Burden prediction in blasting operation using rock geomechanical properties

Burden prediction is a vital task in the production blasting. Both the excessive and insufficient burden can significantly affect the result of blasting operation. The burden which is determined by empirical models is often inaccurate and needs to be adjusted experimentally. In this paper, an attempt was made to develop an artificial neural network (ANN) in order to predict burden in the blasting operation of the Mouteh gold mine, using considering geomechanical properties of rocks as input parameters. As such here, network inputs consist of blastability index (BI), rock quality designation (RQD), unconfined compressive strength (UCS), density, and cohesive strength. To make a database (including 95 datasets), rock samples are used from Iran’s Mouteh goldmine. Trying various types of the networks, a neural network, with architecture 5-15-10-1, was found to be optimum. Superiority of ANN over regression model is proved by calculating. To compare the performance of the ANN modeling with that of multivariable regression analysis (MVRA), mean absolute error (E _a), mean relative error (E _r), and determination coefficient (R ²) between predicted and real values were calculated for both the models. It was observed that the ANN prediction capability is better than that of MVRA. The absolute and relative errors for the ANN model were calculated 0.05 m and 3.85%, respectively, whereas for the regression analysis, these errors were computed 0.11 m and 5.63%, respectively. Moreover, determination coefficient of the ANN model and MVRA were determined 0.987 and 0.924, respectively. Further, a sensitivity analysis shows that while BI and RQD were recognized as the most sensitive and effective parameters, cohesive strength is considered as the least sensitive input parameters on the ANN model output effective on the proposed (burden).     

Prediction of thermal conductivity of rocks by soft computing

The transfer of energy between two adjacent parts of rock mainly depends on its thermal conductivity. Knowledge of the thermal conductivity of rocks is necessary for the calculation of heat flow or for the longtime modeling of geothermal resources. In recent years, considerable effort has been made to develop artificial intelligence techniques to determine these properties. Present study supports the application of artificial neural network (ANN) in the study of thermal conductivity along with other intrinsic properties of rock due to its increasing importance in many areas of rock engineering, agronomy, and geoenvironmental engineering field. In this paper, an attempt has been made to predict the thermal conductivity (TC) of rocks by incorporating uniaxial compressive strength, density, porosity, and P-wave velocity using artificial neural network (ANN) technique. A three-layer feed forward back propagation neural network with 4-7-1 architecture was trained and tested using 107 experimental data sets of various rocks. Twenty new data sets were used for the validation and comparison of the TC by ANN. Multivariate regression analysis (MVRA) has also been done with same data sets of ANN. ANN and MVRA results were compared based on coefficient of determination (CoD) and mean absolute error (MAE) between experimental and predicted values of TC. It was found that CoD between measured and predicted values of TC by ANN and MVRA were 0.984 and 0.914, respectively, whereas MAE was 0.0894 and 0.2085 for ANN and MVRA, respectively.     

Microparameter Prediction for a Triaxial Compression PFC3D Model of Rock Using Full Factorial Designs and Artificial Neural Networks

This paper presents an integrated approach that predicts the microparameters of the particle flow code in three dimensions (PFC3D) model in triaxial compression simulations. The new approach combines a full factorial design (FFD) with an artificial neural network (ANN). The ANN model maps the input factors (triaxial compressive strength, Poisson’s ratio, and Young’s modulus) onto output variables, which are microparameters that affect the macroscopic responses in a PFC3D model. Emphasis is placed on data collection and optimization of the ANN model using FFD. The data for training and testing the ANN model were obtained from laboratory experiments and numerical simulations of a PFC3D model according to the principles of FFD. Using a backpropagation artificial neural network (BPNN) optimized with FFD principles, the object of the current study (to reliably predict the microparameters for a PFC3D model) has been achieved because the predicting data obtained by the BPNN model were in excellent agreement with the testing data.     

水岩相互作用对砂岩单轴强度的影响研究

针对重庆地区的微风化砂岩,完成了1、3、6、10、15次的干湿循环,对循环后的试件(饱水状态)进行了单轴抗压和劈裂试验。试验结果表明,干湿循环对砂岩造成了不可逆的渐进性损伤,在15次循环后,单轴抗压强度损失达20.73%,抗拉强度达51.96%,弹性模量达33.79%,三者与循环次数之间有良好的对数关系。在干湿循环过程中,砂岩的强度损伤会出现拐点,这取决于水对砂岩的侵蚀程度。     

Effect of Model Scale and Particle Size Distribution on PFC3D Simulation Results

This paper investigates the effect of model scale and particle size distribution on the simulated macroscopic mechanical properties, unconfined compressive strength (UCS), Young’s modulus and Poisson’s ratio, using the three-dimensional particle flow code (PFC3D). Four different maximum to minimum particle size (d _max/d _min) ratios, all having a continuous uniform size distribution, were considered and seven model (specimen) diameter to median particle size ratios (L/d) were studied for each d _max/d _min ratio. The results indicate that the coefficients of variation (COVs) of the simulated macroscopic mechanical properties using PFC3D decrease significantly as L/d increases. The results also indicate that the simulated mechanical properties using PFC3D show much lower COVs than those in PFC2D at all model scales. The average simulated UCS and Young’s modulus using the default PFC3D procedure keep increasing with larger L/d, although the rate of increase decreases with larger L/d. This is mainly caused by the decrease of model porosity with larger L/d associated with the default PFC3D method and the better balanced contact force chains at larger L/d. After the effect of model porosity is eliminated, the results on the net model scale effect indicate that the average simulated UCS still increases with larger L/d but the rate is much smaller, the average simulated Young’s modulus decreases with larger L/d instead, and the average simulated Poisson’s ratio versus L/d relationship remains about the same. Particle size distribution also affects the simulated macroscopic mechanical properties, larger d _max/d _min leading to greater average simulated UCS and Young’s modulus and smaller average simulated Poisson’s ratio, and the changing rates become smaller at larger d _max/d _min. This study shows that it is important to properly consider the effect of model scale and particle size distribution in PFC3D simulations.     

Effect of strain rate on strength properties of low-calcium fly-ash-based geopolymer mortar under dry condition

This paper presents the mechanical and elastic properties of inorganic polymer mortar under varying strain rates. The study includes a determination of the compressive strength, modulus of elasticity and Poisson’s ratio at 0.001, 0.005, 0.01 and 0.05 mm/s strain rate. A total of 21 cylindrical specimens having 100 mm length and 50 mm diameter were investigated, and all tests were carried out pursuant to the relevant Australian Standards. Although some variability between the mixes was observed, the results show that, in most cases, the engineering properties of geopolymer mortar compare favourably to those predicted by the relevant Australian Standards for concrete mixtures. It was found that the change in the strain rate causes different behaviour related to the percentage of the ultimate load. The ultimate strength, Young’s modulus and Poisson’s ratio of the geopolymer mortar depend on the strain rate. It was also found that as the strain rate increases, mechanical and elastic properties of geopolymer mortar substantially increase in logarithmic manner.     

攀枝花尖山矿区细中粒辉长岩力学特性试验研究

对攀枝花钒钛磁铁矿尖山矿区的细粒和中粒辉长岩进行了单轴压缩、常规三轴压缩、抗拉强度和软化等系列岩石力学试验,研究了岩石结构(矿物颗粒大小)、水和围压等因素对岩石强度和变形特性的影响。结果表明,细粒辉长岩单轴抗压强度、弹性模量和压拉比均高于中粒辉长岩,但在三轴压缩情况下,两种岩石的峰值强度、残余强度和弹性模量差异较小;与中粒辉长岩相比,细粒辉长岩的峰值强度的黏聚力C较大,而峰值强度的内摩擦角φ较小;随着围压的增长,辉长岩峰值强度、残余强度与围压近似呈线性关系,剪切破坏角减小,平均模量E增长不明显,割线模量E50增长较显著;辉长岩的软化系数较高,在水的作用下弹性模量降低,泊松比升高。     

Plane Strain Testing with Passive Restraint

A plane strain condition for testing rock is developed through passive restraint in the form of a thick-walled cylinder. The so-called biaxial frame generates the intermediate principal stress that imposes a triaxial state of stress on a prismatic specimen. Major and minor principal stresses and corresponding strains are accurately measured, providing data to calculate the elastic (Young’s modulus and Poisson’s ratio), inelastic (dilatancy angle), and strength (friction angle and cohesion) parameters of the rock. Results of experiments conducted on Indiana limestone in plane strain compression are compared with the results of axisymmetric compression and extension. With proper system calibration, Young’s modulus and Poisson’s ratio are consistent among the tests. The plane strain apparatus enforces in-plane deformation with the three principal stresses at failure being different, and it allows one to determine the Paul-Mohr-Coulomb failure surface, which includes an intermediate stress effect.     

水岩作用下泥质板岩软化非线性机制研究

水岩作用下泥质板岩表现出明显的软化特征。通过单轴压缩试验分析了泥质板岩软化过程中单轴压缩强度、弹性模量和泊松比与吸水时间之间的关系;借助核磁共振试验研究了水岩作用下泥质板岩软化过程中孔隙的产生、扩展和贯通规律,分析了泥质板岩软化过程中孔隙度与吸水时间之间的关系;采用电镜扫描试验分析了水岩作用下泥质板岩软化过程中微观结构的演变规律,基于分形理论研究了不同浸泡时间下泥质板岩分形维数的变化规律;运用非线性动力学理论,选取微观结构孔隙形状分维值、孔隙度、单轴抗压强度、弹性模量作为描述泥质板岩与水溶液相互作用系统的变量,建立了水岩作用下泥质板岩的软化模型,结合试验数据验证了模型的适用性。结果表明：泥质板岩单轴抗压强度、弹性模量随吸水时间增大而减小,呈负线性相关,而泊松比与吸水时间之间的关系不明显;在浸泡初期,水岩作用强烈,泥质板岩内部微孔隙会发生扩展贯通进而形成更大尺寸的孔隙,孔隙度在浸泡初期增长较快;随着浸泡时间的延长,水岩作用减弱,孔隙度增长速率趋缓;随着吸水时间的推移,泥质板岩内部孔隙相互连通,进而形成复杂网状结构的大孔,泥质板岩分形维数呈对数增长,最终趋于稳定;采用非线性模型计算的结果与试验数据较接近,说明泥质板岩的软化过程具有明显的非线性动力学特征,利用非线性动力学模型可以较好地表征水岩作用下泥质板岩的软化规律。研究成果可为软岩?水相互作用理论研究提供参考。     

考虑非协调变形的复合试样力学特性和破坏形式的研究

针对金属矿山接触带复合岩体非协调变形现象,开展物理相似试样单轴压缩试验,结合理论分析,研究不同介质力学性质的差异对复合试样力学特性及破坏形式的影响。试验结果表明:复合试样的单轴抗压强度和弹性模量相对两种介质中较大的单轴抗压强度和弹性模量减小,减小幅度随介质力学性质差异程度（λ）的增大而增大,同时,随着差异程度（λ）的增大,复合试样逐渐由单斜面剪切破坏变为复杂的横向拉伸破坏。理论分析表明,不同介质泊松比的差异（Δv）导致接触面处产生非协调变形,形成的侧向约束应力弱化了复合试样的力学性能,通过引入非协调变形系数α量化了非协调变形程度与泊松比的差异（Δv）之间的相关性;构建了由两种介质力学参数确定的复合试样弹性模量的表达式和轴向应力-应变本构关系式。研究结果可为接触带复合岩体非协调变形破坏的进一步分析提供理论基础。     

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.     

Analysis of size effects on the geomechanical parameters of intact granite samples under unconfined conditions

A total of 28 uniaxial compressive strength tests were performed on cylindrical Blanco Mera granite samples with diameters ranging between 14 and 100 mm, with results indicating that this granite undergoes a significant reverse size effect: the UCS increases as sample diameter increases up to 54 mm, but thereafter decreases. It was also found that the results tend to be more scattered for smaller sample diameters. We also found an apparent correlation between Young’s modulus and sample diameter. It was not possible to draw any clear conclusions regarding the variability in Poisson’s ratio with sample size. With respect to crack initiation and crack damage stresses, the behaviour of the tested samples also indicates a reverse effect. This research would suggest that the traditionally assumed decrease in strength as sample size increases does not hold for granite samples with diameters below 54 mm.     

随机分布贯穿裂隙岩体变形特性研究

洞室开挖后,其周边通常会产生许多随机分布的贯穿裂隙,直接影响洞室围岩稳定,研究随机分布贯穿裂隙岩体的变形及变形特性具有重要意义。基于线弹性理论和线性刚度理论计算岩石和裂隙的位移,用概率的方法建立了随机分布贯穿裂隙岩体变形的计算模型,给出了随机分布贯穿裂隙岩体的等效弹性模量和等效泊松比,研究了岩石和裂隙的材料参数和几何参数对岩体等效弹性模量和等效泊松比的影响。可得如下结论：等效弹性模量和等效泊松比随着岩石弹性模量的增大而增大;等效泊松比随着岩石泊松比的增大而增大;等效弹性模量和等效泊松比随着裂隙法向刚度的增大而增大;随着剪切刚度的增大,等效弹性模量逐渐增大,而等效泊松比则逐渐减少;随着裂隙平均间距的增大,等效弹性模量逐渐减小,等效泊松比在平均倾斜角较小时逐渐增大,在平均倾斜角较大时逐渐减小;随着裂隙平均倾斜角的增大,等效弹性模量先减小后增大,而等效泊松比先增大后减小。模型能较全面地考虑构成岩体的岩石和裂隙的材料参数与几何参数对岩体变形的影响,其结果对研究洞室围岩的变形和工程设计有一定的参考价值。     

Reservoir geomechanical parameters identification based on ground surface movements

Determination of geomechanical parameters of petroleum reservoir and surrounding rock is important for coupled reservoir–geomechanical modeling, borehole stability analysis and hydraulic fracturing design. A displacement back analysis technique based on artificial neural network (ANN) and genetic algorithm (GA) combination is investigated in this paper to identify reservoir geomechanical parameters based on ground surface displacements. An ANN is used to map the nonlinear relationship between Young’s modulus, E, Poisson’s ratio, v, internal friction angle, Φ, cohesion, c and ground surface displacements. The necessary training and testing samples for ANN are created by using numerical analysis. GA is used to search the set of unknown reservoir geomechanical parameters. Results of the numerical experiment show that the displacement back analysis technique based on ANN–GA combination can effectively identify reservoir geomechanical parameters based on ground surface movements as a result of oil and gas production.     

Effects of mechanical layering on hydraulic fracturing in shale gas reservoirs based on numerical models

Generally, induced hydraulic fractures are generated by fluid overpressure and are used to increase reservoir permeability through forming interconnected fracture systems. However, in heterogeneous and anisotropic rocks, many hydraulic fractures may become arrested or offset at layer contacts under certain conditions and do not form vertically connected fracture networks. Mechanical layering is an important factor causing anisotropy in sedimentary layers. Hence, in this study, with a shale gas reservoir case study in the Longmaxi Formation in the southeastern Chongqing region, Sichuan Basin, we present results from several numerical models to gain quantitative insights into the effects of mechanical layering on hydraulic fracturing. Results showed that the fractured area caused by hydraulic fracturing indicated a linear relationship with the neighboring layer’s Young’s modulus. An increase of the neighboring layer’s Young’s modulus resulted in better hydraulic fracturing effects. In addition, the contact between two neighboring layers is regarded as a zone with thickness and mechanical properties, which also influences the effects of hydraulic fracturing in reservoirs. The initial hydraulic fracture was unable to propagate into neighboring layers under a relatively low contact’s Young’s modulus. When associated local tensile stresses exceeded the rock strength, hydraulic fractures propagated into neighboring layers. Moreover, with the contact’s Young’s modulus becoming higher, the fractured area increased rapidly first, then slowly and finally became stable.     

Response of Euler–Bernoulli beam on spatially random elastic soil

A new method is developed for analysis of flexible foundations (beams) on spatially random elastic soil. The elastic soil underneath the beams is treated as a continuum, characterized by spatially random Young’s modulus and constant Poisson’s ratio. The randomness of the soil Young’s modulus is modeled using a two-dimensional non-Gaussian, homogeneous random field. The beam geometry and Young’s modulus are assumed to be deterministic. The total potential energy of the beam-soil system is minimized, and the governing differential equations and boundary conditions describing the equilibrium configuration of the system are obtained using the variational principles of mechanics. The differential equations are solved using the finite element and finite difference methods to obtain the beam and soil displacements. Four different beam lengths, representing moderately short, moderately long and long beams are analyzed for beam deflection, differential settlement, bending moment and beam shear force. The statistics of the beam responses are investigated using Monte Carlo simulations for different beam-soil modulus ratios and for different variances and scales of fluctuations of the soil Young’s modulus. Suggestions regarding the use of the analysis in design are made. A novelty in the analysis is that the two-dimensional random heterogeneity of soil is taken into account without the use of traditional two-dimensional numerical methods, which makes the new approach computationally efficient.     

Prediction of unconfined compressive strength of carbonate rocks using artificial neural networks

The unconfined compressive strength (UCS) of intact rocks is an important geotechnical parameter for engineering applications. Determining UCS using standard laboratory tests is a difficult, expensive and time consuming task. This is particularly true for thinly bedded, highly fractured, foliated, highly porous and weak rocks. Consequently, prediction models become an attractive alternative for engineering geologists. The objective of study is to select the explanatory variables (predictors) from a subset of mineralogical and index properties of the samples, based on all possible regression technique, and to prepare a prediction model of UCS using artificial neural networks (ANN). As a result of all possible regression, the total porosity and P-wave velocity in the solid part of the sample were determined as the inputs for the Levenberg–Marquardt algorithm based ANN (LM-ANN). The performance of the LM-ANN model was compared with the multiple linear regression (REG) model. When training and testing results of the outputs of the LM-ANN and REG models were examined in terms of the favorite statistical criteria, which are the determination coefficient, adjusted determination coefficient, root mean square error and variance account factor, the results of LM-ANN model were more accurate. In addition to these statistical criteria, the non-parametric Mann–Whitney U test, as an alternative to the Student’s t test, was used for comparing the homogeneities of predicted values. When all the statistics had been investigated, it was seen that the LM-ANN that has been developed, was a successful tool which was capable of UCS prediction.     

Elastically-homogeneous lattice models of damage in geomaterials

This study involves the development of the auxiliary stress approach for producing elastically-homogeneous lattice models of damage in geomaterials. The lattice models are based on random, three-dimensional assemblages of rigid-body-spring elements. Unlike conventional lattice or particle models, the elastic constants of a material (e.g., Young’s modulus and Poisson’s ratio) are represented properly in both global and local senses, without any need for calibration. The proposed approach is demonstrated and validated through analyses of homogeneous and heterogeneous systems under uni- and tri-axial loading conditions. Comparisons are made with analytical solutions and finite element results. Thereafter, the model is used to simulate a series of standard laboratory tests: (a) split-cylinder tests, and (b) uniaxial compressive tests of sedimentary rocks at the Horonobe Underground Research Laboratory in Hokkaido, Japan. Model inputs are based on physical quantities measured in the experiments. The simulation results agree well with the experimental results in terms of pre-peak stress-strain/displacement responses, strength measurements, and failure patterns.     

Random field characterization of uniaxial compressive strength and elastic modulus for intact rocks

Rock properties exhibit spatial variabilities due to complex geological processes such as sedimentation,metamorphism, weathering, and tectogenesis. Although recognized as an important factor controlling the safety of geotechnical structures in rock engineering, the spatial variability of rock properties is rarely quantified. Hence, this study characterizes the autocorrelation structures and scales of fluctuation of two important parameters of intact rocks, i.e. uniaxial compressive strength(UCS) and elastic modulus(EM).UCS and EM data for sedimentary and igneous rocks are collected. The autocorrelation structures are selected using a Bayesian model class selection approach and the scales of fluctuation for these two parameters are estimated using a Bayesian updating method. The results show that the autocorrelation structures for UCS and EM could be best described by a single exponential autocorrelation function. The scales of fluctuation for UCS and EM respectively range from 0.3 m to 8.0 m and from 0.3 m to 8.4 m.These results serve as guidelines for selecting proper autocorrelation functions and autocorrelation distances for rock properties in reliability analyses and could also be used as prior information for quantifying the spatial variability of rock properties in a Bayesian framework.