define the number of rules and antecedent membership functions and afterwards linear least squares estimation implemented to obtain fuzzy consequent parameters. An adaptive neuro-fuzzy inference system (ANFIS) was applied to modify the pre-determined TS clustering-based model structures to improve the generalization performance of those. For evaluation of the performance, root mean square error (RMSE) and variance account for (VAF) values have been utilized as performance criteria. It can be said, that ANFIS approach enhances the performances of fuzzy clustering-based models in predicting modulus of deformation of rock masses successfully.     

Empirical estimation of rock mass modulus

The deformation modulus of a rock mass is an important input parameter in any analysis of rock mass behaviour that includes deformations. Field tests to determine this parameter directly are time consuming, expensive and the reliability of the results of these tests is sometimes questionable. Consequently, several authors have proposed empirical relationships for estimating the value of rock mass deformation modulus on the basis of classification schemes. These relationships are reviewed and their limitations are discussed. Based on data from a large number of in situ measurements from China and Taiwan a new relationship, based upon a sigmoid function, is proposed. The properties of the intact rock as well as the effects of disturbance due to blast damage and/or stress relaxation are also included in this new relationship.     

Predicting the deformation moduli of rock masses

Predictive empirical models for the mechanical properties of rock masses have been used in rock engineering because direct measurement of the properties is difficult due to the presence of discontinuities. Such empirical models are open to improvement because they are based on collected data. The purposes of the present study are to assess the existing empirical equations and to develop a new empirical approach. For this reason, in the first stage of the study, the prediction performance of the existing models proposed for predicting the deformation modulus of rock masses were evaluated statistically by using a database including 115 data values obtained from in situ plate loading and dilatometer tests. A new empirical approach with higher prediction capacity than the existing empirical models was developed in the subsequent stage of the study. The new empirical model considers the modulus ratio of intact rock (E_i/UCS), rock quality designation (RQD) and weathering degree (WD). Although, data obtained from very weak and weak rock masses were included in the development of the new empirical equation, the type of rocks employed in the study were limited. Therefore, a crosscheck between the new empirical equation and previous empirical approaches should be performed in the design stage.     

A new estimation method and an anisotropy index for the deformation modulus of jointed rock masses

The deformation modulus of a rock mass is an important parameter to describe its mechanical behavior.In this study,an analytical method is developed to determine the deformation modulus of jointed rock masses,which considers the mechanical properties of intact rocks and joints based on the superposition principle.Due to incorporating the variations in the orientations and sizes of joint sets,the proposed method is applicable to the rock mass with persistent and parallel joints as well as that with nonpersistent and nonparallel joints.In addition,an anisotropy index AIdmfor the deformation modulus is defined to quantitatively describe the anisotropy of rock masses.The range of AIdmis from 0 to 1,and the more anisotropic the rock mass is,the larger the value of AIdmwill be.To evaluate the proposed method,20 groups of numerical experiments are conducted with the universal distinct element code(UDEC).For each experimental group,the deformation modulus in 24 directions are obtained by UDEC(numerical value)and the proposed method(predicted value),and then the mean error rates are calculated.Note that the mean error rate is the mean value of the error rates of the deformation modulus in 24 directions,where for each direction,the error rate is equal to the ratio of numerical value minus predicted value to the numerical value.The results show that(i)for different experimental groups,the mean error rates vary between 5.06%and 22.03%;(ii)the error rates for the discrete fracture networks(DFNs)with two sets of joints are at the same level as those with one set of joints;and(iii)therefore,the proposed method for estimating the deformation modulus of jointed rock masses is valid.     

基于原位旁压试验的切线模量法及其初步验证

切线模量法根据原位压板载荷试验求取不同荷载水平下土体的切线模量,并将其应用于分层总和法进行地基沉降计算,较好地克服了通常取样扰动的不利影响,并能够反映地基沉降的非线性,是目前地基沉降计算中较实用有效的方法之一。而其不足之处则是原位压板试验工作量大、时间长,且难以反映深部土体的特性;相比而言,旁压试验设备轻便、测试时间短,且可在不同深度的土层进行测试,可以算是一种简单实用的原位试验。因此,为了进一步发展和完善切线模量法,本文探讨了利用原位旁压试验获取切线模量法计算参数的方法,并通过位于美国Texas AM University河滨校区的粉细砂地基上4个不同压板尺寸载荷试验结果,检验了其可行性。结果表明:4个不同压板尺寸载荷试验的沉降计算结果与试验结果具有较好的一致性,初步验证了基于原位旁压试验的切线模量法的可行性。     

Determination of rock mass deformation modulus by means of traveling load tests—Part I: Theory of the traveling load test in an open pit

A new scheme named the Traveling Load Test is proposed to measure the macroscopic deformation modulus of the floor rock mass in an open pit, covering a volume of rock mass much larger than conventional loading tests. Facility of the test includes extra-large excavators as load-sources on the flat surface and high-resolution borehole tilt-meters installed in rock to detect the microscopic tilt induced by the load. Emphasis is given to the theory of deformation modulus determination, which is applicable to the field where the floor is fully covered by an accumulation of loose blocks of stone produced by blasting damage and/or stress relief. The relation between the induced tilt and the traveling load is formulated, and subsequently it is shown how the deformation modulus is determined by analyzing the induced tilt-loading distance curve, within acceptable engineering accuracy.     

Applicability of the geological strength index (GSI) classification for very weak and sheared rock masses. The case of the Athens Schist Formation

 The Athens Schist Formation includes a wide variety of metasedimentary rocks, varying from strong or medium strong rocks such as sericite metasandstone, limestone, greywacke, sericite schist through to weak rocks such as metasiltstone, clayey and silty shale and phyllite. The overall rock mass is highly heterogeneous and anisotropic owing to the combined effect of advanced weathering and severe tectonic stressing that gave rise to intense folding and shearing followed by extensional faulting, which resulted in highly weathered rock masses and numerous shear and/or mylonite zones with distinct downgraded engineering properties. This paper is focused on the applicability of the GSI classification system to these highly heterogeneous rock masses and proposes an extension of the GSI system to account for the foliated or laminated weak rocks in the lower range of its applicability. Received: 5 March 1998 · Accepted: 13 July 1998     

An analytical solution of equivalent elastic modulus considering confining stress and its variables sensitivity analysis for fractured rock masses

The equivalent elastic modulus is a parameter for controlling the deformation behavior of fractured rock masses in the equivalent continuum approach. The confining stress, whose effect on the equivalent elastic modulus is of great importance, is the fundamental stress environment of natural rock masses. This paper employs an analytical approach to obtain the equivalent elastic modulus of fractured rock masses containing random discrete fractures (RDFs) or regular fracture sets (RFSs) while considering the confining stress. The proposed analytical solution considers not only the elastic properties of the intact rocks and fractures, but also the geometrical structure of the fractures and the confining stress. The performance of the analytical solution is verified by comparing it with the results of numerical tests obtained using the three-dimensional distinct element code (3DEC), leading to a reasonably good agreement. The analytical solution quantitatively demonstrates that the equivalent elastic modulus increases substantially with an increase in confining stress, i.e. it is characterized by stress-dependency. Further, a sensitivity analysis of the variables in the analytical solution is conducted using a global sensitivity analysis approach, i.e. the extended Fourier amplitude sensitivity test (EFAST). The variations in the sensitivity indices for different ranges and distribution types of the variables are investigated. The results provide an in-depth understanding of the influence of the variables on the equivalent elastic modulus from different perspectives.     

Determination of rock mass deformation modulus by means of Traveling Load Tests—Part II: Traveling Load Test practice in an open pit

A case study makes clear the applicability and high potential of the Traveling Load Test in an open pit. The induced tilt-loading distance curve is measured by means of a series of stationary loading tests over a short time, so as to avoid semidiurnal variation of initial tilt by the earth tide. Through a series of data processing, the deformation modulus of rock mass is determined as a function of Poisson's ratio by the values of the peak tilt and peak distance on the induced tilt-loading distance curve and the magnitude of load subjected, regardless of the depth of tilt measurement and the thickness of surface damages. The test results represent the macroscopic deformation modulus of rock mass, covering an area much wider than the conventional load tests. Additionally, analyzing the signal to noise ratio of the traveling load test in an open pit, it is discussed that the lack of load is a problem to be settled by future studies.     

Experimental study on seismic deformation modes of reinforced-soil walls

A series of 1-g shaking table tests were conducted on 1 m high reinforced-soil wall models. The physical models were subjected to harmonic sinusoidal-like time history input motions at frequencies of 2, 5, 8 and 10 Hz. The effects of parameters such as soil density, reinforcement length, spacing and stiffness on the seismic response of the model walls were studied. Free-sliding toe boundary and wrap-around wall facing were selected to reveal all potential deformation modes of the wall and different deformation shapes of the facing. Different deformation modes (overturning and bulging) of the facing as well as base sliding were observed. Determinant parameters in the formation of each mode were identified by introducing internal failure indexes. A bulging index was introduced to measure the bulging intensity of the wall facing. Additionally, the distribution of the shear stiffness modulus (G) and damping ratio (D) of the reinforced soil along the wall height were assessed. The effect of the confining pressure (σ_v) and shear strain on variations of G and D were traced. G proved to be dependent on σ_v and, as expected, to be incremental with depth below the crest of the wall. Based on measurements and relevant approximations, no incremental or decremental patterns for D were detected along the wall height. Moreover, at large strains of about 10⁻³, an average D of about 20% was observed. Overall, based on the results of physical model testing in this study, which confirm similar findings of previous research, it was concluded that reinforcement stiffness is a key parameter dominating the seismic response and deformation mode of a wall and not reinforcement ultimate tensile strength, which is currently used as the main parameter for wall design in existing codes.     

Elastic modulus of claystone evaluated by nano-/micro-indentation tests and meso-compression tests

Toarcian claystone such as that of the Callovo-Oxfordian is a qualified multiphase material. The claystone samples tested in this study are composed of four main mineral phases: silicates (clay minerals, quartz, feldspars, micas) (≈86%), sulphides (pyrite) (≈3%), carbonates (calcite, dolomite) (≈10%) and organic kerogen (≈1%). Three sets of measurements of the modulus of deformability were compared as determined in (i) nano-indentation tests with a constant indentation depth of 2 μm, (ii) micro-indentation tests with a constant indentation depth of 20 μm, and (iii) meso-compression tests with a constant displacement of 200 μm. These three experimental methods have already been validated in earlier studies. The main objective of this study is to demonstrate the influence of the scaling effect on the modulus of deformability of the material. Different frequency distributions of the modulus of deformability were obtained at the different sample scales: (i) in nano-indentation tests, the distribution was spread between 15 GPa and 90 GPa and contained one peak at 34 GPa and another at 51 GPa; (ii) in the micro-indentation tests, the distribution was spread between 25 GPa and 60 GPa and displayed peaks at 26 GPa and 37 GPa; and (iii) in the meso-compression tests, a narrow frequency distribution was obtained, ranging from 25 GPa to 50 GPa and with a maximum at around 35 GPa.     

In situ TBM penetration tests and rock mass boreability analysis in hard rock tunnels

Boreability is popularly adopted to express the ease or difficulty with which a rock mass can be penetrated by a tunnel boring machine. Because the boreability is related to the rock mass properties, TBM specifications and TBM operation parameters, an accurately definable quantity has not been obtained so far. In order to analyze and compare rock mass boreability, a series of TBM shield friction tests were conducted in a TBM tunneling site. Two sets of TBM penetration tests were performed in different rock mass conditions during tunneling in rock. In each step of the penetration test, the rock muck was collected to perform the muck sieve analyses and the shape of large chips was surveyed in order to analyze the TBM chipping efficiency under different cutter thrusts. The results showed that a critical point exists in the penetration curves. The penetration per revolution increases rapidly with increasing thrust per cutter when it is higher than the critical value. The muck sieve analysis results verified that with increasing thrust force, the muck size increases and the rock breakage efficiency also increases. When the thrust is greater than the critical value, the muck becomes well-graded. The muck shape analysis results also showed with the increase of the thrust, the chip shape changes from flat to elongated and flat. The boreability index at the critical point of penetration of 1 mm/rev. defined as the specific rock mass boreability index is proposed to evaluate rock mass boreability.     

A quantitative comparison of strength criteria for hard rock masses

Knowledge of the rock mass strength is important for the design of all types of underground excavations. A frequently applied approach for estimation of the rock mass strength is through an empirical failure criterion, often in conjunction with rock mass classification/characterisation systems. This paper presents a review of existing methods to estimate the rock mass strength using empirical failure criteria and classification/characterisation systems—in this study, commonly denoted as estimation methods. A literature review of existing methods is presented, after which a set of methods were selected for further studies. The selected methods were used in three case studies, to investigate their robustness and quantitatively compare the advantages and disadvantages of each method. A Round Robin test was used in two of the cases. The case studies revealed that the N, Yudhbir-RMR₇₆, RMi, Q-, and Hoek–Brown-GSI methods, appeared to yield a reasonable agreement with the measured strengths. These methods are thus considered the best candidates for realistic strength estimation, provided that care is taken when choosing values for each of the included parameters in each method. This study has also clearly shown the limits of presently available strength estimation methods for rock masses and further work is required to develop more precise, practical, and easy-to-use methods for determining the rock mass strength. This should be based on the mechanical behaviour and characteristics of the rock mass, which implies that parameters that consider the strength of intact rock, block size and shape, joint strength, and physical scale, are required.     

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.     

The impact of the physical model selection and rock mass stratification on the results of numerical calculations of the state of rock mass deformation around the roadways

At present, the basic methods used for designing and evaluating the stability of mine workings are numerical models. The finite element method is the most popular method for engineering purposes. However successful calculations depend not only on the proper selection of geomechanical properties of rocks but mainly on the proper selection of a physical model describing the behavior of the rock mass and a selection of the correct failure criterion. The best way of verifying results of the calculations is to carry out investigation in the field, then.This article shows how the choice of a numerical model affects the size of the calculated damage zone around the working. To that end, numerical calculations considering elastic and elastic–plastic models were performed for six roadways. The rock mass was further differentiated in terms of its stratification and approach to mechanical properties of the rock mass. The results of these calculations were compared with measurements of mine convergence and the damage zone range in the roof. Such measurements were carried out at hard coal mine roadways.     

Linearization of the Hoek and Brown rock failure criterion for tunnelling in elasto-plastic rock masses

We present a novel methodology for estimation of equivalent Mohr–Coulomb strength parameters that can be used for design of supported tunnels in elasto-plastic rock masses satisfying the non-linear empirical Hoek–Brown failure criterion. We work with a general adimensional formulation of the Hoek–Brown failure criterion in the space of normalized Lambe's variables for plane stress, and we perform linearization considering the stress field in the plastic region around the tunnel. The procedure is validated using analytical solutions to a series of benchmark test cases. Numerical solutions are also employed to validate the procedure in cases for which analytical solutions are not available. Results indicate that the stress field in the plastic region around the tunnel, as well as the linearization method employed and the quality of the rock mass, has a significant impact on computed estimates of equivalent Mohr–Coulomb strength parameters. Results of numerical analyses also show that our proposed linearization method can be employed to estimate loads and moments on the tunnel support system. We recommend the equating model responses (EMR) method to compute equivalent Mohr–Coulomb strength parameters when the tunnel support pressure is accurately known, and we further show that our newly introduced linearization method can be employed as an alternative to the best fitting in the existing stress range (BFe) and best fitting in an artificial stress range (BFa) methods, providing performance estimates that are generally better than estimates of the BFe and BFa methods when differences with the response of the Hoek–Brown rock mass are of engineering significance (say more than 10%).     

Deformational characteristics of weak sandstone and impact to tunnel deformation

In northern Taiwan, a tunnel under construction along a segment where weak sandstone, the Mushan sandstone, was encountered and an excess crown settlement (14–30 cm) has been reported. This paper studies the deformational characteristics of Mushan sandstone and its impact on tunnel deformation. To distinguish the volumetric and the shear deformation of the sandstone, experiments with controlled stress paths, including hydrostatic compression, pure shearing and conventional triaxial compression, were conducted. The measured deformations were then decomposed into elastic and plastic components further exploring the stress–strain behavior of weak sandstone. The results indicate that, similar to other soil-like geo-materials, this sandstone has plastic strain before the stress path reaches the failure envelope and significant shear dilation is induced, especially when approaching the failure envelope. Meanwhile, the distinct features of deformation have also been highlighted by comparing the experimental results to the prediction, derived from existing constitutive models that were originally developed for other geo-materials. These features include significant plastic volumetric strain at low levels of confining stress, suppression of plastic volumetric strain at higher levels of confining stress, and the fact that the actual amount of shear compression is less than that predicted by the model. Numerical analysis indicates that the weak rock leads to the greatest inward displacement, which results from the shear dilation prior to failure state.     

浅埋红层软弱隧道围岩破坏特性模型试验研究

软弱隧道围岩浅埋段在施工时极易出现较大变形和塌方破坏事故,已成为隧道工程施工中的难点。依托广(通)—大(理)铁路南华1号隧道工程项目,通过模型试验对滇中典型红层软弱隧道围岩的变性破坏模式及应力扰动特征进行了研究。研究结果表明:隧道开挖容易引起两侧拱腰处岩体与水平方向夹角成45°+?/2的区域内开始出现初始裂缝,并向上延伸至拱顶最终形成高度约为0.5倍洞径的塌落拱;隧道开挖将引起围岩应力重分布,在隧道周边形成一圈应力降低区,在其外侧是应力升高区,而岩体塌落区则位于应力降低区内;为减少围岩塌落破坏风险,一方面应尽早支护成环,另一方面宜对应力降低区岩体进行适当加固,并充分利用岩体的自承载能力。上述研究成果不仅可用于指导本工程的设计与施工,而且也可为今后类似工程提供借鉴和参考。