Effects of loading rate on rock fracture

By means of a wedge loading applied to a short-rod rock fracture specimen tested with the MTS 810 or SHPB (split Hopkinson pressure bar), the fracture toughness of Fangshan gabbro and Fangshan marble was measured over a wide range of loading rates, =10⁻²–10⁶ MPa m^1/2 s⁻¹. In order to determine the dynamic fracture toughness of the rock as exactly as possible, the dynamic Moiré method and strain–gauge method were used in determining the critical time of dynamic fracture. The testing results indicated that the critical time was generally shorter than the transmitted wave peak time, and the differences between the two times had a weak increasing tendency with loading rates. The experimental results for rock fracture showed that the static fracture toughness K_Ic of the rock was nearly a constant, but the dynamic fracture toughness K_Id of the rock ( ≥10⁴ MPa m^1/2 s⁻¹) increased with the loading rate, i.e. log(K_Id)=a log +b. Macroobservations for fractured rock specimens indicated that, in the section (which was perpendicular to the fracture surface) of a specimen loaded by a dynamic load, there was clear crack branching or bifurcation, and the higher the loading rate was, the more branching cracks occurred. Furthermore, at very high loading rates ( ≥10⁶ MPa m^1/2 s⁻¹) the rock specimen was broken into several fragments rather than only two halves. However, for a statically fractured specimen there was hardly any crack branching. Finally, some applications of this investigation in engineering practice are discussed.     

Data-driven estimation of joint roughness coefficient

Joint roughness is one of the most important issues in the hydromechanical behavior of rock mass. Therefore, the joint roughness coefficient (JRC) estimation is of paramount importance in geomechanics engineering applications. Studies show that the application of statistical parameters alone may not produce a sufficiently reliable estimation of the JRC values. Therefore, alternative data-driven methods are proposed to assess the JRC values. In this study, Gaussian process (GP), K-star, random forest (RF), and extreme gradient boosting (XGBoost) models are employed, and their performance and accuracy are compared with those of benchmark regression formula (i.e. Z₂, R_p, and SD_i) for the JRC estimation. To analyze the models’ performance, 112 rock joint profile datasets having eight common statistical parameters (R_ave, R_max, SD_h, i_ave, SD_i, Z₂, R_p, and SF) and one output variable (JRC) are utilized, of which 89 and 23 datasets are used for training and validation of models, respectively. The interpretability of the developed XGBoost model is presented in terms of feature importance ranking, partial dependence plots (PDPs), feature interaction, and local interpretable model-agnostic explanations (LIME) techniques. Analyses of results show that machine learning models demonstrate higher accuracy and precision for estimating JRC values compared with the benchmark empirical equations, indicating the generalization ability of the data-driven models in better estimation accuracy.     

Comparison of machine learning methods for ground settlement prediction with different tunneling datasets

This study integrates different machine learning (ML) methods and 5-fold cross-validation (CV) method to estimate the ground maximal surface settlement (MSS) induced by tunneling. We further investigate the applicability of artificial intelligent (AI) based prediction through a comparative study of two tunnelling datasets with different sizes and features. Four different ML approaches, including support vector machine (SVM), random forest (RF), back-propagation neural network (BPNN), and deep neural network (DNN), are utilized. Two techniques, i.e. particle swarm optimization (PSO) and grid search (GS) methods, are adopted for hyperparameter optimization. To assess the reliability and efficiency of the predictions, three performance evaluation indicators, including the mean absolute error (MAE), root mean square error (RMSE), and Pearson correlation coefficient (R), are calculated. Our results indicate that proposed models can accurately and efficiently predict the settlement, while the RF model outperforms the other three methods on both datasets. The difference in model performance on two datasets (Datasets A and B) reveals the importance of data quality and quantity. Sensitivity analysis indicates that Dataset A is more significantly affected by geological conditions, while geometric characteristics play a more dominant role on Dataset B.     

Effects of confining pressure and temperature on mixed-mode (I–II) fracture toughness of a limestone rock

Studying fracture toughness behavior at elevated temperatures and confining pressures is valuable for a number of practical situations such as hydraulic fracturing used to enhance oil and gas recovery from a reservoir, and the disposal or safe storage of radioactive waste in underground cavities. Mixed-mode (I–II) fracture toughness under simulated reservoir conditions of high temperature and confining pressure was studied using straight notched Brazilian disk (SNBD) specimens under diametrical compression. Rock samples were collected from a limestone formation outcropping in the Central Province of Saudi Arabia. Tests were conducted under an effective confining pressure (σ₃) of up to 28 MPa (4000 psi), and a temperature of up to 116°C. The results show a substantial increase in fracture toughness under confining pressure. The pure mode-I fracture toughness (K_IC) increased by a factor of about 3.7 under a σ₃ of 28 MPa compared to that under ambient conditions. The variation of K_IC was found to be linearly proportional to σ₃. The pure mode-II fracture toughness (K_IIC) increased by a factor of 2.4 upon increasing σ₃ to 28 MPa. On the other hand, K_IC at 116°C was only 25% more than that at ambient conditions. Some ductile behavior was displayed by the rock samples at a high temperature and confining pressure.     

Estimation of convergence of a high-speed railway tunnel in weak rocks using an adaptive neuro-fuzzy inference system(ANFIS) approach

Estimation of tunnel diameter convergence is a very important issue for tunneling construction,especially when the new Austrian tunneling method(NATM) is adopted.For this purpose,a systematic convergence measurement is usually implemented to adjust the design during the whole construction,and consequently deadly hazards can be prevented.In this study,a new fuzzy model capable of predicting the diameter convergences of a high-speed railway tunnel was developed on the basis of adaptive neuro-fuzzy inference system(ANFIS) approach.The proposed model used more than 1 000 datasets collected from two different tunnels,i.e.Daguan tunnel No.2 and Yaojia tunnel No.1,which are part of a tunnel located in Hunan Province,China.Six Takagi-Sugeno fuzzy inference systems were constructed by using subtractive clustering method.The data obtained from Daguan tunnel No.2 were used for model training,while the data from Yaojia tunnel No.1 were employed to evaluate the performance of the model.The input parameters include surrounding rock masses(SRM) rating index,ground engineering conditions(GEC) rating index,tunnel overburden(H),rock density(?),distance between monitoring station and working face(D),and elapsed time(T).The model’s performance was assessed by the variance account for(VAF),root mean square error(RMSE),mean absolute percentage error(MAPE) as well as the coefficient of determination(R2) between measured and predicted data as recommended by many researchers.The results showed excellent prediction accuracy and it was suggested that the proposed model can be used to estimate the tunnel convergence and convergence velocity.     

Shear fracture (Mode II) of brittle rock

Mode II fracture initiation and propagation plays an important role under certain loading conditions in rock fracture mechanics. Under pure tensile, pure shear, tension- and compression-shear loading, the maximum Mode I stress intensity factor, K_Imax, is always larger than the maximum Mode II stress intensity factor, K_IImax. For brittle materials, Mode I fracture toughness, K_IC, is usually smaller than Mode II fracture toughness, K_IIC. Therefore, K_Imax reaches K_IC before K_IImax reaches K_IIC, which inevitably leads to Mode I fracture. Due to inexistence of Mode II fracture under pure shear, tension- and compression-shear loading, classical mixed mode fracture criteria can only predict Mode I fracture but not Mode II fracture. A new mixed mode fracture criterion has been established for predicting Mode I or Mode II fracture of brittle materials. It is based on the examination of Mode I and Mode II stress intensity factors on the arbitrary plane θ,K_I(θ) and K_II(θ), varying with θ(−180°θ+180°), no matter what kind of loading condition is applied. Mode I fracture occurs when (K_IImax/K_Imax)<1 or 1<(K_IImax/K_Imax)<(K_IIC/K_IC) and K_Imax=K_IC at θ_IC. Mode II fracture occurs when (K_IImax/K_Imax)>(K_IIC/K_IC) and K_IImax=K_IIC at θ_IIC. The validity of the new criterion is demonstrated by experimental results of shear-box testing.Shear-box test of cubic specimen is a potential method for determining Mode II fracture toughness K_IIC of rock since it can create a favorable condition for Mode II fracture, i.e. K_IImax is always 2–3 times larger than K_Imax and reaches K_IIC before K_Imax reaches K_IC. The size effect on K_IIC for single- and double-notched specimens has been studied for different specimen thickness B, dimensionless notch length a/W (or 2a/W) and notch inclination angle α. The test results show that K_IIC decreases as B increases and becomes a constant when B is equal to or larger than W for both the single- and double-notched specimens. When a/W (or 2a/W) increases, K_IIC decreases and approaches a limit. The α has a minor effect on K_IIC when α is within 65–75°. Specimen dimensions for obtaining a reliable and reproducible value of K_IIC under shear-box testing are presented. Numerical results demonstrate that under the shear-box loading condition, tensile stress around the notch tip can be effectively restrained by the compressive loading. At peak load, the maximum normal stress is smaller than the tensile strength of rock, while the maximum shear stress is larger than the shear strength in the presence of compressive stress, which results in shear failure.     

Dynamic cracked chevron notched Brazilian disc method for measuring rock fracture parameters

The cracked chevron notch Brazilian disc (CCNBD) method is widely used in characterizing rock fracture toughness. We explore here the possibility of extending the CCNBD method to dynamic rock fracture testing. In dynamic rock fractures, relevant fracture parameters are the initiation fracture toughness, the fracture energy, the fracture propagation toughness, and the fracture velocity. The dynamic load is applied with a split Hopkinson pressure bar (SHPB) apparatus. A strain gauge is mounted on the sample surface near the notch tip to detect the fracture-induced strain release, and a laser gap gauge (LGG) is used to monitor the crack surface opening distance (CSOD) during the test. With dynamic force balance achieved in the tests, the stable–unstable transition of the crack propagation crack is observed and the initiation fracture toughness is obtained from the peak load. The dynamic fracture initiation toughness values obtained for the chosen rock (Laurentian granite) using this method are consistent with those measured using other methods. The dynamic fracture initiation toughness is in the range 2.5–4.6 MPa m^1/2 and the propagation fracture toughness is in the range 7.1–10.6 MPa m^1/2, which is consistently larger than the initiation toughness.     

Prediction of rock fragmentation due to blasting in Gol-E-Gohar iron mine using fuzzy logic

Usually, the rock fragmentation is used in the mining industry as an index to estimate the effect of bench blasting. However, a good fragmentation is a concept that it mainly depends on the downstream process characteristics i.e. mucking equipment, processing plant, mining goal etc. As a matter of fact, the fragmentation has a direct effect on the costs of drilling and blasting as well as economics of the subsequent operations. Using regression analysis and fuzzy inference system (FIS), the present paper tries to develop predictive models in order to predict fragmentation caused by blasting at Gol-E-Gohar iron mine. It is worth mentioning that the rock fragmentation is influenced by various parameters such as rock mass properties, blast geometry and explosive properties. With regard to the aforementioned fuzzy system, the paper prepares a database of the blasting operations, which includes burden, spacing, hole-depth, specific drilling, stemming length, charge-per-delay, rock density and powder factor as input parameters and fragmentation as output parameter. Since the explosive was unchanged in all the blasts, therefore, it cannot be considered. To validate and compare the obtained results, determination coefficient (R²) and root mean square error (RMSE) index are chosen and calculated for both the models. It is observed that the fuzzy predictor performs, significantly, better than the statistical method. For the fuzzy model, R² and RMSE are equal to 0.96 and 3.26, respectively, whereas for regression model, they are 0.80 and 6.83, respectively.     

Developing cation exchange capacity and soil index properties relationships using a neuro-fuzzy approach

Artificial intelligence methods are employed to predict cation exchange capacity (CEC) from five different soil index properties, namely specific surface area (SSA), liquid limit, plasticity index, activity (ACT), and clay fraction (CF). Artificial neural networks (ANNs) analyses were first employed to determine the most related index parameters with cation exchange capacity. For this purpose, 40 datasets were employed to train the network and 10 datasets were used to test it. The ANN analyses were conducted with 15 different input vector combinations using same datasets. As a result of this investigation, the ANN analyses revealed that SSA and ACT are the most effective parameters on the CEC. Next, based upon these most effective input parameters, the fuzzy logic (FL) model was developed for the CEC. In the developed FL model, triangular membership functions were employed for both the input (SSA and ACT) variables and the output variable (CEC). A total of nine Mamdani fuzzy rules were deduced from the datasets, used for the training of the ANN model. Minimization (min) inferencing, maximum (max) composition, and centroid defuzzification methods are employed for the constructed FL model. The developed FL model was then tested against the remaining datasets, which were also used for testing the ANN model. The prediction results are satisfactory with a determination coefficient, R ² = 0.94 and mean absolute error, (MAE) = 7.1.     

An evolutionary adaptive neuro-fuzzy inference system for estimating field penetration index of tunnel boring machine in rock mass

Field penetration index (FPI) is one of the representative key parameters to examine the tunnel boring machine (TBM) performance. Lack of accurate FPI prediction can be responsible for numerous disastrous incidents associated with rock mechanics and engineering. This study aims to predict TBM performance (i.e. FPI) by an efficient and improved adaptive neuro-fuzzy inference system (ANFIS) model. This was done using an evolutionary algorithm, i.e. artificial bee colony (ABC) algorithm mixed with the ANFIS model. The role of ABC algorithm in this system is to find the optimum membership functions (MFs) of ANFIS model to achieve a higher degree of accuracy. The procedure and modeling were conducted on a tunnelling database comprising of more than 150 data samples where brittleness index (BI), fracture spacing, α angle between the plane of weakness and the TBM driven direction, and field single cutter load were assigned as model inputs to approximate FPI values. According to the results obtained by performance indices, the proposed ANFIS_ABC model was able to receive the highest accuracy level in predicting FPI values compared with ANFIS model. In terms of coefficient of determination (R²), the values of 0.951 and 0.901 were obtained for training and testing stages of the proposed ANFIS_ABC model, respectively, which confirm its power and capability in solving TBM performance problem. The proposed model can be used in the other areas of rock mechanics and underground space technologies with similar conditions.     

Prediction of flyrock distance induced by mine blasting using a novel Harris Hawks optimization-based multi-layer perceptron neural network

In mining or construction projects, for exploitation of hard rock with high strength properties, blasting is frequently applied to breaking or moving them using high explosive energy. However, use of explosives may lead to the flyrock phenomenon. Flyrock can damage structures or nearby equipment in the surrounding areas and inflict harm to humans, especially workers in the working sites. Thus, prediction of flyrock is of high importance. In this investigation, examination and estimation/forecast of flyrock distance induced by blasting through the application of five artificial intelligent algorithms were carried out. One hundred and fifty-two blasting events in three open-pit granite mines in Johor, Malaysia, were monitored to collect field data. The collected data include blasting parameters and rock mass properties. Site-specific weathering index (WI), geological strength index (GSI) and rock quality designation (RQD) are rock mass properties. Multi-layer perceptron (MLP), random forest (RF), support vector machine (SVM), and hybrid models including Harris Hawks optimization-based MLP (known as HHO-MLP) and whale optimization algorithm-based MLP (known as WOA-MLP) were developed. The performance of various models was assessed through various performance indices, including a10-index, coefficient of determination (R²), root mean squared error (RMSE), mean absolute percentage error (MAPE), variance accounted for (VAF), and root squared error (RSE). The a10-index values for MLP, RF, SVM, HHO-MLP and WOA-MLP are 0.953, 0.933, 0.937, 0.991 and 0.972, respectively. R² of HHO-MLP is 0.998, which achieved the best performance among all five machine learning (ML) models.     

Gene expression programming for total bed material load estimation—a case study

This paper presents Gene-Expression Programming (GEP), which is an extension to the genetic programming (GP) approach to predict the total bed material load for three Malaysian rivers. The GEP is employed without any restriction to an extensive database compiled from measurements in the Muda, Langat, and Kurau rivers. The GEP approach demonstrated a superior performance compared to other traditional sediment load methods. The coefficient of determination, R² (= 0.97) and the mean square error, MSE (= 0.057) of the GEP method are higher than those of the traditional method. The performance of the GEP method demonstrates its predictive capability and the possibility of the generalization of the model to nonlinear problems for river engineering applications.     

Rock fracture toughness testing in Mode II—punch-through shear test

A new testing method called punch-through shear test for measurement of Mode II fracture toughness, K_IIC, of rock is introduced. Results from a finite element modelling (FEM) and a series of laboratory tests on limestone, marble and granite are presented. Core samples with 50 mm diameter are cut to length equal to diameter. Circular notches are drilled to different depths at both ends leaving an intact portion in the centre of the core. The sample is subjected to different confining pressures up to 70 MPa and an axial load is applied to punch through the central portion of the core. K_IIC is calculated from a displacement gradient approach using FEM, assuming linear elasticity to be valid according to the fracture breakdown zone model by Cowie and Scholz. Results from testing show that K_IIC increases with increasing confining pressure and in the order of limestone, marble and granite. At confining pressures higher than 30 MPa the Mode II fracture toughness approaches a constant value. Fracture initiation and propagation differ among the three rock types where grain size is found to have a strong influence on the mechanism of microfracturing and failure. It is suggested that data of K_IIC should be presented for high confining pressures as large confining pressures enhance the appearance of shear fractures.     

Fracture toughness study for a brittle rock subjected to mixed mode I/II loading

A semi-disk specimen containing an angled edge crack has been used in the past for conducting fracture tests on a brittle rock named Johnstone [Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 2—mixed mode. Int J Rock Mech Min Sci Geomech Abstr 1994b;31(3):199–212]. The test specimen is appropriate for investigating brittle fracture when the rock samples are subjected to the combined effects of tension and shear along the crack line. However, the experimental results reported in Lim, Johnston, Choi, Boland [Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 2—mixed mode. Int J Rock Mech Min Sci Geomech Abstr 1994b;31(3):199–212.] are inconsistent with all of the well-known theoretical criteria available for predicting mixed mode brittle fracture. In this paper, a modified criterion is used to provide accurate predictions for the reported experimental results. The modified criterion makes use of a three-parameter model (based on K_I, K_II and T) for describing the crack tip stresses. It is shown that the non-singular stress term T has a significant role when the rock fracture tests are conducted on the semi-disk specimens.     

基于强度参数脆性指数的岩石Ⅰ型断裂韧度评价

在试验数据收集基础上,选取3种典型强度脆性指数作为考察对象,建立Ⅰ型断裂韧度与脆性指数之间的线性关系,得到基于不同脆性指数的岩石Ⅰ型断裂韧度参数化模型。通过引入交叉验证法获得准确的模型参数,并对模拟结果进行检验,评价各模型的适用性和相互之间的差异。结果表明:3种评价模型在评价和预测岩石Ⅰ型断裂韧度上均有很强的可靠性,可以借助脆性指数评价岩石的Ⅰ型断裂韧度;3种模型的评价和预测精度存在一定差异,总体来看,基于莫尔圆脆性指数的评价模型优于压拉强度脆性指数评价模型和抗压强度脆性指数评价模型,从而证明Ⅰ型断裂韧度是岩石综合力学性质的体现,利用多强度指标建立评价模型将会获得更准确、合理的Ⅰ型断裂韧度值;由于抗压强度获取便捷,利用其建立的评价模型也具有较高的评价精度,在要求快速评价时,可优先考虑选择基于抗压强度脆性指数的岩石Ⅰ型断裂韧度评价模型。     

Influence of rock mass fracturing on the net penetration rates of hard rock TBMs

Penetration rates during excavation using hard rock tunnel boring machines (TBMs) are significantly influenced by the degree of fracturing of the rock mass. In the NTNU prediction model for hard rock TBM performance and costs, the rock mass fracturing factor (k_s) is used to include the influence of rock mass fractures. The rock mass fracturing factor depends on the degree of fracturing, fracture type, fracture spacing, and the angle between fracture systems and the tunnel axis. In order to validate the relationship between the degree of fracturing and the net penetration rate of hard rock TBMs, field work has been carried out, consisting of geological back-mapping and analysis of performance data from a TBM tunnel. The rock mass influence on hard rock TBM performance prediction is taken into account in the NTNU model. Different correlations between net penetration rate and the fracturing factor (k_s) have been identified for a variety of k_s values.     

利用测井资料预测岩石II型断裂韧性 的方法研究

 根据直缝巴西圆盘(SNBD)试验获取应力强度因子的计算原理,设计组建一套岩石II型断裂韧性测试系统,测定20块取自WG油田岩石试样的II型断裂韧性。基于试验数据,分析II型断裂韧性和围压、抗拉强度的关系,建立利用测井资料预测断裂韧性的模型。利用H341井声波测井、密度测井和伽马测井资料预测水平地应力和抗拉强度,结合建立的断裂韧性模型成功预测II型断裂韧性连续值,并在压裂实践中得到验证。该方法解决了现场压裂作业缺少断裂韧性全井筒连续数据的难题。     

Assessment of rock fracture surface roughness using Riemannian statistics of linear profiles

The mechanical behaviour of rock masses is complex, due partly to the presence of discontinuities within them. Of the geometrical parameters of discontinuities, surface roughness, which encapsulates the topographical features of a rock surface, is known to play a significant role. Here, a new parameter for quantitative roughness determination based on the distribution of unit normal vectors to a rock profile is presented.The analysis of unit normal vectors in terms of directional statistics is customarily performed in Euclidean space using a Cartesian co-ordinate system. Here, the analysis is developed using Riemannian geometry, with Mahalanobis distances being proposed for discrimination between different rock profiles. Statistical parameters on the unit circle are extracted using Riemannian geometry, and from that a roughness parameter, D_R1, is obtained. This parameter corresponds to 1D Riemannian dispersion, and as such D_R1 increases as profile roughness increases.D_R1 is applied to the analysis of synthetic profiles and some real rock profiles. Conclusions are drawn that demonstrate the advantages of the new method in terms of investigating the scale effect in roughness determination as well as in comparing different profiles.A preliminary study into the correlation between D_R1 and the shear strength of a fracture, using analytical and numerical investigation of the strength of profiles comprising symmetric triangular asperities sheared at different normal stress levels, shows a clear relation between Riemannian roughness parameter and profile shear strength.     

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.