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.      

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.     

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.     

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.     

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.     

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.     

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.     

Shock-induced fracture of dolomite rock in small-scale blast tests

This paper attempts to study dolomite failure using small-scale blast tests. The experimental setup consisted of a cylindrical specimen with a central borehole fitted with a detonation cord inside a copper pipe. The specimen was confined using lead material. During the test, acceleration histories were recorded using sensors placed on the lead confinement. The results showed that heterogeneity and initial cracks significantly influenced the observed failure and cracking patterns. The tests were numerically represented using the previously validated Johnson-Holmquist II (JH-2) constitutive model. The properties of the detonation cord were first determined and verified in a special test with a lead specimen to compare the deformation in the test with that of numerical simulation. Then, the small-scale blast test was simulated, and the failure of the dolomite was compared with the test observations. Comparisons of acceleration histories, scabbing failure, and number of radial cracks and crack density confirmed the overall repeatability of the actual testing data. It is likely that the proposed model can be further used for numerical studies of blasting of dolomite rock.     

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.     

Interaction of shotcrete with rock and rock bolts—A numerical study

The shotcrete–rock interaction is very complex and is influenced by a number of factors. The influence of the following factors was investigated by a series of numerical analyses: the surface roughness of the opening, the rock strength and Young's modulus, the discontinuities, the extent and properties of the excavated disturbed zone, the mechanical properties of the interface between shotcrete and rock, and the thickness of the shotcrete lining and the rock bolts. The study was carried out as a sensitivity analysis. The results showed that the rock strength and the surface roughness had significant impact on the number of failures at the rock–shotcrete interface and in the shotcrete lining. Furthermore, the behaviour of the lining is sensitive to small amplitudes of the surface roughness. In all the cases investigated, a high interface strength was favourable. The results indicate that if a thick shotcrete lining is dependent on the bond strength. The benefit of using a thicker lining can be doubtful. The analyses showed that for an uneven surface the extent of the EDZ had a minor effect on the behaviour of the shotcrete lining. Furthermore, if rock bolts were installed at the apex of the protrusion instead of at the depression, the number of failures decreased both at the interface and in the lining.     

Face stability analysis of circular tunnels in layered rock masses using the upper bound theorem

An analysis of tunnel face stability generally assumes a single homogeneous rock mass. However, most rock tunnel projects are excavated in stratified rock masses. This paper presents a two-dimensional (2D) analytical model for estimating the face stability of a rock tunnel in the presence of rock mass stratification. The model uses the kinematical limit analysis approach combined with the block calculation technique. A virtual support force is applied to the tunnel face, and then solved using an optimization method based on the upper limit theorem of limit analysis and the nonlinear Hoek–Brown yield criterion. Several design charts are provided to analyze the effects of rock layer thickness on tunnel face stability, tunnel diameter, the arrangement sequence of weak and strong rock layers, and the variation in rock layer parameters at different positions. The results indicate that the thickness of the rock layer, tunnel diameter, and arrangement sequence of weak and strong rock layers significantly affect the tunnel face stability. Variations in the parameters of the lower layer of the tunnel face have a greater effect on tunnel stability than those of the upper layer.     

Estimation of rock modulus: For intact rocks with an artificial neural network and for rock masses with a new empirical equation

The elastic modulus of intact rock is used for many rock engineering projects, such as tunnels, slopes, and foundations, but due to the requirements of high-quality core samples and associated sophisticated test equipment, instead the use of empirical models to obtain this parameter has been an attractive research topic. In the rock mechanics literature, some empirical relations exist between the elastic modulus of intact rock and other rock properties, such as the uniaxial compressive strength (σ_ci), unit weight (γ), Schmidt hammer rebound number, point load index and petrographic composition. However, the past use of specific rock types is the main limitation of the existing empirical equations. In other words, they are not open to the general purpose use. To eliminate this deficiency, a total of 529 datasets, including uniaxial compressive strength, unit weight and elastic modulus of intact rock (E_i), were collected via an extensive literature review. In addition to these datasets, a further total of 80 datasets was obtained from laboratory tests performed on greywacke and agglomerate core samples for this study. To prepare a chart for the prediction of the elastic modulus of intact rock, an artificial neural network was constructed using the large database. In addition, after a brief overview of existing empirical equations, a new empirical equation, which considers RMR and the elastic modulus of intact rock (E_i) as input parameters, is also proposed using worldwide data.     

上海地区地基土变形模量的试验探讨

通过常规三轴固结排水剪切试验的方法获取上海地区地基土的应力—应变关系,进而取得这些地基土的变形模量（割线模量E50与卸荷/重新加载模量Eur）,最后根据本次试验成果,总结了上海地区深部地基土变形模量的一些规律。     

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     

The plastic zones and displacements around underground openings in rock masses containing a fault

Faults are the commonly encountered large geological discontinuities in hard rock masses, most severe underground structure instability is found to be closely associated with the faults presence nearby. The parametric study carried out in this paper using numerical method (UDEC) has identified some fault parameters to be really critical for the underground structure stability. These fault parameters are fault dips, fault shear strength and fault locations relative to the underground structure. This numerical investigation revealed that faults affect the stability of underground structure by the tendency of increasing the plastic zones, displacements and causing both asymmetrically distributed in the rock masses adjacent to the excavation. The relationship of the induced plastic zones, maximum displacements varying with these fault parameters was established. The distribution of plastic zone and displacement was graphically presented and the mechanisms such effects were discussed. These results offer a guideline in support design.     

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%).     

《爆破安全规程》(GB 6722—2014)边坡岩体爆破振动速度安全允许值的理论探讨

开挖爆破诱发的地震波对岩质边坡有显著影响,我国《爆破安全规程》(GB 6722—2014)给出了边坡岩体的爆破振动速度允许值,但未明确说明取值的理论依据。为此,分析露天开挖爆破条件下邻近边坡岩体的附加动应力和质点振动速度场分布特征,推导以坡表质点振动速度表征的岩体附加动应力表达式。以边坡岩体不发生剪切和张拉破坏为控制要求,考虑边坡岩体分级特征和坡体结构特征,提出基于简单边坡模型的浅层岩体的爆破振动速度允许值。分析表明,岩体强度、边坡坡度、滑动面深度和地震波频率等均对边坡岩体的允许振动速度存在显著影响。其次,无剪切破坏条件下计算的爆破振动速度允许值与《爆破安全规程》(GB 6722—2014)的控制标准在量级上较接近,而无张拉破坏时各级岩体的爆破振动速度允许值差别不大,《爆破安全规程》(GB 6722—2014)中岩质边坡爆破振动控制标准应在理论分析和工程实践基础上进一步细化。     

Modeling the effect of water, excavation sequence and rock reinforcement with discontinuous deformation analysis

A powerful numerical method that can be used for modeling rock-structure interaction is the discontinuous deformation analysis (DDA) method developed by Shi in 1988. In this method, rock masses are treated as systems of finite and deformable blocks. Large rock mass deformations and block movements are allowed. Although various extensions of the DDA method have been proposed in the literature, the method is not capable of modeling water-block interaction, sequential loading or unloading and rock reinforcement; three features that are needed when modeling surface or underground excavation in fractured rock. This paper presents three new extensions to the DDA method. The extensions consist of hydro-mechanical coupling between rock blocks and steady water flow in fractures, sequential loading or unloading, and rock reinforcement by rockbolts, shotcrete or concrete lining. Examples of application of the DDA method with the new extensions are presented. Simulations of the underground excavation of the ‘Unju Tunnel’ in Korea were carried out to evaluate the influence of fracture flow, excavation sequence and reinforcement on the tunnel stability. The results of the present study indicate that fracture flow and improper selection of excavation sequence could have a destabilizing effect on the tunnel stability. On the other hand, reinforcement by rockbolts and shotcrete can stabilize the tunnel. It is found that, in general, the DDA program with the three new extensions can now be used as a practical tool in the design of underground structures. In particular, phases of construction (excavation, reinforcement) can now be simulated more realistically. However, the method is limited to solving two-dimensional problems.