Probabilistic assessment of tunnel convergence considering spatial variability in rock mass properties using interpolated autocorrelation and response surface method

This study aims at the probabilistic assessment of tunnel convergence considering the spatial variability in rock mass properties. The method of interpolated autocorrelation combined with finite difference analysis is adopted to model the spatial variability of rock mass properties. An iterative procedure using the first-order reliability method(FORM) and response surface method(RSM) is employed to compute the reliability index and its corresponding design point. The results indicate that the spatial variability considerably affects the computed reliability index. The probability of failure could be noticeably overestimated in the case where the spatial variability is neglected. The vertical scale of fluctuation has a much higher effect on the probabilistic result with respect to the tunnel convergence than the horizontal scale of fluctuation. And the influence of different spacing of control points on the computational accuracy is investigated.     

The effect of cubic specimen size on uniaxial compressive strength of carbonate rocks from Western Turkey

One of the most important quality and design parameters of natural rock materials is uniaxial compressive strength (UCS). UCS value of a building stone determines its application area such as cladding, roofing, facing, and coverings. In rock mechanics and engineering practice determination of UCS values of rock materials is suggested on core specimens whereas in construction and building stone sector, cubic specimens are suggested. In this experimental study, the effect of cubic specimen size on UCS values of some carbonate rocks which are being used as dimension stones are investigated. A total of 299 cubic specimens at five different edge sizes (3, 5, 7, 9, and 11 cm) from limestone, marble, and travertine are prepared. Chemical, petrographic analyses and physical properties of specimens are determined and after that UCS tests are carried out. It is observed that as the specimen sizes increase from 3 to 11 cm, average UCS values decrease about 7% for the tested carbonate rocks. In the light of this finding, results of UCS tests could be interpreted considering cubic specimen sizes for the same rock types in various fields.     

Evaluation of rock property variability

ABSTRACT

Rocks are natural geo-materials, whose properties are affected by many spatially-varying factors, such as the properties of their parent materials, weathering processes, and discontinuity conditions. Engineering properties of rocks therefore vary spatially and exhibit significant variability. To evaluate rock property variability, an extensive literature review is performed in this study to collect data reported in literature for igneous, sedimentary and metamorphic rocks during the last several decades. The typical ranges of rock property data, mean values and coefficient of variations of rock properties are evaluated and summarized. These typical ranges of rock properties can be used as guidelines for approximation when rock property data are not available at a project site. Furthermore, they can be used as prior knowledge when developing Bayesian framework for quantifying the variability of rock properties at a specific project site.     

A Simplified Failure Criterion for Intact Rocks Based on Rock Type and Uniaxial Compressive Strength

The uniaxial compressive strength (UCS) of intact rock, which can be estimated using relatively straightforward and cost-effective techniques, is one of the most practical rock properties used in rock engineering. Thus, constitutive laws to represent the strength and behavior of (intact) rock frequently use it, along with additional intrinsic rock properties. Although triaxial tests can be employed to obtain best-fit failure criterion parameters that provide best strength predictions, they are more expensive and require time-consuming procedures; as a consequence, they are often not readily available at early stages of a project. Based on the analysis of an extensive triaxial test database for intact rocks, we propose a simplified empirical failure criterion in which rock strength at failure is expressed in terms of confining stress and UCS, with a new parameter which can be directly estimated from the UCS for a specified rock type in the absence of triaxial test data. Performance of the proposed failure criterion is then tested for validation against experimental data for eight rock types. The results show that strengths of intact rock estimated by the proposed failure criterion are in good agreement with experimental test data, with small discrepancies between estimated and measurements strengths. Therefore, the proposed criterion can be useful for preliminary (triaxial) strength estimation of intact rocks when triaxial tests data are not available.     

基于GIS的甘肃北山花岗岩裂隙密度地质统计分析

以甘肃北山花岗岩中发育的构造裂隙(主要指节理)为研究对象,采用高精度GPS、罗盘等对其进行现场测量,获取裂隙的迹长及产状信息,并将信息导入ArcGIS平台建立裂隙属性数据库; 进而应用地质统计分析理论,以裂隙面密度P21为地质统计分析的区域性变量,探索花岗岩岩体裂隙空间分布特征; 然后借助ArcGIS软件平台建立变异函数模型,利用地质统计学的普通克里金插值方法得到整个区域的面密度预测分布图。结果表明:芨芨槽块段所测某区域裂隙面密度值的半变异函数变程值在20～30m之间,NS和EW方向有明显差异,由此知该区域裂隙面密度分布具有显著空间自相关性,但分布特征不均匀; 此结论对北山花岗岩裂隙空间分布特征的深入研究以及三维裂隙网络建模具有重要参考价值。     

Performance of Core Strangle Test (CST) on Porous Rocks

The Core Strangle Test (CST) has been proposed in 2009 by author as an index test permitting indirect estimation of the Uniaxial Compressive Strength. In this test, load is applied through a circle perpendicular to the core axis as a strangle. The mentioned advantage of the experiment is the possibility of testing quite short rock cores on which the UCS experiment cannot be performed. In the original paper published at 2009, the author performed several experiments on non-porous rocks on which the UCS has also been measured. The results showed a linear correlation between the UCS and the CST index permitting an indirect evaluation of the UCS by performing CST experiments. The current paper is quite similar to the original paper with the difference that the experiments are performed here on porous rocks of various porosity. CST and UCS of the rocks are shown to have both exponential correlations with the rock porosity. Once again a linear relation, quite close to the one in the original paper, is obtained for the UCS of the porous rocks as a function of the CST index. This study confirms that the CST experiment can also be used for porous rocks. Studying the feasibility of CST method on porous rocks seems to be a logical next step in the development of this experiment and the results clearly support it.     

A Neuro-Genetic Network for Predicting Uniaxial Compressive Strength of Rocks

Uniaxial Compressive Strength (UCS) is considered as one of the most important parameters in designing rock structures. Determination of this parameter requires preparation of rock samples which is costly and time consuming. Moreover discrepancy of laboratory test results is often observed. To overcome the drawbacks of traditional method of UCS measurement, in this paper, predictive models based on neuro-genetic approach and multivariable regression analysis have been developed for predicting compressive strength of different type of rocks. Coefficient of determinatoin (R2) and the Mean Square Error (MSE) were calculated for comparison of the models’ efficiency. It was observed that accuracy of the neuro-genetic model is significantly better than regression model. For the neuro-genetic and regression models, R2 and MSE were equal to 95.89 % and 0.0045 and 77.4 % and 1.61, respectively. According to sensitivity analysis for neuro-genetic model, Schmidt rebound number is the most effective parameter in predicting UCS.     

Selecting Equivalent Strength for Intact Rocks in Heterogeneous Rock Masses

Many surface and underground structures are constructed in heterogeneous rock formations. These formations have a combination of weak and strong rock layers. Due to the alternation of the weak and strong layers, selecting the equivalent and appropriate geomechanical parameters for these formations is challenging. One of these problems is choosing the equivalent strength (i.e., uniaxial compressive strength) of intact rock for a group of rocks. Based on the volume of weak and strong parts and their strength, the equivalent strength of heterogeneous rocks changes. Marinos and Hoek (Bull Eng Geol Environ 60(2):85–92, 2001) presented the “weighted average method” for defining the uniaxial compressive strength (UCS) of heterogeneous rock masses based on the volume of weak and strong parts. Laubscher (1977) used the volume ratio of the strength of a weak part to a strong part (UCS weak/UCS strong) to determine the equivalent strength. In this study, the two methods are compared and their validity is evaluated by experimental data and numerical analyses. The geomechanical parameters of two heterogeneous formations (Aghajari and Lahbari) in the west of Iran were estimated using these methods. The results of the present study obtained through numerical analyses using particle flow code are compared with those of previous studies and discussed. Laboratory and numerical results show UCS decrease and approach to weak strength with an increasing in volume of weak part. When strength ratio of strong to weak rock increase, equivalent strength decrease more severely. The findings show that Laubscher’s method gives more appropriate results than the weighted average method.     

An Investigation into the Rock Properties Influencing the Strength in Some Granitoid Rocks of KwaZulu-Natal,South Africa

The uniaxial compressive strength (UCS) of rocks is a critical parameter required for most geotechnical projects. However, it is not always possible for direct determination of the parameter. Since determination of such a parameter in the lab is not always cost and time effective, the aim of this study is to assess and estimate the general correlation trend between the UCS and indirect tests or indexes used to estimate the value of UCS for some granitoid rocks in KwaZulu-Natal. These tests include the point load index test, Schmidt hammer rebound, P-wave velocity (V_p) and Brazilian tensile strength (σ_t). Furthermore, it aims to assess the reliability of empirical equations developed towards estimating the value of UCS and propose useful empirical equations to estimate the value of UCS for granitoid rocks. According to the current study, the variations in mineralogy, as well as the textural characteristics of granitoid rocks play an important role in influencing the strength of the rock. Simple regression analyses exhibit good results, with all regression coefficients R² being greater than 0.80, the highest R² of 0.92 being obtained from UCS versus σ_t. Comparison of equations produced in the current study as well as empirical equations derived by several researchers serves as a validation. Also illustrate that the reliability of such empirical equations are dependent on the rock type as well as the type of index tests employed, where variation in rock type and index tests produces different values of UCS. These equations provide a practical tool for estimating the value of UCS, and also gives further insight into the controlling factors of the strength of the granitoid rocks, where the strength of a rock is a multidimensional parameter.     

Evaluation of the new dynamic needle penetrometer in estimating uniaxial compressive strength of weak rocks

Studying the mechanical characteristics of weak sedimentary rocks is a burning issue in civil and mining engineering designs and analysis since obtaining rock mechanical properties of these has always faced lots of problems and uncertainties due to the structural weaknesses. One of the main causes of these problems is the difficulty of preparing high-quality core specimens recommended by testing standards or suggested methods for uniaxial compressive strength (UCS). For resolving this issue, in this study, common methods for indirect estimation of UCS of weak rocks were initially studied, their merits and demerits were analyzed, and then, in light of their positive and negative points, a new modified device was designed with a different mechanical structure and force exertion system, which could be practically used to present a new method for indirect estimation of UCS. Thus, in this study, we initially had a general view of the new dynamic needle penetrometer and its modified parts and their capabilities. After introduction, as the first phase of the practical studies on this, dynamic needle penetration resistance (DNPR) was measured, as the dynamic needle penetrometer test result, from 65 specimens collected from three different projects. Then, the relationships between DNPR and UCS of the rock specimens and the regressions of correlations were statistically analyzed. Finally, a linear equation with considerable accuracy resulted from analysis, and using this led to solving the main problem of this research by proposing a developed method for indirect estimation of uniaxial compressive strength of weak rocks.     

Relationship between density,compressive strength,tensile strength and aggregate properties of andesites from Hungary

Aggregate properties and strength parameters of four andesites from two operating Hungarian quarries of Nógrádkövesd (one lithotype) and Gyöngyössolymos (three lithotypes) are presented in this paper. Air-dry, water-saturated and freeze–thaw subjected specimens were tested on core-drilled cylindrical specimens, and the aggregate properties were also determined from the remaining part of the drilled rock blocks. Tensile strength values rapidly decreased from air-dry to water-saturated and finally to freeze–thaw subjected specimens. Linear relationships between air-dry and water-saturated bulk densities and between UCS and modulus of elasticity were found. Micro-fabric influences strength and aggregate parameters of studied andesites; fine porphyritic andesite has the highest UCS and tensile strength and the best micro-Deval results, while coarser porphyritic andesite has lower strength and aggregate parameters. Test results were compared with previously published rock mechanical data of intermediate and basic igneous rocks. A good exponential correlation was found between micro-Deval and UCS values of this paper and previously published data sets, but there was no indication that micro-Deval values correlate well with Los Angeles values.     

Prediction of strength parameters of sedimentary rocks using artificial neural networks and regression analysis

Accurate laboratory measurement of geo-engineering properties of intact rock including uniaxial compressive strength (UCS) and modulus of elasticity (E) involves high costs and a substantial amount of time. For this reason, it is of great necessity to develop some relationships and models for estimating these parameters in rock engineering. The present study was conducted to forecast UCS and E in the sedimentary rocks using artificial neural networks (ANNs) and multivariable regression analysis (MLR). For this purpose, a total of 196 rock samples from four rock types (i.e., sandstone, conglomerate, limestone, and marl) were cored and subjected to comprehensive laboratory tests. To develop the predictive models, physical properties of studied rocks such as P wave velocity (V_p), dry density (γ_d), porosity, and water absorption (A_b) were considered as model inputs, while UCS and E were the output parameters. We evaluated the performance of MLR and ANN models by calculating correlation coefficient (R), mean absolute error (MAE), and root-mean-square error (RMSE) indices. The comparison of the obtained results revealed that ANN outperforms MLR when predicting the UCS and E.     

Generation of correlated properties in heterogeneous porous media

The spatial distribution of rock properties in porous media, such as permeability and porosity, often is strongly variable. Therefore, these properties usefully may be considered as a random field. However, this variability is correlated frequently on length scales comparable to geological lengths (for example, scales of sand bodies or facies). To solve various engineering problems (for example, in the oil recovery process) numerical models of a porous medium often are used. A need exists then to understand correlated random fields and to generate them over discretized numerical grids. The paper describes the general mathematical methods required to do this, with one particular method (the nearest neighbor model) described in detail. How parameters of the mathematical model may be related to rock property statistics for the nearest neighbor model is shown. The method is described in detail in one, two, and three dimensions. Examples are given of how model parameters may be determined from real data.     

A novel random discrete element analysis of rock fragmentation

This paper presents a novel probabilistic approach of random discrete element analysis (RDEA) to investigate the mechanism of rock fragmentation under uniaxial compression. This model combines the advantages of both random field theory and discrete element method in characterizing the spatial variation and uncertainty of microscopic material properties. The numerical results reveal that the stress-strain curves of a group of tests can match well the general trend of the experimental data, with the mean uniaxial compressive strength (UCS) of 10.18 MPa and the mean Young modulus of 1.73 GPa. The coefficient of variation (COV) for the rock samples is much lower than that of the initial random fields of particles because of the averaging effect of microscopic material property in obtaining the bulk values. The rock fragmentation is initiated by the breakage of weak particles within the rock mass, and it develops rapidly as the vertical loading stress approaches the UCS. The final damage zone resides dominantly in the weak region of the rock sample, and the distribution of material property coefficients follows a similar beta distribution as the corresponding initial random field. Rock samples with persistent “pillar-like” structures of strong particles can effectively resist the normal compression, resulting in high rock strengths. The traditional DEM simulation with a set of constant material properties can only represent one extreme realization of random field, which could significantly overestimate the rock strength. The proposed RDEA approach can effectively capture the uncertainty and complex interactions of rock fragmentation in a more realistic and reliable way.     

Prediction of Probabilistic Settlements by the Perturbation-Based Spectral Stochastic Meshless Local Petrov–Galerkin Method

Originating an attempt of understanding the reliability and serviceability of foundations, an interest of comparing the difference between settlements predicted with and without considering the uncertainty in such as the spatial variability of soil properties is born. This study selectively compares between settlements predicted with and without considering the uncertainty in the spatial variability of Young’s modulus. The tool is a coupling of perturbation expansions of Young moduli and a two-dimensional meshfree weak-strong form in elastostatics. Two further examples show that the spatial variability of Young’s modulus causes apparent difference between probabilistic and deterministic settlement components along the direction of a surcharge. We can derive an autocorrelation function to describe the spatial variability of Young’s modulus and understand how it affects predicted settlements depending upon autocorrelation function values. In addition, the spectral stochastic meshless local Petrov–Galerkin method is a time-saving tool for predicting probabilistic settlements with the uncertainty in the spatial variability of soil properties.     

Artificial neural networks and nonlinear regression techniques to assess the influence of slake durability cycles on the prediction of uniaxial compressive strength and modulus of elasticity for carbonate rocks

Understanding rock material characterizations and solving relevant problems are quite difficult tasks because of their complex behavior, which sometimes cannot be identified without intelligent, numerical, and analytical approaches. Because of that, some prediction techniques, like artificial neural networks (ANN) and nonlinear regression techniques, can be utilized to solve those problems. The purpose of this study is to examine the effects of the cycling integer of slake durability index test on intact rock behavior and estimate some rock properties, such as uniaxial compressive strength (UCS) and modulus of elasticity (E) from known rock index parameters using ANN and various regression techniques. Further, new performance index (PI) and degree of consistency (Cd) are introduced to examine the accuracy of generated models. For these purposes, intact rock dataset is established by performing rock tests including uniaxial compressive strength, modulus of elasticity, Schmidt hammer, effective porosity, dry unit weight, p‐wave velocity, and slake durability index tests on selected carbonate rocks. Afterward, the models are developed using ANN and nonlinear regression techniques. The concluding remark given is that four‐cycle slake durability index (I_d4) provides more accurate results to evaluate material characterization of carbonate rocks, and it is one of the reliable input variables to estimate UCS and E of carbonate rocks; introduced performance indices, both PI and Cd, may be accepted as good indicators to assess the accuracy of the complex models, and further, the ANN models have more prediction capability than the regression techniques to estimate relevant rock properties. Copyright © 2011 John Wiley & Sons, Ltd.     

Fuzzy and Multiple Regression Modelling for Evaluation of Intact Rock Strength Based on Point Load, Schmidt Hammer and Sonic Velocity

Summary. Uniaxial Compressive Strength (UCS), considered to be one of the most useful rock properties for mining and civil engineering applications, has been estimated from some index test results by fuzzy and multiple regression modelling. Laboratory investigations including Uniaxial Compressive Strength (UCS), Point Load Index test (PL), Schmidt Hammer Hardness test (SHR) and Sonic velocity (V_p) test have been carried out on nine different rock types yielding to 305 tested specimens in total. Average values along with the standard deviations (Stdev) as well as Coefficients of variation (CoV) have been calculated for each rock type. Having constructed the Mamdani Fuzzy algorithm, UCS of intact rock samples was then predicted using a data driven fuzzy model. The predicted values derived from fuzzy model were compared with multi-linear statistical model. Comparison proved that the best model predictions have been achieved by fuzzy modelling in contrast to multi-linear statistical modelling. As a result, the developed fuzzy model based on point load, Schmidt hammer and sonic velocity can be used as a tool to predict UCS of intact rocks.     

3-D geochemical interpolation guided by geophysical inversion models

3-D geochemical subsurface models, as constructed by spatial interpolation of drill-core assays, are valuable assets across multiple stages of the mineral industry's workflow.However, the accuracy of such models is limited by the spatial sparsity of the underlying drill-core, which samples only a small fraction of the subsurface.This limitation can be alleviated by integrating collocated 3-D models into the interpolation process, such as the 3-D rock property models produced by modern geophysical inversion procedures, provided that they are sufficiently resolved and correlated with the interpolation target.While standard machine learning algorithms are capable of predicting the target property given these data, incorporating spatial autocorrelation and anisotropy in these models is often not possible.We propose a Gaussian process regression model for 3-D geochemical interpolation, where custom kernels are introduced to integrate collocated 3-D rock property models while addressing the trade-off between the spatial proximity of drill-cores and the similarities in their collocated rock properties, as well as the relative degree to which each supporting 3-D model contributes to interpolation.The proposed model was evaluated for 3-D modelling of Mg content in the Kevitsa Ni-Cu-PGE deposit based on drill-core analyses and four 3-D geophysical inversion models.Incorporating the inversion models improved the regression model's likelihood(relative to a purely spatial Gaussian process regression model) when evaluated at held-out test holes, but only for moderate spatial scales(100 m).     

克里金参数估值法及其在参数估计分析中的应用

为考虑岩土介质参数的空间分布的结构性和随机性等不确定因素,引入了克里金参数估值法。采用变异函数描述参数在空间结构上的变化,建立其空间变异规律的数学模型,从而实现对岩土参数的估值。通过实例分析揭示了克里金估值法具有反映“过滤效应”和“集团效应”的优点,对不同位置的数据赋予不同的权重系数,能够有效地反映参数空间变异结构,有利于对参数的合理化分析     

Application of statistical methods for predicting uniaxial compressive strength of limestone rocks using nondestructive tests

Uniaxial compressive strength (UCS) of an intact rock is an important geotechnical parameter for engineering applications. Using standard laboratory tests to determine UCS is a difficult, expensive and time-consuming task. The main purpose of this study is to develop a general model for predicting UCS of limestone samples and to investigate the relationships among UCS, Schmidt hammer rebound and P-wave velocity (V _P). For this reason, some samples of limestone rocks were collected from the southwestern Iran. In order to evaluate a correlation, the measured and predicted values were examined utilizing simple and multivariate regression techniques. In order to check the performance of the proposed equation, coefficient of determination (R ²), root-mean-square error, mean absolute percentage error, variance accounts for (VAF %), Akaike Information Criterion and performance index were determined. The results showed that the proposed equation by multivariate regression could be applied effectively to predict UCS from its combinations, i.e., ultrasonic pulse velocity and Schmidt hammer hardness. The results also showed that considering high prediction performance of the models developed, they can be used to perform preliminary stages of rock engineering assessments. It was evident that such prediction studies not only provide some practical tools but also contribute to better understanding of the main controlling index parameters of UCS of rocks.