Rocks In Cold Regions Research Articles

Durability and Permeability Characteristics of Consolidated Bodies After Grouting in Freeze–Thaw Rock in Cold Regions

Durability and Permeability Characteristics of Consolidated Bodies After Grouting in Freeze–Thaw Rock in Cold Regions

Nonuniform frost heave of saturated porous rocks in cold regions during cyclic unidirectional freeze-thaw: influence of the temperature gradient

Nonuniform frost heave of saturated porous rocks in cold regions during cyclic unidirectional freeze-thaw: influence of the temperature gradient

Multifactor-coupled study on freeze-thaw forces of rocks in cold regions

This study delves into the mechanical properties of steep and rocky slopes subjected to long-term freeze-thaw actions. Considering the unique climatic conditions in cold regions, especially the significant impact of seasonal and diurnal temperature variations on slope excavation, the research focuses on a high-cold region iron ore mine. Four types of rocks commonly found in the mining area are thoroughly examined, taking into account the hydrogeological conditions of the mining area. The study systematically analyzes the mechanisms of various factors such as weathering, freeze-thaw cycles, and ice-water phase changes on the stability of cold region fractured rock masses. The research reveals that under prolonged freeze-thaw actions, crack water within the rock continuously undergoes ice-water phase changes, generating substantial freeze expansion forces that result in structural damage to the rock mass. This damage is evident not only in the development of existing microcracks but also leads to the generation of new fractures, ultimately causing deterioration in the rock mass structure. The study of the evolution patterns of freeze-thaw forces contributes to a better understanding of slope stability issues in cold region mineral resource extraction, offering crucial insights for the design, construction, and operation of related engineering projects.

Fracture Mechanism and Damage Constitutive Model of Freeze–Thaw Fissured Granite Subjected to Fatigue Loading

The failure of rock in cold regions due to repeated freeze–thaw (F-T) cycles and periodic load-induced fatigue damage presents a significant challenge. This study investigates the evolution of the multi-scale structure of fractured granite under combined freeze–thaw (F-T) cycles and periodic loading and develops a constitutive damage model. The results indicate that after F-T cycles, network cracks develop around pre-existing cracks, accompanied by block-like spalling. After applying the fatigue load, the nuclear magnetic resonance (NMR) T2 spectrum shifts to the right, significantly increasing the amplitude of the third peak. The freeze–thaw process induces a “liquid–solid” phase transition, weakening the original pore structure of the rocks and leading to meso-damage accumulation. The pores in fractured granite progressively enlarge and interconnect, reducing the rock’s load-bearing capacity and fatigue resistance. The combined effects of F-T cycles and periodic loading induce particle movement and alter fracture modes within the rock, subsequently affecting its macro-damage characteristics. The theoretical curves of the constitutive model align with the experimental data. The findings can serve as a theoretical reference for preventing and controlling engineering disasters in fractured rock masses in cold regions.

Mechanical properties and acoustic emission characteristics of mixed granite after different numbers of freeze‒thaw cycles

The mechanical properties of rocks in cold regions undergo significant changes as a result of decades of freeze‒thaw cycles with seasonal variations, which can lead to a series of geological disasters, such as collapse. This study investigates the evolution of the mechanical characteristics and internal progressive damage characteristics of mixed granite under freeze‒thaw cycling and axial loading. By measuring the mass, wave velocity, and uniaxial compressive strength of rock samples and combining these metrics with acoustic emission (AE) characteristics, the physical and mechanical properties and microfracture development of mixed granite after different numbers of freeze‒thaw cycles were investigated. The results indicate that as the number of freeze‒thaw cycles increases, the longitudinal wave velocity, uniaxial compressive strength, and elastic modulus of the mixed granite decrease nonlinearly, while the peak strain gradually increases. Combined with the stress‒strain curve, the AE characteristics can be divided into four stages. As the number of freeze‒thaw cycles increases, the AE cumulative count decreases, and the AE counts of the four stages are different. The low-frequency-high-amplitude signals first increases and then tends to stabilize, and they only appeared in the third and fourth stages. At the same time, the proportion of the low-frequency ratio gradually increases, and the proportion of the high-frequency ratio decreases. In addition, based on the rise time/amplitude (RA) and average frequency (AF) characteristics and failure modes, it was found that the internal crack types of mixed granite transition from shear cracks to tensile cracks, among which tensile cracks play a crucial role in rock failure.

A rational multiscale nonlinear constitutive model for freeze–thaw rocks under triaxial compression

The stability and durability of rocks in cold regions are significantly impacted by the degradation of mechanical properties caused by freeze–thaw (F–T) environment. In this work, we shall propose a rational multiscale nonlinear constitutive model based on thermodynamics, micromechanics, and fractional calculus theory to describe the complete deformation and failure process of F–T rocks under triaxial compression. The F–T rocks at the mesoscale are regarded as consisting of porous matrix and cracks, while porous matrix is composed of the micropores and elastic solid grains at the microscale. According to experimental observations, we assume the F–T action mainly causes micropores growth and cracks opening, and mechanical damage is resulted from the initiation and propagation of cracks. In this context, the effects of F–T and mechanical damage on effective elastic properties of rocks can be quantitatively analyzed by using the two-step Mori–Tanaka (M-T) homogenization method. After subtly deriving the total free energy function of F–T rocks under compression, we systematically develop specific criteria for describing open cracks closure deformation, mechanical damage evolution and frictional sliding induced plastic distortion. Note that to correctly capture the plastic deformation characteristics, the non-orthogonal flow rule based on fractional differential calculations is employed. Following that, analytical analyses and numerical implementation of the proposed model are conducted. The performance of the model is evaluated by the simulations with experimental data on two kinds of F–T rocks, and discussions on parameters sensitivity and effects of fractional order are followed.

Machine Learning Algorithms in Rock Strength Prediction: A Novel Method for Evaluating Dynamic Compressive Strength of Rocks Under Freeze-Thaw Cycles

The combined impact of freeze-thaw cycles and dynamic loads significantly influences the long-term durability of rock engineering in high-cold regions. Consequently, investigating the dynamic compressive strength (DCS) of rocks subjected to freeze-thaw cycles has emerged as a crucial area of scientific research to advance rock engineering construction in cold regions. Presently, the determination of the DCS of rocks under freeze-thaw cycles primarily relies on indoor experiments. However, this approach has faced criticism due to its drawbacks, including prolonged duration, high costs, and reliance on rock samples. To address these limitations, the exploration of using artificial intelligence technology to develop more accurate and convenient DCS prediction models for rocks under freeze-thaw cycles is a promising attempt. In this context, this paper introduces a DCS prediction model for rocks under freeze-thaw cycles, which integrates the Sparrow Search Algorithm (SSA) with Random Forest (RF). Firstly, employing a dataset of 216 samples, Principal Component Analysis (PCA) is utilized to reduce the dimensionality of ten influential factors. Subsequently, five optimization algorithms are employed to optimize the hyperparameters of both the BP and RF algorithms. Finally, a comprehensive evaluation and comparative analysis are carried out to assess the predictive performance of the optimized model, using evaluation metrics such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Coefficient of Determination (R2).The research findings demonstrate that the SSA-RF model exhibits the best predictive performance, surpassing the other nine models in terms of generalization. The prediction model proposed in this study has good applicability for predicting DCS of freeze-thaw rock in cold regions, and also provides new ideas for the combination of machine learning and rock mass engineering in cold regions.

Fracturing behavior and damage model of spatial-rotation fissured sandstone: An experimental study on freeze–thaw and fatigue loads coupling

Earthquake exposure can greatly weaken the mechanical properties and affect the failure process of fractured rocks in cold regions. Creep tests of the spatial-rotation (SR) fissured rock with sandstone as the bedrock under different fatigue combinations and angles were carried out. The effects of freeze–thaw and fatigue loads (FT-FLs) on the deformation behaviour of samples, for example, creep, fatigue deformation, frost heave pressure, and creep rate, were explored. The mechanical responses and failure modes of the specimens were analysed in detail. Based on the experimental results, a new coupled damage model was explored. The results show that in addition to the typical creep stage, the rheological curve also included the phase of disturbance deformation under fatigue loading. The attenuation rates of the rock samples had downward trends with increasing load level under the fatigue combinations and angles, and these decreasing trends had linear characteristics. Moreover, the fatigue rate values increased gradually as the fatigue amplitude, fissure angle and rotation angle increased. In addition, with the change in the fissure and rotation angles, the curves of the tensile crack number had inverted U-shaped trends. The 3D fracture patterns under fatigue were dominated by vertical and vertical-lateral penetration, in which secondary fissure expansion also occurred at different angles. A combined damage model based on the damage variable of freeze–thaw cycles, fatigue loading, and spatial rotation of fissures was established. Compared with test data and other models, the coupled model has good accuracy in describing the entire failure process of specimens under FT-FLs and provides a new framework for the stability of fractured rock masses.

A unified model for frost wedging in an open fissure under unidirectional freezing

The propagation of joints and fissures, included by the frost heaving pressure arising from the water-ice phase transition is considered as frost wedging. This process is widely observed and plays a crucial role in weathering of jointed hard rocks in cold regions. Despite some fundamental results achieved in former experimental studies, a unified theoretical model is still absent, hindering a thorough understanding of this process. To further explore the mechanism of frost wedging during the freezing process, this paper firstly carries out a frost heave test on a rock block bearing a single open fissure. The results indicate that the evolution of frost heaving pressure in the fissure can be divided into four stages: sealing of the open fissure by ice wedge, ice wedge slipping, crack propagation, as well as stabilization of the ice-filled fissure. Based on the laboratory test results, a unified model for the frost heaving pressure in a single open fissure is established, which comprehensively takes into account the mechanical interaction between ice, water and rock. The model is validated by the test result, and it can reasonably describe the formation of the sealing conditions and the process of crack propagation. Fracture of the ice-rock interface near the free surface increases the likelihood of ice wedge slip, while frost wedging mainly damages geological bodies during crack propagation.

An experimental study on the influence of ice saturation and sub-zero temperatures on the dynamic mechanical properties of sandstones

The influence of ice saturations on the mechanical properties of rocks in cold regions is of great significance for many engineering projects. This study adopted a nuclear magnetic resonance (NMR) technology to measure the different ice saturations of sandstone specimens accurately. The split Hopkinson pressure bar (SHPB) was espoused to conduct dynamic compressive tests on sandstone with different ice saturations at room (26 ͦ C) and various low temperatures of 0 ͦ C, −5 ͦ C, −10 ͦ C, −20 ͦ C, −30 ͦ C and − 40 ͦ C. The findings revealed an increase in the dynamic mechanical strength's parameters, including dynamic elastic modulus (Ed) and dynamic compressive strength of sandstone with decreasing temperatures from 0 °C to −20 °C. The dynamic mechanical strength of sandstone reaches its peak value when the temperature drops from −20 ͦ C to −30 ͦ C, and a reduction in dynamic strength is evidenced when the temperature declines from −30 ͦ C. The results indicated that the dynamic mechanical strength of dry and fully saturated sandstone initially increased and then decreased when the temperature reached −40 °C, showing a clear negative trend. A reduction in temperature increases the dynamic mechanical strength of unsaturated sandstone, and the lower saturation leads to a more pronounced enhancement effect. Furthermore, the Ed and strength damage factors elucidate that varying ice saturations greatly affect the strength of sandstones with different porosities.

Characterization of Freeze-Thaw Cycle Damage to Mudstone in Open Pit in Cold Regions—Based on Nuclear Magnetic Resonance Method

Damage deterioration of rocks in cold regions under seasonal changes and daily cycles of freezing and thawing generate a series of engineering geological problems. These problems will seriously affect the safe and efficient production of open-pit mines. In this paper, a freeze–thaw cycle test and uniaxial compression test considering the natural conditions of the slope were carried out. Mechanical properties and damage mechanisms of open-pit mine mudstone under freeze–thaw conditions were investigated based on nuclear magnetic resonance (NMR) technology. The test results show that the microscopic internal pore structure of mudstone was changed under the superimposed effect of freeze–thaw damage and hydration damage. The internal pore size of mudstone increased with the number of freeze–thaw cycles, while the average pore size of the natural mudstone test increased more. Macroscopically, the compressive strength and modulus of elasticity of mudstone varied linearly with the number of freezing cycles, and the compressive strength and modulus of elasticity showed a decreasing trend. The strain-softening characteristics of mudstone samples were significant for more freeze–thaw cycles. The study explains the microscopic causes of mudstone deterioration in open-pit mines in cold regions and offers guidance for solving engineering disasters caused by mudstone deterioration.

Degradation of physico-mechanical properties and damage mechanisms of sandstone under the combined action of freeze–thaw cycles, chemical solution, and compressive stress

Rocks in cold regions subjected to freeze–thaw cycles are often affected by the surrounding hydro-chemical solutions and external load. In this study, the evolution of physical and mechanical characteristics and the damage mechanism of sandstone under the combined action of freeze–thaw cycles, chemical solution, and compressive stress were investigated. A series of quick cyclic freeze–thaw tests in different chemical solutions and stress levels were conducted. The dry mass, wave velocity, and compressive strength decrease as the number of freeze–thaw cycles increases. The variations in dry mass, wave velocity, and rock appearance indicate that lower stress levels (<0.5σ0, σ0 is the saturated uniaxial compressive strength of the original specimen) can limit the effect of repeated freeze–thaw cycles and chemical corrosion, whereas higher stress levels (>0.5σ0) can exacerbate the combined effect on rock damage. In addition, a modified decay model is proposed that incorporates the initial properties and residual integrity of the rock to describe the evolution of rock strength and wave velocity. Both the residual strength and wave velocity of sandstone are constants that are independent of stress level and chemical solution. The degradation rate of compressive strength increases abruptly at higher stress, whereas that of wave velocity generally decreases with increasing stress level. The continuous action of the cyclic frost-heaving force, hydrolysis and chemical corrosion, and external compressive stress promote generation and propagation of pores and microcracks, causing deterioration of the mass, wave velocity, and compressive strength.

Analysis of Damage Characteristics for Skarn Subjected to Freeze-Thaw Cycles Based on Fractal Theory

A large number of rock works in cold areas suffer from long-term freeze-thaw damage, and it seriously affects the stability of mine slopes. In this paper, the XRD component measurement, P-wave velocity, freeze-thaw cycling test at different times, uniaxial compression test, and scanning electron microscope (SEM) test were carried out to obtain the mechanical properties and microstructure evolution of skarn under the effect of freeze-thaw cycles. The results of the study indicate that with an increase in the number of freeze-thaw cycles, the mass of the rock gradually increases and the P-wave velocity, uniaxial compressive strength, elastic modulus, and Poisson’s ratio all decrease. Based on the SEM image of the rock after crushing, fine pores and fissures gradually developed, expanded, and penetrated each other under the action of freezing and thawing; the inter-particle bonding force decreased; and the cement gradually loosened. The fractal dimension of the specimens under different numbers of freeze-thaw cycles was obtained using the box dimension method, and the degradation of the fine structure of the rock was quantitatively elaborated. By establishing the relationship between the compressive strength of rocks and the fractal dimension, the mechanism of damage to skarn under freeze-thaw action was further investigated. It provides some theoretical basis for the characterization of freeze-thaw damage of rocks in cold regions.

Mesoscopic Freeze-Thaw Damage Evolution Characteristics of Fractured Sandstone at Different Saturations

To study the effect of saturation on the freeze-thaw damage of fractured rocks in cold regions, five prefabricated oval double-hole red sandstones with different saturations were prepared. Three-dimensional images of rock fractures were obtained by CT technology. The freeze-thaw damage mechanism and critical saturation of the red sandstone were explored through the fracture propagation evolution and quantitative characterization of the pore structure. The experimental results show that the pore size distribution can reflect the complex pore structure. Pores can be divided according to their sizes: small pores, mesopores, and macropores; mesopores account for the largest proportion and more than 70% of the total, and the proportion of mesopores in high-saturation sandstone (90% or 100%) increases under the action of freeze-thaw cycle. This is also accompanied by a small increase in the proportion of macropores. An 80% critical saturation of the sandstone was obtained. In addition, prefabricated cracks make the ice separation mechanism more likely to occur. The low-saturation sandstone mainly damaged the fracture area during freeze-thaw cycles, while the prefabricated cracks provided a good seepage channel for high-saturation sandstone. The corresponding rock bridge area eventually demonstrated a connectivity trend. This study more realistically reflects the freeze-thaw damage of actual rock masses in cold regions and provides a theoretical basis for the prediction of rock mass engineering disasters in cold regions.

Mechanical characteristics and damage evolution of granite under freeze–thaw cycles

Rocks in cold regions experience freeze–thaw (F–T) cycles, which have a significant impact on their mechanical properties, causing a series of engineering challenges that threaten engineering stability. To investigate the mechanical characteristics and damage evolution of granite under the influence of F–T cycles, the microstructural evolution and macroscopic mechanical properties of granite were analyzed by conducting P-wave velocity tests, computed tomography scanning, and uniaxial compression tests subjected to different F–T cycles. The results revealed the following: 1) the number of F–T cycles and saturated water content significantly impact on the mechanical properties of granite; 2) as the number of F–T cycles increases, the P-wave velocity, peak strength, elastic modulus, and coefficient of frost resistivity of granite gradually decrease, but the F–T damage values increase; 3) when the number of F–T cycles is less than 40 but within a certain range (0–100), the damage variable of granite increases rapidly, but then gradually tends to stabilize; 4) the damage gradually steadily spreads to the central region of the granite sample as the number of F–T cycles increases, and the ends and marginal regions of the granite samples are more susceptible to damage, and 5) three damage variables with different definitions (elastic modulus, density, and porosity) can be used to predict the degree of damage of granite under F–T cycles.

Mechanical properties and two damage models of frozen-thawed rocks under triaxial compression

Freeze-thaw induced damage in rock engineering is common in cold regions. However, a damage model for capturing the whole failure process of frozen-thawed rocks is still lacking. In this paper, triaxial compression tests of red sandstone experienced with different freeze-thaw cycles (FTCs) were conducted. Subsequently, the variation of mechanical properties with the numbers of FTCs under different confining pressures were obtained, including peak deviator stress, peak strain, linear elastic modulus, residual strength, friction angle and cohesion. The completely compacted point on stress-strain curve of rock was determined by calculating the strain difference between the stress-strain curve and a reference line. On theses bases, two damage constitutive models considering the initial compaction phase and residual deformation phase were established by means of the continuum damage mechanics and statistical microelement strength theory together with the random exponential function of strain difference. The calculated data obtained from the two proposed models and measured data were then compared. The results shows that the proposed model I is suitable for all rocks samples experienced with FTCs, while the proposed model II is suitable for rocks with small residual strength or large stress difference between peak strength and residual strength. Meanwhile, the two proposed models were compared with the existing ones by evaluating the factor Ω . The influence of confining pressure and FTCs on damage evolution of rock was discussed, and the physical meanings of the parameters in the two models were analyzed in details. The findings are beneficial for providing a reference in developing a constitutive damage model for rocks in cold regions.

Research on Frost Heaving Characteristics of Hydraulic Tunnels’ Wall Rock in Cold Regions Based on Phase Transition and Water-Heat-Stress Coupling

In order to study the problem of frost damage to wall rock caused by hydraulic tunnels’ phase transition between water and ice at low temperatures in cold regions, a three-field coupling governing equation considering temperature, seepage and stress was deduced. Taking a water conveyance tunnel in Xinjiang as the research object, a three-dimensional frost heaving finite element model was established based on the deduced coupling equations using finite element software. By numerically simulating the process of frost heaving, the spatial distribution and variation law of the frozen area and frost heaving force were obtained. The present study showed that the frozen area of wall rock at the tunnel entrance is spatially distributed in a long-necked funnel shape, and the frost depth of the section gradually decreases along the depth of the tunnel. Due to the hysteresis of heat conduction, the peak point of the maximum freezing depth of wall rock appears after the minimum ambient temperature. The circumferential distribution law of frost heaving force in wall rock remains consistent with the depth, that is, the maximum frost heaving tension occurs at the arch top and arch bottom and decreases to zero in the circumferential direction, and then it turns into the frost heaving pressure which gradually increases to the maximum at the arch waist. Along the depth, at 20 m away from the tunnel entrance, the frost heaving force at the arch top, arch waist and arch bottom is divided into a steep decline zone and a slow decline zone. After being frozen for 30 to 150 days, the growth rate of the absolute value of the maximum frost heaving force at the arch top and arch bottom is about 1.5 times that of the arch waist. The frost heaving force has greater influence on the arch top and arch bottom than on the arch waist.

Effect of Moisture Content on Bursting Liability of Sandstone due to Freeze-Thaw Action

Moisture content (MC) and freeze-thaw (F-T) process have an important influence on the mechanical properties of rock and its rockburst tendency in the cold region. In addition, uniaxial compressive strength (UCS) of rock is of great importance in evaluating weathering durability, frost resistance, and bursting liability of rock. In this study, the UCS of rock and bursting liability index of rock including elastic energy index (WET), impact energy index (WCF), elastic strain energy index (ES), and modified values of brittleness index (BIM) were measured by laboratory tests. These tests were implemented in six different MC (0, 0.58, 1.06, 1.82, 2.43, and 2.80%) and 20 F-T cycles. The relationship between rock mechanical properties, bursting liability of rock, and MC after freeze-thaw damage was established, and the control mechanism of moisture content on mechanical properties and rockburst tendency of rocks in cold regions was revealed. Uniaxial compressive test results showed that the UCS of rock decreases significantly with the increase of MC. Under the action of F-T cycles, WET, WCF, and ES decrease with the increase of MC, and BIM of rock increases gradually. This indicates that the rockburst tendency of sandstone decreases with the increase of MC. To calculate WET, WCF, ES, and BIM of sandstone samples, new empirical equations were established and put forward under different MC after 20 F-T cycles.

Acoustic emission and CT investigation on fracture evolution of granite containing two flaws subjected to freeze–thaw and cyclic uniaxial increasing-amplitude loading conditions

The deterioration mechanism and fatigue fracturing evolution of granite with two pre-existing flaws experiencing freeze–thaw (F-T) treatment are investigated in this work. The flaws in the rock sample were prepared as a combination of a horizontal flaw with an upper inclined flaw above the horizontal flaw according to the joint characteristics in an open pit slope. In-situ acoustic emission monitoring combined with the post-test 3D computed tomography (CT) technique was employed to reveal the fracture evolution behaviors of rock treated with 0, 50, and 80 freeze–thaw cycles. Results show that the freeze–thaw damage impacts the frost heaving force, cyclic deformation, AE activates, crack coalescence pattern and fatigue life of the granite samples. The accumulative AE count/energy decreases with increasing number of freeze–thaw cycles, and the accumulated AE count/energy in a loading stage gradually grows faster. In addition, AE spectral frequency analysis reveals the impact of previous freeze–thaw damage on the formation of the crack scale, the sample is prone to producing large scale cracks under high freeze–thaw treatment. Moreover, 3D reconstructed CT images present an internal crack network pattern, and the most striking finding is that a simple crack network forms for a sample experiencing high F-T fatigue damage. It is suggested that deterioration of the rock bridge structure is strongly impacted by the accumulative freeze–thaw damage. The testing results are helpful to understand the influence of freeze–thaw and fatigue loading on the fracture evolution characteristics of rock in cold regions.

Micro-structural, petro-graphical and mechanical studies of schist rocks under the freezing-thawing cycles

Freezing-thawing (F-T) process significantly affects the mechanical parameters of rocks in cold regions. Consequently, the effect of this phenomenon on rock properties should be evaluated before and during the construction of any engineering projects. In this regard, uniaxial compressive strength (UCS) of rocks is a good criterion for assessing the rock durability against the weathering factors. In this paper, some boreholes were drilled in the schist rock of Angouran open-pit mine of Iran to prepare the required specimens. Then, 25 specimens were cut and polished to perform the UCS tests. These tests were implemented in 0, 7, 15, 40 and 75 F-T cycles. For this purpose, samples were put in a freezer for about 12 h at −20 °C and then moved them to the water bath for 12 h at 20 °C. For any F-T cycle, 5 specimens were tested under the unconfined compressive conditions. In addition, optical microscopy and X-ray diffraction (XRD) analysis were used to determine the specimen's mineralogical composition and textural properties. According to the obtained results, Chlorite, Biotite, Calcite and Quartz are the main constitutive minerals of the schist rocks. To evaluate the effect of weathering on the micro-structure of the rock, the texture of specimens was also studied using a scanning electron microscope (SEM). The SEM results showed that after 75 F-T cycles, new cracks are created in samples body and their porosity are increased. Furthermore, uniaxial compressive tests results showed that rock UCS and elastic modulus (E) are decreased exponentially by increasing the number of F-T cycles. However, Poisson ratio (ν) of specimens was increased by increasing the weathering grade. Finally, to calculate the UCS, E and ν of the schist specimens, new empirical equations were developed and proposed at different F-T cycles.