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.     

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.     

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     

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.     

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.     

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.     

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.     

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.     

软岩隧道围岩变形分析及处理

从介绍软岩隧道的基本变形特征出发,系统分析了引起软岩隧道变形的原因,全面讨论了软岩隧道的支护原理、原则与方法,并详细介绍了底鼓问题的防治方法,对软岩地质条件下的施工具有重要的现实意义。     

Evaluation of depth-dependent porosity and bulk modulus of a shear using permeability–depth trends

Both porosity and deformation properties of porous media are dependent on stress. For geological media, the stress-dependent porosity and deformation properties can be shown to be depth related. Unfortunately, both in situ porosity and in situ deformation properties are difficult to measure. In the current study, a method is developed to evaluate the changes in porosity and bulk modulus with depth by using in situ measurements of permeability, which can be easily obtained by employing packer tests. In the case study, the change in permeability of a shear in the Baihetan hydropower station in Southwest China is estimated. Then, the permeability–depth correlation is utilized to calculate the porosity and the bulk modulus at different depths. The results clearly show that the porosity decreases with depth while the bulk modulus increases with depth. Based on the proposed model, the bulk modulus is calculated to increase from 4–6 MPa on the ground surface to 18–30 MPa at the depth of 160 m. The Young's modulus of the shear estimated with this depth-dependent bulk modulus is consistent with in situ measurement.     

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.     

Physical and mechanical properties of rock masses at Stromboli: a dataset for volcano instability evaluation

Stromboli island has a complex geological history with repeated changes in the volcanic activity alternating with destructive events, caldera collapses and flank landslides. The last activity resulted in the creation of the Sciara del Fuoco depression which was modified by the recent 2002–2003 landslide. The variation in lithology, degree of tectonization and disturbance has resulted in the presence of a wide spectrum of geotechnical materials. This paper summarises the physical and mechanical properties of Stromboli’s intact rocks, rock masses and loose deposits, based on field surveys and laboratory tests. A new classification of the rock succession is introduced and four lithotechnical units defined: Lava, Lava-Breccia, Breccia and Pyroclastic deposit. The range of variability in bulk volume, porosity, intact rock compressive strength and geological strength index is presented. The Hoek and Brown’s failure criterion was applied for each lithotechnical unit and the rock mass friction angle, apparent cohesion, tensile and compressive strength, global strength and modulus of deformation calculated in a specified stress range.      

Assessment of clay stiffness and strength parameters using index properties

A new approach is developed to determine the shear wave velocity in saturated soft to firm clays using measurements of the liquid limit, plastic limit, and natural water content with depth. The shear wave velocity is assessed using the site-specific variation of the natural water content with the effective mean stress. Subsequently, an iterative process is envisaged to obtain the clay stiffness and strength parameters. The at-rest earth pressure coefficient, as well as bearing capacity factor and rigidity index related to the cone penetration test, is also acquired from the analyses. Comparisons are presented between the measured clay parameters and the results of corresponding analyses in five different case studies. It is demonstrated that the presented approach can provide acceptable estimates of saturated clay stiffness and strength parameters. One of the main privileges of the presented methodology is the site-specific procedure developed based on the relationships between clay strength and stiffness parameters, rather than adopting direct correlations. Despite of the utilized iterative processes, the presented approach can be easily implemented using a simple spreadsheet, benefiting both geotechnical researchers and practitioners.     

混凝土抗压强度和弹性模量与其超声声速之间关系的试验研究

在混凝土超声无损检测法的基础上,本文对三种强度等级,各龄期的混凝土试块进行超声波测试,并同时进行抗压强度和弹性模量试验,由试验数据经回归分析得到了抗压强度、弹性模量和超声声速之间的函数关系,为用超声法测试混凝土抗压强度和弹性模量提供了一定的试验数据和参考依据。     

Development of a transparent triaxial cell and observation of rock deformation in compression and creep tests

A transparent triaxial cell was designed and manufactured using acrylic resin. The cell was used to conduct strength and creep tests. Photographs were taken of the specimens at constant time intervals during the constant strain rate test. Photographs were also taken at constant intervals of strain during the creep test, but this rate was changed to one image per second when the specimens first showed tertiary creep. Comparison of the axial and lateral strains during the constant strain-rate and creep tests indicated no significant differences between the two tests. It is well known that the axial creep strain rate is inversely proportional to remaining life in tertiary creep. This study showed that the lateral creep strain rate is also inversely proportional to remaining life. The constant strain-rate tests were conducted with transparent end pieces attached firmly to the upper and lower ends of the specimens. Three holes were drilled into the end pieces, and water was expelled into the holes when the specimens were compressed. It was clearly observed that the water began flowing from the holes back into the specimen during the volumetric expansion of the specimen. The transparent triaxial cell permitted easy observation of water ejection and re-absorption into the specimens.     

软弱破碎直立岩质边坡渐进性破坏及其锚固效应的模型试验研究

软弱破碎岩质边坡在自然界中广泛存在,且多表现为局部化渐进破坏模式。为进一步了解该类边坡的破坏性状及其锚固效应,以Ⅳ类破碎围岩为参照对象,并将其等效为单一均值地层,随后利用模型试验对有、无锚杆加固情况下直立岩质边坡的破坏特性进行研究。结果表明,软弱破碎岩质边坡的塌方主要是由于坡顶岩体的张拉和坡脚岩体的压剪共同作用的结果,且往往呈渐进性破坏机制;锚杆的锚固效应主要体现在抗剪止裂和抗拉伸两个方面,并且锚杆的加固不仅可以提高边坡岩体在破坏前的竖向承载力,而且还可减小岩体的竖向沉降,并允许岩体边墙有较大的侧向变形。