Permeability of granular soil employing flexible wall permeameter

Understanding the changes in permeability of soil, when soil is subjected to high confining pressure and flow pressure, which may alter the textural and geomechanical characteristics of soil, is of great importance to many geo-engineering activities such as, construction of high-rise buildings near the coast or the water bodies, earthen dams, pavement subgrades, reservoir, and shallow repositories. It is now possible to evaluate the changes in permeability of soil samples under varying conditions of confining pressure and flow pressure using flexible wall permeameter (FWP). In the present study, investigation was carried out on a cylindrical sample of granular soil employing FWP under varied conditions of confining pressure (σ₃)—50–300 kPa, which can simulate the stress conditions equivalent to depth of about 20 m under the earth’s crust, and a flow pressure (f_p)—20–120 kPa, which is mainly present near the small earthen embankment dams, landfill liners, and slurry walls near the soft granular soil with high groundwater table. The obtained results indicate a linear relationship between hydraulic conductivity (k) with effective confining pressure (σ_eff.), k, decreasing linearly with an incremental change in σ_eff.. Further, k increases significantly with an increase in f_p corresponding to each σ_eff., and q increases significantly with increase in the f_p corresponding to each (σ₃). It was also observed that corresponding to the low f_p of 20 kPa, the reduction in k is nonlinear with σ_3. The percentage reduction in k is observed to be 9, 13, and 27% corresponding to σ₃ of 50–100, 100–200, and 200-300 kPa, respectively.     

Impact of pore water conductivity and porosity on the electrical conductivity of kaolinite

The purpose of this study is to quantify the magnitudes of surface conduction and pore water conduction from the measured electrical conductivity of kaolinite, with the ultimate goal of estimating the electrical conductivity of kaolinite with a wide range of pore water conductivities (σ _w = 0.013–3.356 S/m) and porosities (n = 0.368–1.0). Therefore, the theoretical background of the electrical conductivity in soils was reviewed, and electrical conductivity measurements on kaolinite were performed using both slurry and consolidation tests in this study. The results of this study demonstrate that the variations of measured electrical conductivity (σ _mix) with n are debatable according to the values of σ _w, because a decrease in n results in both an increase in surface conduction (K _s) and a decrease in pore water conduction (K _w); this causes the relative magnitude of K _s compared to that of K _w to vary with σ _w and n. Consequently, this study develops the relation between the porosity-normalized K _s/K _w and 1/σ _w. Additionally, the surface conductivity of the tested kaolinite is back-calculated and compared with the previous relationship between K _s and zeta potential of kaolinite. The measured and estimated σ _mix values are compared with the varying pore water conductivity and porosity values.     

Characterization of locally available soil as a liner material for solid waste landfills in Sri Lanka

This study aimed to develop a low-cost and effective clay liner material for solid waste landfills in Sri Lanka. A locally available clayey soil and its admixtures with 5 and 10% bentonite were examined for this purpose. Laboratory experiments to determine soil plasticity and swell index were carried out on the tested samples. Hydraulic conductivity (k) tests were carried out in the laboratory using water and an aqueous solution of CaCl₂ on unconsolidated samples prepared by either dry or slurry packing and pre-consolidated samples with five different consolidation pressures (p) from 10 to 200 kPa. Measured liquid limits for tested admixtures increased with increasing bentonite contents and correlated well with measured values of the swell index. The difference in permeant solutions had little effect on measured k values for both unconsolidated and pre-consolidated samples. The hydraulic conductivities were highly affected by changing p, i.e., the k values decreased on two orders of magnitude as p increased from 10 to 200 kPa. The Kozeny–Carman equation, a theoretical permeability model that expresses the k-porosity relationship, was applied to measured data including reported values. Results showed the Kozeny–Carman equation captured well the porosity-dependent k values for tested soils and their admixtures with bentonite under a wide range of void ratios, suggesting that the Kozeny–Carman equation is a useful tool to estimate the magnitude of k values for differently compacted soil and its bentonite admixtures.     

Studies on Hydraulic Conductivity of Fly Ash-Stabilised Expansive Clay Liners

Earthen barriers or clay liners are a major concern in geo-environmental engineering. They are designed to preclude or reduce leachate migration. Hence, a low hydraulic conductivity (k) is an important parameter in the design of clay liners. Materials such as bentonite and lateritic clays, which have a low hydraulic conductivity at high dry densities, are used in the construction of clay liners. Compacted expansive clays which are high in montmorillonite content also have a very low hydraulic conductivity. When expansive clays are blended with fly ash, an industrial waste, the hydraulic conductivity further reduces as the ash-clay blends result in increased dry densities at increased fly ash contents. Hence, fly ash-stabilised expansive clay can also be proposed as an innovative clay liner material. It is, therefore, required to study various physical and engineering properties of this new clay liner material. Liquid limit (LL) and free swell index (FSI) are important index properties to be studied in the case of this clay liner material. The hydraulic conductivity of this new clay liner material depends on the fly ash content in the blend. Further, parameters such as solute concentration and kinematic viscosity also influence hydraulic conductivity of clay liners. This paper presents experimental results obtained on hydraulic conductivity (k) of fly ash-stabilised expansive clay liner at varying fly ash content and solute concentration. The tests were performed with deionised water (DIW), CaCl₂, NaCl and KCl as permeating fluids. Fly ash content in the blend was varied as 0, 10, 20 and 30 % by weight of the expansive clay, and the solute concentration was varied as 5 mM (milli molar), 10, 20, 50, 100 and 500. It was found that hydraulic conductivity (k) decreased with increasing fly ash content, solute concentration and kinematic viscosity. Further, hydraulic conductivity (k) was correlated with LL and FSI of the clay liner material for different fly ash contents and solute concentrations. Useful correlations were obtained.     

Nonlinear consolidation in randomly heterogeneous highly compressible aquitards

Severe land subsidence due to groundwater extraction may occur in multiaquifer systems where highly compressible aquitards are present. The highly compressible nature of the aquitards leads to nonlinear consolidation where the groundwater flow parameters are stress-dependent. The case is further complicated by the heterogeneity of the hydrogeologic and geotechnical properties of the aquitards. The effect of realistic vertical heterogeneity of hydrogeologic and geotechnical parameters on the consolidation of highly compressible aquitards is investigated by means of one-dimensional Monte Carlo numerical simulations where the lower boundary represents the effect of an instant drop in hydraulic head due to groundwater pumping. Two thousand realizations are generated for each of the following parameters: hydraulic conductivity (K), compression index (C _c), void ratio (e) and m (an empirical parameter relating hydraulic conductivity and void ratio). The correlation structure, the mean and the variance for each parameter were obtained from a literature review about field studies in the lacustrine sediments of Mexico City. The results indicate that among the parameters considered, random K has the largest effect on the ensemble average behavior of the system when compared to a nonlinear consolidation model with deterministic initial parameters. The deterministic solution underestimates the ensemble average of total settlement when initial K is random. In addition, random K leads to the largest variance (and therefore largest uncertainty) of total settlement, groundwater flux and time to reach steady-state conditions.     

Dewatering Behaviour of a Uranium Ore Slurry Containing Clays

The main objective of this paper was to investigate the dewatering behaviour of a clayey uranium ore slurry. The slurry (containing 28% clay size) exhibited moderate water adsorption (w _l  = 83% and w _p  = 30%). Primarily composed of muscovite (46%) and quartz (30%), the clay minerals included illite (8%), chlorite (5%) and kaolinite (2%) alongside a CEC of 41 (cmol(+)/kg) with Ca²⁺ and Mg²⁺ as the dominant cations. Likewise, the high EC (17,600 μS/cm) and ionic strength (1.15 mol/L) indicated a flocculated microstructure due to the presence of SO₄ ^2? (22,600 mg/L) and Mg²⁺ (1340 mg/L) in the slurry water. Settling included sedimentation and consolidation at low initial solids condition (25–35%) whereas only consolidation was observed at high initial solids contents (40–50%). The average k reduced from 1.2 × 10^?6 m/s (initial s = 25%) to 5.3 × 10^?8 m/s (initial s = 50%) along with a void ratio reduction from 7.4 to 2.6. Due to thixotropic strength, volume compressibility during consolidation showed apparent pre-consolidation at low effective stress (0.3–2 kPa) with a reduction in void ratio from 2.6 to 2.5. The e _s was found to be 2.46 at σ′ = 2 kPa and was followed by a steeper slope with the void ratio reducing to 2.1 at σ′ = 31 kPa. Likewise, the hydraulic conductivity during consolidation decreased from 2.6 × 10^?9 m/s (at e = 2.6) to 2.0 × 10^?10 m/s (at e = 2.1).     

Distribution rule of the in situ stress state and its influence on the permeability of a coal reservoir in the southern Qinshui Basin,China

The recent development of the coalbed methane (CBM) industry has a significant role in advancing hydraulic fracturing theory and technology. However, further development requires a better understanding of how fractures influence reservoir permeability. In situ stress data from 54 CBM wells in the southern Qinshui Basin, China, were obtained by the injection/falloff test method to analyse the effect of in situ stress on the permeability of the CBM reservoir. The types of in situ stress states were classified, and the coal reservoir permeability under different in situ stress states was analysed. The results indicate that the maximum horizontal principal stress (σ_H), minimum horizontal principal stress (σ_h) and vertical principal stress (σ_v) all have positive linear relationships with the coal seam burial depth. Three in situ stress states were observed from the shallow to deep regions of the CBM reservoir in the study area: σ_H?>?σ_h?>?σ_v, σ_H?>?σ_v?>?σ_h and σ_v?>?σ_H?>?σ_h, which account for 9, 76 and 15% of the test wells, respectively. Coal reservoir permeability decreases with increasing horizontal principal stress, whereas it first decreases with increasing σ_v, then increases and finally decreases. The variation in permeability with σ_v is due to the conversion of the in situ stress states. Coal reservoir permeability has obvious differences under different in situ stress states. The permeability is the largest when σ_v?>?σ_H?>?σ_h, followed by σ_H?>?σ_h?>?σ_v and smallest when σ_H?>?σ_v?>?σ_h. The permeability differences are caused by the fracture propagation shape of the rock strata under different in situ stress states.     

Effects of salt solutions on the hydro-mechanical behavior of compacted GMZ01 Bentonite

In this study, the effects of salinity of infiltrating solutions on the swelling strain, compressibility, and hydraulic conductivity of compacted GMZ01 Bentonite were investigated. After swelling under vertical load using either distilled water or NaCl solutions with concentrations of 0.1, 0.5 M, and 1 M, laboratory oedometer tests were conducted on the compacted GMZ01 Bentonite. Based on the oedometer test results, hydraulic conductivity was determined using the Casagrande’s method. Results show that the swelling strain of highly compacted GMZ01 Bentonite decreases as the concentration of NaCl solution increases. The compression index C _c ^* increases and then turns to decrease with an increase in the vertical stress or a decrease in the void ratio for different solutions, and the C _c ^* decreases as the concentration of NaCl solution increases. The secondary consolidation coefficient C _α increases linearly with the increase of the compression index C _c ^* . Furthermore, a bi-linear relationship between the swelling index C _s ^* and the secondary consolidation coefficient C _α can be characterized clearly. The hydraulic conductivity increases as the concentration of NaCl solution increases, however, this increase can be prevented if a high confining stress is applied.     

不同砂−膨润土垂直防渗墙填筑土料的掺量研究

土?膨润土垂直防渗墙在美国已广泛应用于城市卫生填埋场中,我国的工程中则应用较少。由国产膨润土与原地层土混合在自重应力作用下固结形成的防渗墙,其渗透性、孔隙和压缩性如何受膨润土掺量的影响,针对该一问题,使用福建标准砂模拟原地层,以3种典型膨润土作为混合料,在各掺量下对砂?膨润土填筑土料开展改进柔性壁渗透试验固结试验,研究不同膨润土掺量对填筑料渗透系数k、孔隙率n与压缩系数av影响。结果表明,膨润土和砂形成防渗墙时存在一个对应最小n和av的最优掺量Copt,当膨润土掺量小于等于Copt时,随着掺量增加,填筑料k下降很快,av缓慢减小;当掺量大于Copt后,随掺量上升,k降低速度趋缓,av快速地升高。理论上,膨润土掺入较少时黏土颗粒仅填充砂粒间的孔隙而不影响砂粒堆积,掺量达到一定程度后膨润土使砂粒彼此分离,悬浮在其中,填筑料的孔隙率随掺量而增大,可能是宏观上造成最优掺量产生的主要原因。     

Experimental Investigation into Hydraulic Fracture Network Propagation in Gas Shales Using CT Scanning Technology

Multistage fracturing of the horizontal well is recognized as the main stimulation technology for shale gas development. The hydraulic fracture geometry and stimulated reservoir volume (SRV) is interpreted by using the microseismic mapping technology. In this paper, we used a computerized tomography (CT) scanning technique to reveal the fracture geometry created in natural bedding-developed shale (cubic block of 30 cm × 30 cm × 30 cm) by laboratory fracturing. Experimental results show that partially opened bedding planes are helpful in increasing fracture complexity in shale. However, they tend to dominate fracture patterns for vertical stress difference Δσ _v  ≤ 6 MPa, which decreases the vertical fracture number, resulting in the minimum SRV. A uniformly distributed complex fracture network requires the induced hydraulic fractures that can connect the pre-existing fractures as well as pulverize the continuum rock mass. In typical shale with a narrow (<0.05 mm) and closed natural fracture system, it is likely to create complex fracture for horizontal stress difference Δσ _h  ≤ 6 MPa and simple transverse fracture for Δσ _h  ≥ 9 MPa. However, high naturally fractured shale with a wide open natural fracture system (>0.1 mm) does not agree with the rule that low Δσ _h is favorable for uniformly creating a complex fracture network in zone. In such case, a moderate Δσ _h from 3 to 6 MPa is favorable for both the growth of new hydraulic fractures and the activation of a natural fracture system. Shale bedding, natural fracture, and geostress are objective formation conditions that we cannot change; we can only maximize the fracture complexity by controlling the engineering design for fluid viscosity, flow rate, and well completion type. Variable flow rate fracturing with low-viscosity slickwater fluid of 2.5 mPa s was proved to be an effective treatment to improve the connectivity of induced hydraulic fracture with pre-existing fractures. Moreover, the simultaneous fracturing can effectively reduce the stress difference and increase the fracture number, making it possible to generate a large-scale complex fracture network, even for high Δσ _h from 6 MPa to 12 MPa.     

DEM simulations of sandstone under true triaxial compressive tests

Numerically simulated true triaxial compression tests (σ ₁ ≥ σ ₂ ≥ σ ₃) are conducted in this study to elucidate the failure mechanism of sandstone using 3D discrete element method (DEM), in particular the effect of the intermediate principal stress (σ ₂). Eight series of tests (σ ₃ = 0, 10, 20, 30, 40, 50, 70, and 100 MPa) are conducted. Within each series, σ ₂ is varied from σ ₂ = σ ₃ to σ ₂ = σ ₁ from test to test. For each test, σ ₁ is raised monotonically to failure while keeping σ ₂ and σ ₃ constant. The DEM simulations reveal the effect of σ ₂ on the variations of peak stress, Young’s modulus, failure plane angles, the brittle–ductile transition, and the evolution of failure modes, the effect beyond the well-understood effect of σ ₃. The simulation is in qualitative agreement with the results obtained experimentally. Detailed analyses performed on the particle-scale responses further the understanding of the microscopic mechanisms. The distribution of contact force becomes more homogeneous with the increase of σ ₃, which leads to the resulting damage being more localized rather than diffused. The interaction between contact force distribution and coalescence of cracks determines the processes and patterns of fracturing in the sample scale. σ ₂ is found to affect the microscopic stress distribution as well as structure evolution, and this effect weakens with the increase of σ ₃.     

Spatial information of soil hydraulic conductivity and performance of cokriging over kriging in a semi-arid basin scale

Unlike the studies in small parcels by systematic measurements, the spatial variability of soil properties is expected to increase in those over relatively large areas or scales. Spatial variability of soil hydraulic conductivity (K _h) is of significance for the environmental processes, such as soil erosion, plant growth, transport of the plant nutrients in a soil profile and ground water levels. However, its variability is not much and sufficiently known at basin scale. A study of testing the performance of cokriging of K _h compared with that of kriging was conducted in the catchment area of Sarayköy II Irrigation Dam in Cank?r?, Turkey. A total of 300 soil surface samples (0–10 cm) were collected from the catchment with irregular intervals. Of the selected soil properties, because the water-stable aggregates (WSA) indicated the highest relationship with the hydraulic conductivity by the Pearson correlation analysis, it is used as an auxiliary variable to predict K _h by the cokriging procedure. In addition, the sampling density was reduced randomly to n = 175, n = 150, n = 75 and n = 50 for K _h to determine if the superiority of cokriging over kriging would exist. Statistically, the results showed that all reduced K _h was as good as the complete K _h when its auxiliary relations with WSA were used in cokriging. Particularly, the results of the “Relative Reduction in MSE” (RMSE) revealed that the reduced data set of n = 75 produced the most accurate map than the others. In this basin-scaled study, there was a clear superiority of the cokriging procedure by the reduction in data although a very undulating topography and topographically different aspects, two different land uses with non-uniform vegetation density, different parent materials and soil textures were present in the area. Hence, using the statistically significant auxiliary relationship between K _h and WSA might bring about a very useful data set for watershed hydrological researches.     

Heterogeneity of hydraulic conductivity and Darcian flux in the submerged streambed and adjacent exposed stream bank of the Beiluo River,northwest China

Recognizing the heterogeneity of hydraulic conductivity and hyporheic flow is critical for understanding contaminant transfer and biogeochemical and hydrological processes involving streams and aquifers. In this study, the heterogeneity of hydraulic conductivity and Darcian flux in a submerged streambed and its adjacent exposed stream banks were investigated in the Beiluo River, northwest China. In the submerged streambed, Darcian flux was estimated by measurement of vertical hydraulic conductivity (K _v) and vertical head gradient (VHG) using in-situ permeameter tests. On exposed stream banks, both horizontal hydraulic conductivity (K _h) and K _v were measured by on-site permeameter tests. In the submerged streambed, K _v values gradually decreased with depth and the higher values were concentrated in the center and close to the erosional bank. Compared to the exposed stream banks, the K _v values were higher in the streambed. From stream stage to the topmost layer of tested sediment, through increasing elevation, the K _h values increased on the erosional bank, while they decreased on the depositional bank. The values of VHG along the thalweg illustrate that downwelling flux occurred in the deepest area while upwelling flux appeared in the other areas, which might result from the change of streambed elevation. The higher value of the Darcian flux in the submerged streambed existed near the erosional bank.     

Criteria of Acceptance for Constant Rate of Strain Consolidation Test for Tropical Cohesive Soil

In this study, the rapid consolidation equipment (RACE) was developed as an alternative device to the conventional consolidation test using Oedometer, consuming merely a few hours for the whole precedure to determine the consolidation characteristics of cohesive soil. RACE operates based on the constant rate of strain (CRS) consolidation theory, which is a continuous loading method of testing, requiring a good estimation of the loading rate such that it is ideal for the achievement of steady state condition during testing. The steady state condition is achieved when the c _v values from drained and undrained face of CRS converged with the c_v from Oedometer test. A slightly modification has been made on the normal constant rate of strain (CRS) test by proposing a direct back pressure system to the specimen using a tube to saturate the soil sample. This research has produced a set of criteria for determining the suitable rate for the rapid consolidation test based on the ratio of normalized strain rate, β, and proposed a new coefficient in terms of a ratio of β to clay fraction (CF), as a part of new criteria for testing a fine soil. Four types of sample were tested with different rates of strain using the RACE and their results were compared with those conducted using the Oedometer on the same soil type, from which fairly good agreements were evident in many specimens. It was found from the study that the minimum value of normalized strain rate, β, for the CRS test is 0.005 and for the u _a /σ _v ratio is suggested as 0.01. Also, the maximum β/CF for soils with clay friction lower and higher than 50 % are 0.008 and 0.001, respectively. The minimum β/CF value for both conditions is 0.0001.     

Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin

Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin was investigated. The Izbash equation is used to describe the non-Darcian flow in the horizontal direction, and the vertical flow is described as Darcian. The solution for the newly developed non-Darcian flow model can be obtained by applying the linearization procedure in conjunction with the Laplace transform and the finite Fourier cosine transform. The flow model combines the effects of the non-Darcian flow, partial penetration of the well, and the finite thickness of the well skin. The results show that the depression cone spread is larger for the Darcian flow than for the non-Darcian flow. The drawdowns within the skin zone for a fully penetrating well are smaller than those for the partially penetrating well. The skin type and skin thickness have great impact on the drawdown in the skin zone, while they have little influence on drawdown in the formation zone. The sensitivity analysis indicates that the drawdown in the formation zone is sensitive to the power index (n), the length of well screen (w), the apparent radial hydraulic conductivity of the formation zone (K _r2), and the specific storage of the formation zone (S _s2) at early times, and it is very sensitive to the parameters n, w and K _r2 at late times, especially to n, while it is not sensitive to the skin thickness (r _s).     

Portland Cement Stabilization of Soil–Bentonite for Vertical Cutoff Walls Against Diesel Oil Contaminant

The objective of this study was to evaluate the effect of water-cement ratio and cement content on the hydraulic behavior of soil–cement–bentonite (SCB) and soil–bentonite (SB) mixtures permeated with water and diesel oil, to assist with the design of vertical cutoff walls constructed with those mixtures. The experimental program included unconfined compression tests, hydraulic conductivity tests and X-ray diffraction analysis. The test results indicated changes in hydraulic conductivity take place due to the variation of the water-cement ratio and permeant fluid. The hydraulic conductivity of the SB mixtures permeated with diesel oil was higher than the hydraulic conductivity of the same samples permeated with water. X-ray diffraction analyses suggest that this might be due to the decrease in double layer thickness and increase of seepage pore space imparted by diesel oil permeation. Conversely, Portland cement addition increased the hydraulic conductivity of the SCB specimens permeated with water, whereas subsequent diesel oil permeation reduced the hydraulic conductivity of the SCB specimens; this might be due to the relatively lower impact imparted by diesel permeation on the double layer characteristics of the bentonite stabilized with Portland cement.     

Orthogonal test and regression analysis of the strain on silty soil in Shanghai under metro loading

Cyclic triaxial test by means of the geotechnical digital system is conducted for the soil near the Guoquan Road Station of Metro Line 10 in Shanghai to analyze the strain characteristics and the variation law of saturated silty soil under subway loading. Orthogonal design method is used to arrange the experiment, considering the following factors: frequency ratio f _R, cyclic stress ratio σ _R, vibration time ratio N _R, and the interaction function among them. Results show that the cyclic stress ratio σ _R, the frequency ratio f _R, the vibration time ratio N _R, and the interaction between the cyclic stress ratio σ _R and the vibration time ratio N _R have a significant effect on the axial strain of the subway tunnel. The effect of the interaction between the cyclic stress ratio σ _R and the vibration time ratio N _R is also significant. From the analysis of variance and regression theory, the nonlinear regression equation of the cumulative plastic strain of silty soil under subway loading is established. Residual analysis proves that the equation is ideal and credible. The results have important value for the design of subway tunnels.     

Determination of optimum cutoff grade with considering dilution

In open pit mining, cutoff grade is one of the most important factors in production planning, which is simply defined as a grade that discriminates between ore and waste. It is also a sensitive parameter can have a major impact on the net present value and cash flow of the projects. On the other hand, dilution is one of the most important and sensitive parameters in the mining projects, which is closely related to the cutoff grade. Choosing the optimum cutoff grade is of considerable importance, since it has a significant impact on the mining operations. One of the most popular algorithms for determination of the optimum cutoff grade is the Lane’s algorithm. But in the Lane’s algorithm, mining dilution and its cost is not considered during the cutoff grade optimization. In this paper, effects of dilution on the cutoff grade are studied using Lane’s theory. Dilution and its cost is inserted directly into cutoff grade optimization process. The cutoff grades obtained using suggested method will be more realistic rather than ones by using the original form of the Lane’s formulation. Results of the study showed that with an increase of dilution, average grade decreases and consequently the cutoff grade increases. As a result of dilution, the quantity Q _m increases and the quantities Q _c and Q _r decrease. Therefore, the annual profit and NPV of project is very significantly reduced.     

Detailed comparison of nine intact rock failure criteria using polyaxial intact coal strength data obtained through PFC<Superscript>3D</Superscript> simulations

Study of intact rock failure criteria is an important topic in rock mechanics. In this study, applicability of nine different intact rock failure criteria is investigated for intact coal strength data. PFC^3D modeling was used to simulate the laboratory polyaxial tests for cubic intact coal blocks of side dimension 110 mm under different confining stress combinations. A modified grid search procedure is proposed and used to find the best-fitting parameter values and to calculate the coefficient of determination (R ²) values for each criterion. Detailed comparisons of the nine criteria are made using the following aspects: R ² values, σ ₁ ? σ ₂ plots for different σ ₃, shapes on the deviatoric plane, linearity or nonlinearity on the meridian planes. Through the comparisons of R ² values, σ ₁ ? σ ₂ plots and meridian lines, the modified Wiebols–Cook and modified Lade criteria were found to fit the intact coal strength data best. The nine failure criteria are categorized into three types based on the appearances on the deviatoric plane.