Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation

Random finite element method (RFEM) provides a rigorous tool to incorporate spatial variability of soil properties into reliability analysis and risk assessment of slope stability. However, it suffers from a common criticism of requiring extensive computational efforts and a lack of efficiency, particularly at small probability levels (e.g., slope failure probability P _f ?<?0.001). To address this problem, this study integrates RFEM with an advanced Monte Carlo Simulation (MCS) method called “Subset Simulation (SS)” to develop an efficient RFEM (i.e., SS-based RFEM) for reliability analysis and risk assessment of soil slopes. The proposed SS-based RFEM expresses the overall risk of slope failure as a weighed aggregation of slope failure risk at different probability levels and quantifies the relative contributions of slope failure risk at different probability levels to the overall risk of slope failure. Equations are derived for integrating SS with RFEM to evaluate the probability (P _f ) and risk (R) of slope failure. These equations are illustrated using a soil slope example. It is shown that the P _f and R are evaluated properly using the proposed approach. Compared with the original RFEM with direct MCS, the SS-based RFEM improves, significantly, the computational efficiency of evaluating P _f and R. This enhances the applications of RFEM in the reliability analysis and risk assessment of slope stability. With the aid of improved computational efficiency, a sensitivity study is also performed to explore effects of vertical spatial variability of soil properties on R. It is found that the vertical spatial variability affects the slope failure risk significantly.     

Effect of 2-D Random Field Discretization on Failure Probability and Failure Mechanism in Probabilistic Slope Stability

This paper investigates, using the random field theory and Monte Carlo simulation, the effects of random field discretization on failure probability, p _f, and failure mechanism of cohesive soil slope stability. The spatial sizes of the discretized elements in random field Δx, Δy in horizontal and vertical directions, respectively, are assigned a series of combinational values in order to model the discretization accuracy. The p _f of deterministic critical slip surface (DCSS) and that of the slope system both are analyzed. The numerical simulation results have demonstrated that both the ratios of Δy/λ _y (λ _y  = scale of fluctuation in vertical direction) and Δx/λ _x (λ _x  = scale of fluctuation in horizontal direction) contribute in a similar manner to the accuracy of p _f of DCSS. The effect of random field discretization on the p _f can be negligible if both the ratios of Δx/λ _x and Δy/λ _y are no greater than 0.1. The normalized discrepancy tends to increase at a linear rate with Δy/λ _y when Δx/λ _x is larger than 0.1, and vice versa for p _f of DCSS. The random field discretization tends to have more considerable influence on the p _f of DCSS than on that of the slope system. The variation of p _f versus λ _x and λ _y may exhibit opposite trends for the cases where the limit state functions of slope failure are defined on DCSS and on the slope system as well. Finally, the p _f of slope system converges in a more rapid manner to that of DCSS than the failure mechanism does to DCSS as the spatial variability of soil property grows from significant to negligible.     

Pile reinforcement mechanism of soil slopes

Stabilizing piles are widely used as an effective and economic reinforcement approach for slopes. Reasonable designs of pile reinforcement depend on the understanding of reinforcement mechanism of slopes. A series of centrifuge model tests were conducted on the pile-reinforced slopes and corresponding unreinforced slopes under self-weight and vertical loading conditions. The deformation of the slope was measured using image-based analysis and employed to investigate the pile reinforcement mechanism. The test results showed that the piles significantly reduced the deformation and changed the deformation distribution of the slope, and prevented the failure occurred in the unreinforced slope. The pile influence zone was determined according to the inflection points on the distribution curves of horizontal displacement, which comprehensively described the features of the pile–slope interaction and the characteristics of reinforced slopes. The concepts of anti-shear effect and compression effect were proposed to quantitatively describe the restriction features of the piles on the deformation of the slope, namely the reduction in the shear deformation and the increase in the compression deformation, respectively. The pile reinforcement effect mainly occurred in the pile influence zone and decreased with increasing distance from the piles. There was a dominated compression effect in the vicinities of the piles. The compression effect developed upwards in the slope with a transmission to the anti-shear effect. The anti-shear effect became significantly dominated near the slip surface and prevented the failure that occurred in the unreinforced slope.     

Evaluating the susceptibility of landslide landforms in Japan using slope stability analysis: a case study of the 2016 Kumamoto earthquake

This study analyzed 267 landslide landforms (LLs) in the Kumamoto area of Japan from the database of about 0.4 million LLs for the whole of Japan identified from aerial photos by the National Research Institute for Earth Science and Disaster Resilience of Japan (NIED). Each LL in the inventory is composed of a scarp and a moving mass. Since landslides are prone to reactivation, it is important to evaluate the sliding-recurrence susceptibility of LLs. One possible approach to evaluate the susceptibility of LLs is slope stability analysis. A previous study found a good correlation (R ² = 0.99) between the safety factor (F _s ) and slope angle (α) of F _s  = 17.3α ^?0.843. We applied the equation to the analysis of F _s for 267 LLs in the area affected by the 2016 Kumamoto earthquake (M _j  = 7.3). The F _s was calculated for the following three cases of failure: scarps only, moving mass only, and scarps and moving mass together. Verification with the 2016 Kumamoto earthquake event shows that the most appropriate method for the evaluation of LLs is to consider the failure of scarps and moving mass together. In addition, by analyzing the relationship between the factors of slope of entire landslide and slope of scarp for LLs and comparing the results with the Aso-ohashi landslide, the largest landslide caused by the 2016 Kumamoto earthquake, we also found that morphometric analysis of LLs is useful for forecasting the travel distance of future landslides.     

Integration of root systems into a GIS-based slip surface model: computational experiments in a generic hillslope environment

Root systems of trees reinforce the underlying soil in hillslope environments and therefore potentially increase slope stability. So far, the influence of root systems is disregarded in Geographic Information System (GIS) models that calculate slope stability along distinct failure plane. In this study, we analyse the impact of different root system compositions and densities on slope stability conditions computed by a GIS-based slip surface model. We apply the 2.5D slip surface model r.slope.stability to 23 root system scenarios imposed on pyramidoid-shaped elements of a generic landscape. Shallow, taproot and mixed root systems are approximated by paraboloids and different stand and patch densities are considered. The slope failure probability (P_f) is derived for each raster cell of the generic landscape, considering the reinforcement through root cohesion. Average and standard deviation of P_f are analysed for each scenario. As expected, the r.slope.stability yields the highest values of P_f for the scenario without roots. In contrast, homogeneous stands with taproot or mixed root systems yield the lowest values of P_f. P_f generally decreases with increasing stand density, whereby stand density appears to exert a more pronounced influence on P_f than patch density. For patchy stands, P_f increases with a decreasing size of the tested slip surfaces. The patterns yielded by the computational experiments are largely in line with the results of previous studies. This approach provides an innovative and simple strategy to approximate the additional cohesion supplied by root systems and thereby considers various compositions of forest stands in 2.5D slip surface models. Our findings will be useful for developing strategies towards appropriately parameterising root reinforcement in real-world slope stability modelling campaigns.     

The formation and development of debris flows in large watersheds after the 2008 Wenchuan Earthquake

The Wenchuan earthquake has caused abundance of loose materials supplies for debris flows. Many debris flows have occurred in watersheds in area beyond 20 km², presenting characteristics differing from those in small watersheds. The debris flows yearly frequency decreases exponentially, and the average debris flow magnitude increases linearly with watershed size. The rainfall thresholds for debris flows in large watersheds were expressed as I?=?14.7 D ^?0.79 (2 h?<?D?<?56 h), which is considerably higher than those in small watersheds as I?=?4.4 D ^?0.70 (2 h?<?D?<?37 h). A case study is conducted in Ergou, 39.4 km² in area, to illustrate the formation and development processes of debris flows in large watersheds. A debris flow develops in a large watershed only when the rainfall was high enough to trigger the wide-spread failures and erosions on slope and realize the confluence in the watershed. The debris flow was supplied by the widely distributed failures dominated by rill erosions (14 in 22 sources in this case). The intermittent supplying increased the size and duration of debris flow. While the landslide dam failures provided most amounts for debris flows (57 % of the total amount), and amplified the discharge suddenly. During these processes, the debris flow velocity and density increased as well. The similar processes were observed in other large watersheds, indicating this case is representative.     

Nature of occurrence of phosphatic bands in Owk Formation,Neoproterozoic Kurnool basin,Andhra Pradesh

Rock slope instabilities are a major hazard for human activities often causing economic losses, property damages and maintenance costs, as well as injuries or fatalities. For slope stability analysis of open pit mines, series of studies must be carried out in order to identify the criteria which should take into consideration. In this research geotechnical parameters; Geological Strength Index (GSI), Rock Quality Designation (RQD), Cohesion (C), angle of internal friction (φ), uniaxial compressive strength (UCS) and Rock mass deformation modulus (E_m) which are obtained from data measured within geotechnical boreholes and pore pressure (U) are considered as the criteria to evaluate stability of pit No.1 of the Gole Gohar iron mine, located in Kerman province, south east of Iran. Since human judgments and preferences are often vague and complex and decision makers cannot estimate their preferences with an exact scale, we can only give linguistic assessments instead of exact ones. So fuzzy set theory introduced into Analytical Hierarchy Process (AHP). Fuzzy AHP (FAHP) is put forward to solve such uncertain problems. In this paper, FAHP method is used to determine the weights of the criteria by decision makers and then classification of the stability of blocks are determined by TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method by the shortest distance to positive ideal solution (PIS) and the longest distance to negative ideal solution (NIS).     

Does parameterization influence the performance of slope stability model results? A case study in Rio de Janeiro,Brazil

We produce factor of safety (FOS) and slope failure susceptibility index (SFSI) maps for a 4.4-km² study area in Rio de Janeiro, Brazil, in order to explore the sensitivity of the geotechnical and geohydraulic parameterization on the model outcomes. Thereby, we consider parameter spaces instead of combinations of discrete values. SFSI is defined as the fraction of tested parameter combinations within a given space yielding FOS <1. We repeat our physically based calculations for various parameter spaces, employing the infinite slope stability model and the sliding surface model of the software r.slope.stability for testing the geotechnical parameters and the Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability Model (TRIGRS) for testing the geohydraulic parameters. Whilst the results vary considerably in terms of their conservativeness, the ability to reproduce the spatial patterns of the observed landslide release areas is relatively insensitive to the variation of the parameterization as long as there is sufficient pattern in the results. We conclude that landslide susceptibility maps yielded by catchment-scale physically based models should not be interpreted in absolute terms and suggest that efforts to develop better strategies for dealing with the uncertainties in the spatial variation of the key parameters should be given priority in future slope stability modelling efforts.     

Reliability back analysis of shear strength parameters of landslide with three-dimensional upper bound limit analysis theory

It is essential to determine the shear strength parameters c and φ on the sliding surface for stability evaluation and engineering design of a landslide. In this study, a new parameter back analysis method is proposed by combining the 2D/3D upper bound method of limit analysis and reliability theory to accurately determine the shear strength parameters for a 3D slope with a single failure surface. The proposed reliability back analysis method overcomes the shortcomings of the traditional deterministic analysis method of slope stability that cannot take into account the randomness and uncertainty of geotechnical parameters. Based on the reliability theory, two methods were studied: first-order reliability method (implemented by spreadsheet and Matlab, called spreadsheet method and constrained optimization method, respectively, in this paper) and Monte Carlo simulation. The optimized values of c and φ were obtained by establishing only one balance equation with the consideration of the pore water pressure or other complex conditions, which can solve the problem of the back analysis of strength parameters for a single 3D sliding surface condition. The correlation research showed that the negative correlation between c and φ greatly affected the back analysis results, and the reliability index values were conservative without considering such a negative correlation. A case study for the back analysis of shear strength parameters is conducted based on a practical landslide model with a broken line slip surface slope in Zhuquedong village, Luxi town, Xiangxi County, Hunan Province, China, and a suggestion for the selection of landslide cross section is presented. The results show that the back analysis results determined by the reliability theory coincide well with the survey and experimental results. The proposed method is found to be more accurate and effective in determining the values of shear parameters than that of the traditional deterministic inversion method.     

Seasonal Factors Influencing Copepod Abundance in the Maryland Coastal Bays

Maryland Coastal Bays differ in hydrography from river-dominated estuaries because of limited freshwater inflow from tributary creeks and more marine influence. Consequently, the copepod community structure may be different from that of the coastal ocean and river-dominated estuaries in the mid-Atlantic region. A 2-year study was conducted to describe copepod species composition and seasonal patterns in abundance and factors influencing the community structure. Seven copepod genera, Acartia, Centropages, Pseudodiaptomus, Parvocalanus, Eurytemora, Oithona, and Temora, in addition to harpacticoids were found. The copepod community was dominated by Acartia spp. (64%), followed by Centropages spp. (30%), unlike in river-dominated estuaries in the region where the copepod community is usually dominated by Acartia spp. followed by Eurytemora affinis. Acartia tonsa was the most abundant in summer and fall whereas Centropages spp., Temora sp., Oithona similis, E. affinis, and harpacticoids were most abundant in winter and early spring. Parvocalanus crassirostris and Pseudodiaptomus pelagicus were present in fall and winter but at relatively low densities. The highest mean density of copepods occurred in winter 2012 (36,437 m^?3) and the lowest in spring 2013 (347 m^?3). Low densities occurred through early summer (614 m^?3) coinciding with peak spawning by bay anchovy (Anchoa mitchilli). Bottom-up control via low phytoplankton biomass coupled with top-down control by ctenophores (Mnemiopsis sp.), mysids (Neomysis americana), and bay anchovy was probably responsible for the low copepod densities in spring and early summer. Temperature and salinity were also important factors that influenced the seasonal patterns of copepod species occurrence. The observed seasonal differences in the abundance of copepods have important implications for planktivorous fishes as they may experience lower growth rates and survival due to food limitation in spring/early summer when copepod densities are relatively low than in late summer/fall when copepod abundance is higher.     

New models to predict rock failure by linking the volume dilatant point with the peak stress point

The rock mass failure process can be divided into several distinct deformation stages: the compaction stage, elastic stage, stable failure stage, accelerated failure stage, and post-peak stage. Although each stage has been well studied, the relationship among the stages has not been established. Here, we establish two models which are the Strain model Q and Energy density model S by using the renormalization group theory and investigate the mechanical relationship between the volume dilatant point and peak stress point on the rock stress-strain curve. Our models show that the strain ratio (ε _f /ε _c ) and energy ratio (E _f /E _c ) at the volume dilatant point and peak stress point are solely functions of the shape parameter m. To verify our models, we further studied the failure process of rock specimens through several uniaxial compression experiments and found that the relationship between ε _f /ε _c or E _f /E _c and m shares a notably similar pattern to that from our theoretical model. However, the ε _f /ε _c and E _f /E _c values in our experiments are slightly smaller than those predicted by the models. In brief, we demonstrate that our models can be used to predict the failure process of the laboratory-scale hard brittle rock samples.     

Mechanical Properties and Deformation and Failure Characteristics of Surrounding Rocks of Tunnels Excavated in Soft Rocks

As soft rocks are likely to soften, slime and swell while contacting water, the existence of soft rocks is harmful for stability of surrounding rocks and supporting structures of tunnels. Through uniaxial and triaxial tests under dry condition and triaxial test with different moisture contents, the mechanical properties and failure modes of soft rocks were studied under conditions that the schistosity plane of the rock samples was vertical to, presented an oblique angle with, and paralleled to the loading direction. The results showed that peak strengths in natural and water-bearing states increased with increasing confining pressures, while those in water-bearing state were 40% lower than those in natural state. The samples were mainly subjected to ductile failure in both natural and water-bearing states while the samples in natural state exhibited a certain brittle failure characteristic in post-peak phase. With the increase of confining pressures, the post-peak curve gradually became gentle after certain brittle failure while the post-peak stresses had an insignificant change. In comparison, the samples in water-bearing state showed significant post-peak disparity, that is, exhibited strong ductile failure characteristic. Moreover, the fitting relationship between triaxial compressive strength and moisture of soft rocks can be expresses as σ ₁ = Aω + B (A < 0, B > 0) while that between elasticity modulus and moisture can be expresses as E = Aω + B (A < 0, B > 0).     

Retrogression characteristics of landslides in fine-grained permafrost soils, Mackenzie Valley, Canada

Thirteen landslides (retrogressive thaw flows) were investigated to study the behavior of thaw retrogression in permafrost in the Mackenzie Valley, Northwest Territories (NWT), Canada. Those landslides are all in fine-grained ice-rich permafrost soils. Such landslides usually start from small-scale slope failures followed by retrogressive thaw flows when ice-rich permafrost soils are exposed to the atmosphere. The landslides were marked with survey stakes to measure their retreat rates for the thawing season of 2007. Two correlations are presented: one is between scarp wall height and retreat rate; another is between overall slope angle and retreat rate. It was found that thaw flow retrogression rate increases with increase in scarp wall height and slope angle up to a certain limit. It was also confirmed that thaw flow retrogression is not influenced by slope orientation.     

On the efficient estimation of small failure probability in slopes

The random finite element method (RFEM) combines the random field theory and finite element method in the framework of Monte Carlo simulation. It has been applied to a wide range of geotechnical problems such as slope stability, bearing capacity and the consolidation of soft soils. When the RFEM was first developed, direct Monte Carlo simulation was used. If the probability of failure (p _f ) is small, the direct Monte Carlo simulation requires a large number of simulations. Subset simulation is one of most efficient variance reduction techniques for the simulation of small p _f . It has been recently proposed to use subset simulation instead of direct Monte Carlo simulation in RFEM. It is noted, however, that subset simulation requires calculation of the factor of safety (FS), while direct Monte Carlo requires only the examination of failure or non-failure. The search for the FS in RFEM could be a tedious task. For example, the search for the FS of slope stability by the strength reduction method (SRM) usually requires much more computational time than a failure or non-failure checking. In this paper, the subset simulation is combined with RFEM, but the need for the search of FS is eliminated. The value of yield function in an elastoplastic finite element analysis is used to measure the safety margin instead of the FS. Numerical experiments show that the proposed approach gives the same level of accuracy as the traditional subset simulation based on FS, but the computational time is significantly reduced. Although only examples of slope stability are given, the proposed approach will generally work for other types of geotechnical applications.     

Testing Study of Subcritical Crack Growth Mechanism During Water Rock Interaction

Subcritical crack growth plays an important role in evaluating the long-term stability of structures in rocks. By applying the constant-displacement-relax method, two groups of test specimens that one immersed in groundwater and the other in air were tested to get the parameters of subcritical crack growth in double torsion test. The relations of the stress intensity factor K _I versus the subcritical crack growth velocity V were obtained under the two different environments, and the behavior of subcritical crack growth was also analyzed. The results showed: the relations of lg K _I  ? lg V accorded with linear rules, which is in good agreement with Charles theory; Compared with specimens in nature state, the lg K _I  ? lg V curves of saturated water specimens locate top left comer of those of air specimens. The slope of curve is smaller, and the intercept is bigger, which shows that the water–rock interaction speeds up the subcritical crack growth. And A increases 2.9 × 10¹⁸ folds but n decreases from 85.12 to 40.83 because of the water–rock interaction. Meanwhile, the fracture toughness K _IC also decreases obviously from 2.55 in air to 2.26 in water due to water rock interaction. The testing results provide a basis for time-dependence of rock engineering stability.     

Effect of Soil–Water Characteristic Parameters on Saturation Line and Stability of Slope

Rainfall infiltration is the main factor that causes slope instability. To study the effect of hydraulic parameters on the final saturation line and stability of slopes, a numerical slope model is established with a saturated–unsaturated seepage analysis method. Analysis results show the following, (1) When parameter a increases, the effective rainfall duration decreases linearly, and the ultimate safety factor increases gradually; when parameter m increases, the effective rainfall duration increases linearly, and the ultimate safety factor decreases linearly; when parameter n increases, both the effective rainfall duration and the ultimate safety factor decrease first and then remain stable. (2) When the saturated permeability coefficient decreases, the effective rainfall duration presents a crescent trend, and the ultimate safety factor decreases first and then remains the same after rainfall intensity exceeds the saturated permeability coefficient of soil. (3) When rainfall intensity is less than the saturated permeability coefficient of soil, the location of the final saturation line rises as the saturated permeability coefficient decreases and is thus independent of parameters a, m, and n.     

Fractal dimension of pore space in carbonate samples from Tushka area (Egypt)

To investigate inhomogeneous and porous structures in nature, the concept of fractal dimension was established. This paper briefly introduces the definition and measurement methods of fractal dimension. Three different methods including mercury injection capillary pressure (MICP), nuclear magnetic resonance (NMR), and nitrogen adsorption (BET) were applied to determine the fractal dimensions of the pore space of eight carbonate rock samples taken from West Tushka area, Egypt. In the case of fractal behavior, the capillary pressure P _c and cumulative fraction V _c resulting from MICP are linearly related with a slope of D-3 in a double logarithmic plot with D being the value of fractal dimension. For NMR, the cumulative intensity fraction V _c and relaxation time T ₂ show a linear relation with a slope of 3-D in a double logarithmic plot. Fractal dimension can also be determined by the specific surface area S _por derived from nitrogen adsorption measurements and the effective hydraulic radius. The fractal dimension D shows a linear relation with the logarithm of S _por . The fractal dimension is also used in models of permeability prediction. To consider a more comprehensive data set, another 34 carbonate samples taken from the same study area were integrated in the discussion on BET method and permeability prediction. Most of the 42 rock samples show a good agreement between measured permeability and predicted permeability if the mean surface fractal dimension for each facies is used.     

Shear wave velocity imaging of landslide debris deposited on an erodible bed and possible movement mechanism for a loess landslide in Jingyang,Xi’an,China

The South Jingyang Plateau, with a total area of 70 km², is located in Shaanxi Province, China. Since 1976, more than 50 landslides of different types have occurred repeatedly on the edge slopes of the plateau due to the start of diversion irrigation on the plateau, resulting in great loss of lives and property. To better understand the initiation and movement mechanisms of these loess landslides, we surveyed them and carried out a detailed investigation of a large landslide in the Xihetan area. Our field survey results revealed that although most of these landslides had a long runout with high mobility, most of the landslide materials originating from the edge slopes may have been in an unsaturated state when the landslide occurred. This suggests that the materials at the toe of the edge slope as well as on the travel path along the river terrace might have played a key role in landslide movement. To examine how the materials on the travel path were involved in the landsliding, we used a multichannel surface wave technique and surveyed shear wave velocity (V _s ) profiles of the landslide deposits. We also examined the internal geometry of the deposits that outcropped on the right-side slope of the landslide foot. The longitudinal profile of V _s along the direction of movement showed that terrace deposits near the toe of the edge slope may have been sheared upward, indicating that at the toe, the surface of rupture might be located inside the terrace deposits. The V _s contours showed an A-shaped fold within the landslide deposits in the middle part of the travel path and became greater in the most distal toe part. The V _s profile across the deposits showed a U-shaped belt, in which the soil layers have smaller V _s . This belt may be the boundary between the sliding landslide debris and terrace deposits. The observed internal geometry of the landslide deposits indicates that a sliding surface developed within the sandy layer underlying the gravel layer. Therefore, we inferred that after failure, the displaced landslide materials overrode and sheared the terrace deposits along its main sliding direction, resulting in the formation of thrust folds within the terrace deposits, and greater V _s on the distal toe part of the landslide.     

Stability and phase relations of nonstoichiometric clinopyroxenes in the join diopside-Ca-Eskola component at high pressures

The stability of nonstoichiometric clinopyroxenes in the Di-CaEsk join was experimentally studied, and phase diagrams were constructed for this join at pressures of 2.0 and 3.0 GPa. It was found that melting in the diopside part of the join occurs at anomalously low temperatures, and nonstoichiometric clinopyroxene coexists with a phase approaching diopside in composition. Phase relations along the Di-CaEsk join can be described and consistently interpreted only assuming that the diopside phase (α-diopside) is thermodynamically stable. The following phase volumes were observed along the solidus of the join at a pressure of 3.0 GPa: Cpx, αDi+Cpx, αDi+Cpx+Qtz, αDi+Cpx+Grt+Qtz, Cpx+Grt+Qtz, Cpx+Grt+Ky+Qtz, Grt+Ky+Qtz. Melting occurs via the eutectic reaction αDi+Cpx+Grt+Qtz=L at a temperature of about 1200°C in the diopside part of the system and via the eutectic reaction Cpx+Grt+Ky+Qtz=L at a temperature of 1400°C in the calcium-rich part of the system. At a pressure of 2.0 GPa, melting occurs at temperatures of 1200–1300°C via the eutectic reaction αDi+Cpx+ An + Qtz=L. The invariant equilibrium (L, An, Cpx, Grt, αDi, Qtz) lies within the pressure range 2.0–3.0 GPa. Nonstoichiometric clinopyroxenes form complex solid solutions, the compositions of which are not strictly confined to the Di-CaEsk join and depend on temperature, pressure, and phase association. Grossular garnets coexist with nonstoichiometric clinopyroxenes and α-diopside.     

The Effect of High Temperature on Tensile Strength and Damage Characteristics of Limestone

In this paper, the limestone specimens are heated from room temperature 25 to 800 °C in a high temperature furnace and then are subjected to Brazilian test with the AG-I250 electronic precision material testing machine. The physical properties, mechanical properties, disc failure pattern, energy absorbed per unit area and damage characteristics of disc are comprehensively investigated. The results show that: with the increase of temperature, the changing trends of tensile strength, peak strain, tensile modulus and accumulated energy absorbed per unit area of disc are similar, they are first increases, then decrease, the energy consumption index is consistent with the macroscopic damage characteristics; the value of ε_s increase first and then reduce, reaches the maximum at 600 °C. The value of n is increasing and fluctuating, but the change trend of D_c is opposite, which is decreasing and fluctuating. The slope of the damage variable-strain curves decreases first and then increases, the minimum value at 600 °C. This study is of significance to the prediction and evaluation of the stability and safety of rock mass post-high temperature.