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Mechanical properties and modified binary–medium constitutive model for red–bed soft rock subjected to freeze–thaw cycles
... Red bed formations are extensively employed in various engineering projects, such as highways, railways, water resources, and hydropower applications [1,2]. Different from typical filling materials such as rocky soil and industrial slag, which have high friction coefficients, are easily compressed, and exhibit good permeability, red bed soft rock undergoes significant variations in strength due to differences in mineral composition and cementing materials. ...
... When the applied stress on a material remains essentially constant and considering the time-hardening characteristics, the equivalent creep strain rate can be calculated using Equation (1). ...
Post-construction settlement in embankments is a crucial quality indicator and a significant factor influencing the long-term stability of roadbeds. Especially for the mixed-fill materials, by considering the uncertainty of composition and mechanical properties, it is important to predict and take construction measures to control post-construction settlement. In this paper, taking the construction of high-fill embankments with red bed soft rock mixture as the background, the deformation characteristics of mixed-fill materials were revealed first. Then, a dynamic–static coupling method for roadbed filling was proposed, and corresponding control parameters were provided. Finally, by employing ABAQUS 2016 for long-term settlement numerical simulations and conducting load-bearing preloading tests, the deformation patterns of the high embankment with red bed soft rock mixture fill roadbed were revealed.
... As a typical continental sedimentary rock mass, red-bed soft rock primarily consists of interbedded argillaceous sandstone, sandy mudstone, shale, and sandy conglomerate. Its characteristics of poor diagenesis, weak cementation, and water-induced softening/disintegration significantly affect its mechanical properties and engineering stability [6][7][8]. Particularly in tunnel engineering, red-bed soft rock frequently triggers hazards such as large surrounding rock deformation, support structure cracking, and even collapse due to its strong rheological behavior, low strength, and small deformation modulus, posing serious threats to construction safety and long-term tunnel operation [9][10][11]. Neogene red-bed soft rock exhibits more pronounced strength degradation due to its younger geological age and weaker diagenesis. ...
This study focuses on Neogene red-bed soft rock tunnels in the Huicheng Basin, China. Through engineering geological investigation, remote wireless monitoring systems, and total station multi-parameter monitoring, the deformation characteristics of red-bed soft rock surrounding rock under high in situ stress environments and their influencing factors were systematically analyzed. The findings reveal that the surrounding rock deformation follows a three-stage evolutionary pattern of “rapid, slow, and stable”. Construction disturbances can disrupt the stable state, leading to “deep V-shaped” anomalies or double-step responses in deformation curves. Spatially, the deformation exhibits significant anisotropy, with the haunch area showing the maximum deformation (95 mm) and the vault the minimum (65–73 mm). Deformation stabilization requires 30–42 days, and a reserved deformation of 10 cm is recommended based on specifications. Mechanical behavior analysis indicates that the stress–strain curves of red-bed argillaceous sandstone are stepped, with increased confining pressure enhancing both peak and residual strengths, validating the necessity of timely support. The study elucidates a multi-factor coupling mechanism: rock mass classification, temporal–spatial effects (excavation face constraints and rheological properties), construction methods, in situ stress levels, and support timing (timely support during the rapid phase inhibits strength degradation) significantly influence deformation evolution. The spatiotemporal distribution of surrounding rock pressure shows that invert pressure increases most rapidly, while vault pressure reaches the highest magnitude, with construction disturbances triggering stress redistribution. This research provides theoretical and practical guidance for the design, construction optimization, and disaster prevention of red-bed soft rock tunnels.
... When subjected to temperatures above 500-600 °C, rocks usually lose roughly half of their initial strength; the amount of this loss varies according to the mineral composition and texture of the rocks (Ashrafi et al., 2020;Ahmed et al., 2022;Dong et al., 2024). Similarly, cycles of freeze-thaw constitute an important physical weathering agent that can quickly change the mechanical characteristics of rocks, influencing their durability (Momeni et al., 2016;Mei et al., 2021;Chen et al., 2021;He et al., 2023). Freezethaw cycles are found to be the most harmful physical processes influencing rock durability and disintegration, whereas heating-cooling cycles have little effect on the rocks (Hosseini and Khodayari, 2019;Mousavi et al., 2019). ...
This manuscript thoroughly investigates the effects of temperature variations on the physico-mechanical properties of limestone taken from the Nowshera formation in northwestern Pakistan. The rock samples were subjected to heat treatment at various temperatures, ranging from 150 °C to 600 °C for 24 hours. Additionally, the samples underwent freeze-thaw cycles, alternating between room temperature and-40 °C, with each cycle lasting 8 hours (4 hours of freezing followed by 4 hours of thawing). Both destructive tests (uniaxial compressive strength, point load index) and non-destructive tests (specific gravity, ultrasonic pulse wave velocity, porosity, and water absorption) were performed to evaluate the rocks' responses to these temperature variations. The density of induced fractures was calculated at the investigated temperatures and after 50 and 100 freeze-thaw cycles. The results indicate reductions in uniaxial compressive strength (UCS), specific gravity, ultrasonic pulse velocity (UPV), and point load (PL) strength with increasing temperature or number of freeze-thaw cycles. After thermal treatment at 600 °C, UCS decreased by 71 %, point load strength by 74 %, UPV by 49 %, and specific gravity by 7.8 %. Similarly, after 100 freeze-thaw cycles, these properties decreased by 23 %, 19 %, 15 %, and 2.6 %, respectively. Conversely, fracture density, porosity, and water absorption increased with elevated temperatures and freeze-thaw cycles. At 600 °C, increases of 2.51 % in fracture density, 66.5 % in porosity, and 67 % in water absorption were observed. Additionally, after 100 freeze-thaw cycles, these properties increased by 1.44 %, 10 %, and 12.8 %, respectively. Significant changes in all properties were noted when the temperature exceeded 300 °C or the number of freeze-thaw cycles surpassed 50. These findings highlight the degradation of rocks and alterations in their physico-mechanical properties due to thermal variations, which have important implications for industries such as mining and construction. ARTICLE INFO Article history:
... When subjected to temperatures above 500-600 °C, rocks usually lose roughly half of their initial strength; the amount of this loss varies according to the mineral composition and texture of the rocks (Ashrafi et al., 2020;Ahmed et al., 2022;Dong et al., 2024). Similarly, cycles of freeze-thaw constitute an important physical weathering agent that can quickly change the mechanical characteristics of rocks, influencing their durability (Momeni et al., 2016;Mei et al., 2021;Chen et al., 2021;He et al., 2023). Freezethaw cycles are found to be the most harmful physical processes influencing rock durability and disintegration, whereas heating-cooling cycles have little effect on the rocks (Hosseini and Khodayari, 2019;Mousavi et al., 2019). ...
... However, the strength of rocks will significantly decrease under freeze-thaw cycles. 15,16 These studies indicate that rock mass strength can be effectively enhanced under low-temperature freezing conditions. In addition, some scholars have found that under low-temperature conditions, the original pore structure inside the coal rock mass will expand and extend, generating new pores. ...
As China's coal mining gradually enters the deep stage, the difficulty of coal and gas outburst prevention and control is increasing. Low-temperature freezing technology has the dual effects of reducing coal seam storage energy and improving coal mass strength and has received widespread attention in the coal mining industry in recent years. When freezing water-bearing coal, frost heave occurs inside the coal mass, which reduces coal mass strength and then affects the application effect of cryogenic outburst prevention technology. In order to investigate the influence mechanism of freezing temperature and gas pressure on the frost heave effect of the coal mass profoundly, the water-bearing gas-containing coal freezing and cooling test was carried out using the self-developed gas-containing coal freezing and cooling test platform. The change rule of the temperature and strain of the coal mass was analyzed during the freezing process. The research results indicate that both freezing temperature and gas pressure impact the frost heave effect of coal. When the freezing temperature is below −10 °C, there is an exponential relationship between the frost heave strain generated by coal and the freezing temperature. When the equilibrium pressure of gas adsorption is less than or equal to 1.5 MPa, there is a linear positive correlation between the frost heave strain generated by coal during the freezing process and the gas pressure. In engineering applications, measures can be taken to reduce the freezing temperature and gas pressure to minimize the amount of coal frost heave strain. However, the freezing temperature should not be lower than −20 °C.
... On the other hand, the prolonged freeze-thaw cycles not only increase the porosity of the rock ), but also cause freeze-thaw damage to the rock, reducing its strength (He et al. 2023;Zhang et al. 2020). Tests by Liping et al. (2019) demonstrated a decrease in uniaxial compressive strength of rocks with an increase in the number of freezethaw cycles. ...
The highway and railroad tunnel engineering are susceptible to frost damage in cold regions, such as ice accumulation in tunnels and lining cracking phenomena, which seriously affect the safety of the engineering. Among them, the lining freezing damage to the tunnel structure is more harmful, the reason for this phenomenon is that in the early tunnel design did not consider the frost heaving force of surrounding rock on the tunnel lining. At low temperatures the water freezes and turns into ice causes frost heaving deformation of the surrounding rock, which in turn produces frost heaving force on the lining, so the investigation of freezing force is based on the frost heaving deformation of the rock. The frost heaving deformation of rocks is greatly affected by the porosity and mechanical properties of rocks. Firstly, the low-temperature frost heaving deformation test and uniaxial compression test of different types of rock specimens were carried out to study the effects of porosity and elastic modulus on the freezing deformation of rocks. And then, based on the test results, the proposed calculation method of rock frost heave ratio considering the strength is proposed and compared with other calculation methods. Finally, combined with actual engineering examples, the proposed frost heave ratio calculation method and freeze-thaw circle freezing expansion force calculation model are used to analyze the influence of rock elastic modulus and porosity on the freezing expansion force of surrounding rock. The conclusions of the study can provide experimental and theoretical basis for the design of tunnel engineering in cold regions.
... The specimens were placed in a drying oven (Fig. 3b) and exposed to a 24 h drying period at 105 °C. Subsequently, they were extracted from the drying oven and cooled to room temperature (He et al. 2023). (c) UCS test and corresponding monitoring: After completing drying, the specimens were ready for uniaxial compression testing. ...
Freeze–thaw cycles (FTCs) are an influential factor in deformation and damage of geotechnical engineering works within seasonal frozen ground. In this study, sandstone specimens with varying parallel planar flaw angles (θ) were subjected to different FTCs, followed by uniaxial compression tests (UCS). The impacts that FTCs and θ have upon the mechanical behaviors were investigated. Furthermore, a new damage constitutive model based on energy evolution was proposed, and the practical significance and evolutionary patterns of damage variables were comprehensively discussed. The findings reveal that flawed sandstone specimens experience a decline in peak stress and elastic modulus as the number of FTCs increases, while these properties exhibit an increasing trend with higher θ. At lower FTCs, no significant changes are observed in the failure mode. However, as the number of FTCs approaches 45, new potential crack propagation paths emerge within the specimens, leading to a change in the failure patterns. The total energy U and elastic strain energy Ue at the peak stress are negatively correlated with FTCs but positively correlated with θ. Furthermore, based on the energy evolution, a new damage constitutive model that considered the effect from θ and FTCs was developed to describe the failure behavior of the specimen. By analysing the damage variables, it is found that damage caused by parallel planar flaws (Dθ) decreases with an increase in θ. The FTC-induced damage (DFTC) is also influenced by θ, and specimens with lower θ experience higher DFTC, while those with higher θ exhibit lower DFTC. Additionally, an increase in FTC numbers leads to an increase in the gap between the damage values of specimens with lower θ and those of higher θ, whereas the parallel planar flaw angles have a smaller impact on the damage growth rate. The research findings provide valuable guidance in evaluating the stabilization and optimizing the design for geotechnical engineering in cold regions.
... The weathering resistance of the red beds is weak, they easily collapse, and their compressive and shear strengths are low Wang et al., 2017;Marat et al., 2022). The red beds have different lithology or poor binding force with other rock strata, which can easily cause differential deformation and lead to mass rock sliding along the bedding plane He et al., 2023;Wang et al., 2024). Therefore, the identification of rock types, especially the rapid determination of red beds, is of great significance for major scientific and engineering issues, such as risk assessment and rapid response to geological disasters, in the red bed distribution area. ...
Red beds belong to slippery formations, and their rapid identification is of great significance for major scientific and engineering issues, such as geological hazard risk assessment and rapid response to geological disasters. Existing research often identifies red beds from a qualitative or semiquantitative perspective, resulting in slow recognition speed and inaccurate recognition results, making it difficult to quickly handle landslide geological disasters. Combined with the correlation between red beds' geomorphic characteristics, mineral compositions, and chemical compositions, this study established a preliminary identification quantitative criterion based on the basic chemical composition combination rules (SiO2+Al2O3, Al2O3/SiO2, FeO+Fe2O3, Fe2O3/FeO, K2O+Na2O, Na2O/K2O, CaO+MgO, and MgO/CaO) in the red beds. Following this, we perform principal component analysis on the basic chemical composition combination rules mentioned above. The results indicate that simultaneously meeting the following principal component features can serve as a rapid quantitative criterion for distinguishing red beds from other rocks: F1=-3.36–23.55; F2=-23.00–3.11; F3=-10.12–4.88; F4=-2.21–4.52; F5=-0.97–7.30; and F=-0.67–1.89. By comparing the chemical composition combinations of 15 kinds of rocks collected from China in this study, it is proven that the quantitative criterion proposed in this study is effective. The study results can be used for rapid identification of red beds, achieving risk assessment and rapid response to geological disasters such as landslides.
... Meng et al. (2023) analyzed the effects of freeze-thaw cycles on the microstructure and mechanical properties of sandstone, and established a constitutive prediction model of freeze-thaw rock damage. He et al. (2023) conducted triaxial tests on red layer soft rocks under different confining pressures and freeze-thaw cycles, and proposed a constitutive model considering initial damage based on the dual medium structure and homogenization theory. Chen et al. (2023) established the statistical damage constitutive of freeze-thaw rock based on the theory of generalized strain equivalent principle. ...
A split Hopkinson pressure bar (SHPB) was used to characterize the high-strain rate behavior of saturated and frozen granite specimens. The effects of low temperatures and strain rates on dynamic mechanical response and failure behavior were investigated. The damage constitutive model of granite was established, considering both strain rate effect and low-temperature effect. The damage constitutive relationship took into account the statistical damage model based on Weibull distribution and nonlinear viscoelastic behavior. Results show that the dynamic compressive strength of the saturated and frozen granite at low temperatures (−20 °C to 15 °C) generally increases first and then decreases with the decrease of temperature. The peak strain decreases with the decrease of temperature and the peak strain at low temperatures (0 °C to −20 °C) decreases more than that at 15 °C. The dynamic Young’s modulus of the samples shows an increasing trend from 0 °C to −20 °C, and the range of variation decreases with the decrease of temperature. At low temperature, the brittle characteristics of saturated granite are more pronounced due to water-ice phase change and cold shrinkage of the rock matrix, while the ductility is gradually reduced. The modeling results on the stress-strain relationships are consistent with experimental data. It is verified that the constitutive relationship can describe the high strain rate characteristics of saturated frozen granite.
... The siliceous material is finely grained. The iron-muddy material is yellowish-brown to black-brown and reddish-brown, mainly in a granular form [18,19]. ...
The Wudongde reservoir region exhibits a notable prevalence of landslides within the red-bed reservoir stratum. The red bed is a clastic sedimentary rock layer dominated by red continental deposits. It is mainly composed of sandstone, mudstone, and siltstone. The lithology is diverse and uneven. In this study, we delve into the impact of mineral dissolution on the development of red-bed landslides in the reservoir area by utilizing the Xiaochatou landslide as a representative case study. Considering the inherent susceptibility of red-bed formations to erosion, collapse, and softening when exposed to water, an investigation was conducted to examine the consequences of mineral dissolution on landslides occurring in these areas. We conducted a mineral analysis and an identification of rock samples from the Xiaochatou landslide site, revealing alternating layers of sandstone and mudstone. Sandstone and conglomerate specimens were immersed in deionized water, and advanced techniques such as scanning electron microscopy (SEM), ion chromatography (IC), and inductively coupled plasma (ICP) analysis were used to examine the effects of water immersion. We also employed the hydrogeochemical simulation software PHREEQC to understand the dissolution mechanism of gypsum during soaking. Our findings reveal that sandstone and conglomerates harbor a notable quantity of gypsum, which readily dissolves in water. Prolonged immersion leads to erosion cavities within the sandstone, thereby augmenting its permeability. The concentration of SO4²⁻ ions in the soaking solution emerges as the highest, followed by Ca²⁺ and Na⁺. The notable significance is the dissolution of gypsum, whose intricate mechanism is contingent upon diverse environmental conditions. Variations in ion concentration profoundly influence the saturation index (SI) value, with the pH value playing a crucial role in shifting the reaction equilibrium. Regarding the deformation mode of the landslide, it manifests as a combination of sliding compression and tension cracking. The fracture surface of the landslide assumes a step-like configuration. As the deformation progresses, the mudstone layer takes control over the sliding process, causing the sandstone to develop internal narrow-top and wide-bottom cracks, which propagate upward until the stability of the slope rock mass is compromised, resulting in its rupture. In this manuscript, we delve into the dissolution traits of red-bed soft rock in the Wudongde reservoir area, using a landslide case as a reference. We simulate this rock’s dissolution under environmental water influences, examining its interaction with diverse water types through rigorous experiments and simulations. This study’s importance lies in its potential to shed light on the crucial engineering characteristics of red-bed soft rock.
... Figure 6 shows complete starin-time curves of sandstone after different numbers of F-T cycles under confining pressures of 3 MPa and 6 MPa. After an F-T cycle, the inner porosity of rock increased [6], resulting in larger deformation and shorter failure time under the same stress loading level. For example, when the confining pressure was 3 MPa, the rock samples with 20 and 40 F-T cycles were damaged during the 6th level loading, those with 60 F-T cycles were damaged during the 5th level loading, and the rock samples with 0 F-T cycles were damaged during the 8th level loading. ...
An understanding of the rheological characteristics of surrounding rock is key to predicting the large deformations of tunnels in soft rock in cold regions, particularly due to freeze–thaw (F–T) damage of the surrounding rock. Therefore, in this study, a series of F–T cycle and triaxial creep tests of surrounding rocks were conducted on the basis of typical tunnel projects in cold regions, and the parameters of the test data were identified by the fractional-order creep damage constitutive equation. Then, a constitutive model was embedded into the Fast Lagrangian Analysis of Continua in 3 Dimensions software to analyze the coupled creep deformations of the surrounding rock and supporting structure in response to F–T cycles while excavating the Ningchan tunnel. The calculated results accurately reflected the creep deformation characteristics of the surrounding monitoring points after tunnel excavation under different numbers of F–T cycles. Finally, a tunnel operation model was derived and used to analyze the creep deformation characteristics of a tunnel during operation in a cold area. The calculation results showed that with increasing time, the lining structure and surrounding rock at different monitoring points in the tunnel underwent various degrees of creep deformation. Additionally, the creep deterioration effect of the surrounding rock was more severe after the F–T cycles, which endangered traffic safety.
To study the mechanical characteristics and patterns of damage of sandstone subjected to freeze‒thaw (F–T) cycles, a damage constitutive model describing the mechanical behavior of rock subjected to F–T cycles under uniaxial/triaxial cyclic loads was proposed. Initially, on the basis of fractional calculus and viscoelastic mechanics theory, cyclic loads were decomposed into a static load and a time-varying load with a zero equilibrium stress value. Second, to incorporate the impacts of F‒T cycles and stress on sandstone damage, F‒T damage was considered throughout the entire cyclic loading process. When the stress state of a rock sample reached the yield limit, the synergistic effect of damage due to stress was considered. On the basis of the use of nuclear magnetic resonance (NMR) spectroscopy to analyze the characteristics of porosity distribution of rock samples exposed to varying numbers of F‒T cycles, a compliance reduction term representing F‒T damage progression was introduced to adjust the time-varying load. Consequently, a fractional damage constitutive model of a rock mass under coupled F–T and stress was formulated. The theoretical fitting outcomes of this model were compared with experimental and simulated results, validating the patterns of influence of F–T damage and stress on rock performance. This comparison reflects the entire stress‒strain process of rocks subjected to F‒T cycles under cyclic loads and proves the rationality of the established model.
As a novel dam type with numerous advantages, the cemented sand and gravel (CSG) dam is increasingly crucial in water conservancy engineering construction. Extensive triaxial shear tests were conducted on specimens with varying confining pressures and gel contents to investigate the intricate mechanical properties of the CSG. Subsequently, a suitable strength criterion and constitutive model for CSG were established. The results indicated that (1) CSG exhibits certain cementation and structural characteristics, displaying significant strain softening, strong shear dilatancy, and other macroscopic mechanical properties. (2) A shear strength criterion based on binary medium theory was developed to describe strength evolution in different gel contents. (3) The shear strength criterion was judiciously transformed into the constitutive model's shear yield surface while considering the material's tensile properties based on the modified Cam-Clay model to obtain the volumetric yield surface. Additionally, the constitutive model focuses on delineating strain softening and strong shear dilatancy of CSG. (4) The stiffness matrix of the constitutive model was derived under general stress conditions with proven good fitting effects during triaxial shear testing of CSG. These findings provide enhanced theoretical guidance for stress-deformation calculations related to CSG dams.
A rate-dependent constitutive model for saturated frozen soil is vital in frozen soil mechanics, especially when simultaneously describing the nonlinearity, dilatancy and strain-softening characteristics. The distribution of the non-uniform strain rate of saturated frozen soil at the meso-scale due to the local ice-cementation breakage is described by a newly binary-medium-based homogenization equation. Based on the field-equation-based approach of the meso-mechanics theory, the interaction expression of the strain rate at macro- and meso-scale is derived, which can give the strain rate concentration tensor at different crushed degrees. With the thermodynamics and empirical assumption, a breakage ratio in the rate-dependent form is determined. This overcomes the limitations of the existing binary-medium-based models that are difficult to simulate rate-dependent mechanical response. Based on these assumptions, a newly binary-medium-based rate-dependent model is proposed considering both the ice bond breakage and material composition characteristics of saturated frozen soil. The proposed constitutive model has been validated by the test results on frozen soils with different temperatures and strain rates.
The paper proposes a three-scale binary medium-based constitutive model on the basis of the meso structures and micro components to describe the elasto-plastic mechanical behavior of mudstone samples. Based on the breakage mechanism of geomaterials, mudstone samples are considered as two different materials (bonded and frictional elements) at mesoscales. From micro to meso scales, given the similar but different mineralogy composition and porosity of the bonded and frictional elements at microscale, as well as their separate mechanical characteristics, different homogenization methods are adopted to obtain their respective meso mechanical properties. At the mesoscale, in view of the unique meso structures and the continuous material transformation, the extended self-consistent scheme (SCS) is improved to be adaptable to elasto-plastic composites with varying meso components. With the consideration of the evolution form of the breakage ratio under the external loading being given based on the assumed strength distribution of the meso bonded elements, the mechanical relations between meso and macro scales are established. Finally, on the basis of the mean-filed method and combined with the critical mechanical connections between different scales, the micro-meso-macro constitutive model for mudstone samples are proposed. The model validation shows that, with a few model parameters, the proposed model can well reflect the stress and deformation features of mudstone samples with complex micro-components.
Acid rain is often formed in southwestern China. Red-bed landslides often occur and cause major social and economic losses. The shear-slip process of red-bed landslides is affected by the creep characteristics of the weak interlayers in the rock mass. Samples of red-bed soft rock with weak interlayers of mudstone in Lufeng County of the Central Yunnan Water Diversion Project were tested in shear-creep tests in an acid environment. Combining with the functional relationship between the viscoelastic modulus and the acidic environment change, a stress-acidity-strain–time model is established based on the Burgers model. The results show that the long-term strength of the red-bed soft-rock weak interlayer in a mudstone gradually decreases with the increase of acidity. The viscoelastic modulus is linearly related to acidity. Compared with the traditional Burgers model, the improved Burgers model taking into account the effect of the acidic environment provides improved accuracy in describing the shear-creep behavior of the red-bed soft-rock weak interlayers.
The internal damage of red-bed soft rock induced by water is pervasive. The accumulation, growth, and localization of damage is a multi-scale process that can lead to significant strength loss in red-bed soft rock. Yet, research on the critical state of deterioration process considering multi-scale failure is limited due to high degree of system freedom. Renormalization group theory is an effective approach to find critical point of phase transition in a disordered system. To apply renormalization group theory in red-bed soft rocks, this article firstly analyzed their microstructures. Then, the granular unit model and stripy unit model are proposed to describe the self-similar characteristics of red-bed soft rocks. The calculation results based on renormalization group theory are consistent with the experimental results. The critical reductions of strength induced by water are 60% in light-yellow silty mudstone and 80% in grey silty mudstone. In addition, the critical state of damage propagation caused by stress is also studied and the analytical solution is derived. Results show that the renormalization group theory can effectively couple the micro damage and strength deterioration which provides guidance to the engineering.
In this study, a new approach based on DEM was developed to simulate the damage of water-rich rock after freeze–thaw cycles. In this way, water-rich rock samples at low temperatures were simplified as rock particles, ice particles, rock–rock contacts, rock–ice contacts, and ice–ice contacts. The volume of the ice particles changed as the temperature changed. The change characteristics were determined by the relationship between the temperature and the unfrozen water content. The developed approach was proven to be effective by comparing the simulation results with the laboratory test results. The physico-mechanical behaviors of water-rich rock samples after freeze–thaw cycles were studied. The results showed that the volume and porosity significantly increased after the freeze–thaw cycles, especially after 15 freeze–thaw cycles, and the increase in the radius was significantly larger than the increase in height. The uniaxial compressive strength, elastic modulus, and peak strain had an exponential reduction as the number of cycles increased. In uniaxial compression tests, the tensile failure rate of the sample after freeze–thaw cycles increased compared with that of the sample without freeze–thaw cycle treatment. With the increase in the number of freeze–thaw cycles, the distribution of cracks in the rock sample was more homogeneous. However, overall, the cracks that formed due to the freeze–thaw cycles were more distributed near the surface of the sample.
Red bed soft rock exhibits poor physical and mechanical properties and certain creep characteristics, which cause continuous deformation of tunnels and underground engineering structures during operation. The rock mass at the bottom of a railway tunnel in Sichuan Province is mudstone of the Penglaizhen Formation of the Upper Jurassic. It has a thin to medium-thick layered structure. Moreover, the rock formation is nearly horizontal. In this paper, the shear creep test and deep learning are employed to study the creep characteristics of gentle dip red bed mudstone.The results indicate that the red bed mudstone in the tunnel site exhibits medium-low creep characteristics. When the stress level is relatively low, the rate of the creep deformation gradually reduces with time, and when it reaches a certain time, the deformation no longer increases, and the final deformation tends to a stable value. Conversely, when the stress level is relatively high, although the rate of the creep deformation gradually reduces as the time increases, it remains unchanged when it reduces to a certain value. At the initial stage of creep, the deformation of each grade is evident; at the middle stage, the deformation is slow; and at the later stage, the deformation remains unchanged, that is, it enters the stable creep stage after a rapid decay in creep rate. The long-term strength of red bed mudstone in the tunnel site is low, which easily causes continuous deformation of the surrounding rock of tunnels under the action of high ground stress. According to the long-term deformation monitoring data at the bottom of the tunnel, combined with 20 groups of red bed mudstone creep parameter samples and the upper arch deformation data of the tunnel numerical model, the deep learning inverse analysis model of the creep parameter of rock mass is established based on the deep learning algorithm. Finally, we obtain the creep parameter of the red bed mudstone via inverse analysis. The research results provide a basis for engineering structure design and long-term deformation prediction of red bed mudstone strata in this area.
In the current paper, the deformation behaviours of rocks during compression are studied by testing 10 groups of sandstone samples with different porosity characteristics. According to the energy theory, the rock material was divided into two parts: solid skeleton and voids. A statistical damage-based approach was adopted to establish a nonlinear statistical damage constitutive model. The validity of the statistical damage constitutive model is verified by the test data. The statistical damage constitutive model performs well in each stage of rock compression before failure. For different types of rocks, different confining pressures, and different water contents, the statistical damage constitutive model fits well. This model can be applied to most types of rocks and in most engineering environments.
The natural rock mass prevailingly exists in the form of a fractured rock mass, and freezing-thawing failure of the fractured rock mass is also frequently encountered during geotechnical projects in cold regions. The previous researches and reports in freezing-thawing field principally focused on intact rocks, while rock joints and fractures were rarely considered, which causes great inconvenience to the safety design and stability assessment of engineering. In response to the special climatic conditions of cold regions, the freezing-thawing damage and degradation mechanism of fractured rock were studied in this paper based on existing laboratory experiments and damage mechanics theory. Primarily, a brief review of the progressive damage process of rock in the conventional triaxial compression experiment was given, as well as the determination methods of four characteristic stresses in the prepeak curve. Then, from the microcosmic perspective, the maximum tensile strain yield criterion was used to reflect the microunit strength which was assumed to statistically satisfy the Weibull distribution, deriving the damage evolution equation of fractured rock under the freezing-thawing cycle and load conditions and quantificationally describing the damage evolution law. Consequently, the statistical empirical constitutive relation of fractured rock considering freezing-thawing and loading damages was established. Ultimately, by combining the existing conventional triaxial compression experimental data of freezing-thawing single fractured rocks with the determination methods of characteristic stresses, the relevant constitutive parameters were solved, and the theoretical constitutive relation curves of the fractured rock after freezing-thawing cycles were obtained, which were compared with the experimental results to verify the validity of the established empirical constitutive relation. The study findings can provide a theoretical basis for revealing the freezing-thawing failure mechanism of the fractured rock mass to some extent.
1. Introduction
China is one of the countries with the largest cold region distribution, accounting for about 75% of the total land area of the country, where an increasing number of rock mass projects have been launched in cold regions driven by national policies in recent years [1–4]. In cold regions, the macroscopic damage, frost heave failure, and instability caused by the freezing-thawing cycle of fissure water under alternating temperature changes are considered as the main weathering process of rock mass [5–7], which has a decisive influence on the stability of rock mass [8–11]. Therefore, the researches on the mechanism of damage and degradation of rock mass under the freezing-thawing cycle condition are of great significance for engineering construction in cold regions [12–14], which have attracted the attention of numerous experts and scholars [15–17]. For example, Mutlutürk et al. [18] proposed an attenuation function model to describe the integrity loss of the freezing-thawing rock materials. Tan et al. [19] conducted research on the strength change of granite after freezing-thawing cycles. Besides, Wang et al. [20], Liu et al. [21], Luo et al. [22], and Zhou et al. [23] have studied the dynamic mechanical responses of freezing-thawing rock from different aspects, and the achievements on other rock properties have also been made [24, 25]. In respect of the constitutive model of rock, Zhang established the freezing-thawing and loading coupling damage evolution equation and damage constitutive model based on the failure and deformation characteristics of red sandstone [26, 27]. Fang et al. [28] proposed a method to solve the constitutive model parameters of random freeze-thaw cycles. According to the internal state variables theory, Wang et al. [29] established a general thermomechanical water migration-coupled plastic constitutive model of rock subjected to freezing-thawing.
These researches have detailedly discussed the damage theory, microstructure, and macromechanical properties of freezing-thawing rocks, as well as the influencing factors, through theoretical derivation and laboratory experiments, which undoubtedly deepen the recognitions and understandings of the freezing-thawing mechanism of rock. Unfortunately, all of those were carried out on intact rocks, with less relevance with fractured rocks, which is the majority of natural rock mass and widely distributed in cold regions. Additionally, the current focus of freezing-thawing fractured rock mostly locates in the crack extension mechanism [30–34], while the freezing-thawing constitutive relation is seldom investigated.
The task of this study is to establish the empirical freezing-thawing constitutive relation of fractured rock from the perspective of damage statistics. In this paper, the progressive failure process of rock in the conventional triaxial compression experiment was firstly reviewed, and the determination methods of four characteristic stress values were listed, which can be applied to accurately calculate the elastic modulus of rock. Secondly, based on the damage statistics theory and Lemaitre strain equivalence principle, the evolution equation and empirical constitutive relation of loading and freezing-thawing damages for fractured rock were deduced by the macroscopic phenomenological damage mechanics method, as well as the constitutive parameter expressions. Finally, on the basis of the existing conventional triaxial experimental results of single fractured rocks under freezing-thawing cycle and loading conditions, the damage statistical empirical constitutive curves of fractured rocks after a specific freezing-thawing cycle were obtained, which presents a great consistency with experimental results, verifying the validity of the established empirical constitutive relation.
2. Progressive Damage Process of Rock in Conventional Triaxial Compression Experiments
During the conventional triaxial compression experiments, the damage process of rock is usually accompanied by crack closure, initiation, extension, and transfixion [35–38] (see Figure 1), and the development of internal cracks is closely associated with the mechanical properties of the rock itself, which can be divided into the following stages: (1)Stage I: Closure stage—the crack closure stress
The analysis of damage process and the characterization of damaged rock masses through numerical models are the most difficult and challenging tasks in geotechnical engineering. This review paper describes and collects information regarding the causes of damage in the rocks and damage models (constitutive and hybrid damage models) for rock damage analysis. The main objective of this review is to discuss the causes of damage process, characterization, constitutive modes, and impact of natural changes on the selection of damage model. The review suggests that releasable strain energy, crack propagation and coalescence, joints, natural changes, and engineering disturbance are the main causes of rock fracture and damage. Most studies showed that a wider range of rock mass characterization will be required to create an ideal numerical model due to the rock reality, inelasticity, fractures, anisotropy, and inhomogeneity. Hybrid models are more efficient computationally as compared with the constitutive models. The review concludes that numerical models are also applicable tools to understand damage scale, damage degree and type, damage location, and damage occurrence time in the rocks.
Red beds are important targets for paleomagnetic studies, yet discriminating secondary chemical remanent magnetization (CRM) from primary depositional remanent magnetization (DRM) in them remains challenging. Here we reanalyze the thermal demagnetization data of and conduct comprehensive rock magnetic, Mössbauer spectroscopic and petrographic studies on red beds from four Cenozoic basins on the eastern Tibetan Plateau (China): the Gongjue, Nangqian, Shanglaxiu, and Jinggu basins. The red beds in the latter two basins are remagnetized, as are most Nangqian red beds. The Gongjue red beds and some Nangqian red beds retain a DRM. Our results reveal that detrital (titano)magnetite and hematite are well preserved in red beds retaining the DRM, whereas remagnetized red beds contain large amounts of authigenic hematite and goethite with detrital Fe‐bearing minerals strongly altered. Postdepositional diagenetic alteration induced by heating and/or fluid circulation related to magmatism and/or crustal deformation is probably the main reason for the remagnetization. Hematite carrying the CRM in remagnetized red beds has wide distribution of grain size and unblocking temperature spectra, while hematite carrying the DRM is usually coarse and has confined unblocking temperature spectrum. This can be used as a criterion for diagnosing remagnetization. Nanoscale goethite appears to occur only in remagnetized red beds: another sensitive criterion for discriminating CRM from DRM. These property‐based criteria constrain the origin of the NRM in red beds better than the classic paleomagnetic field tests. Our research emphasizes that integrated rock magnetic, Mössbauer spectroscopic and petrographic studies provide robust tools to diagnose remagnetization in red beds.
Most red beds demonstrate inferior geotechnical properties in natural conditions and need to be improved when used as construction material. In this study, a serious of triaxial tests, permeability tests, and scanning electron microscopy (SEM) analysis were carried out on lime-stabilized and untreated red bed soil after experiencing different wetting-drying (W-D) cycles. The test results showed that, with the increase in the added lime, the shear strength, strength parameters (including the cohesion and the internal friction angle), and the shear modulus of red bed soil increased gradually. For the untreated specimens, the four parameters decreased considerably after experiencing W-D cycles, while for the lime-stabilized specimens, they generally increased with an increase in the W-D cycles. Without experiencing the W-D cycles, the permeability coefficient increased by two times after it was stabilized with 10% lime. But with an increase in the W-D cycles, the permeability coefficient of the untreated and lime-stabilized specimens continuously increased and significantly decreased, respectively. Finally, variations in microstructure of the red bed soil under the effects of the lime stabilization and W-D cycles were discussed based on the SEM analysis. The results may contribute to improvement of red bed soil when used as roadbed and airfield fillings.
A constitutive model is proposed for tailing soils subjected to freeze–thaw cycles based on the meso-mechanics and homogenization theory. The evolution of meso-structure upon loading was analyzed within the framework of breakage mechanism. When the new model is formed, tailing soils are idealized as composite materials composed of bonded elements described by an elastic brittle model and frictional elements described by a double hardening model. Based on meso-mechanics and homogenization theory, the nonuniform distributions of stress and strain within the representative volume element are given by introducing a structure parameter of breakage ratio with the derivation of the strain coefficient tensor, which connects the strains of the bonded elements and the representative volume element. The methods for determining model parameters are suggested based on the available tested results. The model proposed here can predict the deformation properties of tailing soils experiencing freeze–thaw cycles with acceptable accuracy. The strain-hardening and post-peak strain-softening behaviors of tailing soils under various confining pressures as well as different numbers of freeze–thaw cycles are well captured, and the dilatancy and contraction features are also adequately represented.
In this paper, the stress–strain responses of frozen sands and an elastoplastic constitutive model based on the homogenization theory of heterogeneous materials are presented. In the model, frozen soils are conceptualized as binary-medium materials consisting of bonded blocks and weak bands, and their mechanical behavior is described with elastic–brittle and elastoplastic constitutive models, respectively. By introducing two groups of parameters (i.e., the breakage ratio (λv and λs) and strain concentration coefficient (cv and cs) related to the spherical and deviatoric stress components), the proposed model incorporates the breakage process of ice crystals and nonuniform strain distributions between the matrix (bonded elements) and inclusions (frictional elements) of the heterogeneous frozen soil samples. Moreover, an elasticity-based model and a double hardening constitutive model are employed to simulate the mechanical properties of the bonded elements and the characteristics of the frictional elements, respectively. To provide appropriate and quantitative predictions with the binary-medium constitutive model proposed here, triaxial compression tests are performed on the frozen and unfrozen sands to determine the individual parameters at confining pressures of 300–1800 kPa. The model validations demonstrate that the predictions agree well with the available laboratory results.
The rates of chemical reactions are highly dependent on temperature, meaning that the actual geological rock mass is affected by different temperatures. Only when the temperature effect is considered can the mechanism of the influence of temperature on the interaction between water and rock be further understood. It was found that the condition of turbulent flow is more likely to promote the softening of red-bed sandstone than the conditions of laminar flow and static water in an experimental study on the softening effects of different flow patterns on red-bed sandstone. Therefore, based on a multi-functional self-circulating open channel hydraulic test system, this paper designs and completes equal volume saturated tests of red-bed sandstone at low temperature (1 °C), medium temperature (23 °C), and high temperature (45 °C) under the turbulent conditions of three equal temperature gradients. The chemical action of the circulating solution in water flow at different temperatures, the propagation of micro-cracks in rock and the changes in mechanical indexes are discussed. The influence laws and mechanisms of the different temperatures on the softening of red-bed sandstone in turbulent flow are revealed. The results show that low-temperature flow can inhibit the softening of red-bed sandstone in the range of 1–45 °C. With the increase in water flow temperature, the development degrees of micro-structures and the mechanical damage of the corresponding rock become more notable. That is, temperature affects the physical and chemical water-rock interactions and then changes the internal structure of rock, thus affecting the softening and failure processes of red-bed sandstone. The study provides a theoretical basis for the further investigation of the softening laws and mechanisms of other red layered soft rocks by temperature under turbulent conditions.
This research examined the distribution features of red beds and 1,100 Danxia landform sites across China, while probing the relationship between these spatial patterns and geological elements. This study is based on geological and tectonic maps of China. ArcGIS software was used to process the adjacent index, then perform a spatial analysis of Danxia landforms and red beds, and a coupling analysis of Danxia landforms and red beds with tectonics. Based on a point pattern analysis of Danxia landforms, the adjacent index is 0.31, and the coefficient of variation verified by Thiessen polygon reaches 449%. These figures reflect the clustered distribution pattern of the Danxia landforms. Across the country, Danxia landforms are concentrated into three areas, namely, the Southeast China region, the Sichuan Basin region and the Qilian-Liupan region. The exposure of red beds covers 9.16 × 10 5 km 2 , which accounts for 9.5% of the total land area of China. With this research background, the geological elements of tectonics and their effects on the distribution, number, and spatial pattern of Danxia landforms and red beds were analyzed.
To explore the impact of temperature difference (TD) on the disintegration of redbed softrock, three types of redbed rock, collected from Nanxiong Basin, were analyzed under three different treatments: TD, wetting and drying (WD), and TDWD-temperature difference and WD. To better understand the influence of different ranges of TD on disintegration during WD cycles, pH (hydrogen ion concentration) values, electrical conductivity (EC) values, and concentration of cations in leachate released during treatment were measured. The results show that no significant change can be observed under single TD treatment but that TD can increase the disintegration rate by accelerating the water–rock interaction. The effect of TD is more significant for rock with weak resistance to disintegration.
The Tibetan Plateau (TP) has the largest areas of permafrost terrain in the mid- and low-latitude regions of the world. Some permafrost distribution maps have been compiled but, due to limited data sources, ambiguous criteria, inadequate validation, and deficiency of high-quality spatial data sets, there is high uncertainty in the mapping of the permafrost distribution on the TP. We generated a new permafrost map based on freezing and thawing indices from modified Moderate Resolution Imaging Spectroradiometer (MODIS) land surface temperatures (LSTs) and validated this map using various ground-based data sets. The soil thermal properties of five soil types across the TP were estimated according to an empirical equation and soil properties (moisture content and bulk density). The temperature at the top of permafrost (TTOP) model was applied to simulate the permafrost distribution. Permafrost, seasonally frozen ground, and unfrozen ground covered areas of 1.06 × 106 km2 (0.97–1.15 × 106 km2, 90 % confidence interval) (40 %), 1.46 × 106 (56 %), and 0.03 × 106 km2 (1 %), respectively, excluding glaciers and lakes. Ground-based observations of the permafrost distribution across the five investigated regions (IRs, located in the transition zones of the permafrost and seasonally frozen ground) and three highway transects (across the entire permafrost regions from north to south) were used to validate the model. Validation results showed that the kappa coefficient varied from 0.38 to 0.78 with a mean of 0.57 for the five IRs and 0.62 to 0.74 with a mean of 0.68 within the three transects. Compared with earlier studies, the TTOP modelling results show greater accuracy. The results provide more detailed information on the permafrost distribution and basic data for use in future research on the Tibetan Plateau permafrost.
A typical Danxia stone pillar, Leipishi I, in the World Natural Heritage site at Mt. Langshan, China, collapsed on 2 November 2009. To understand the mechanism controlling this rockfall event, uniaxial compressive strength, tensile strength, resistance against sulfuric acid, and freezing and thawing properties were analyzed from 44 sandstone and conglomerate cores collected from the Lanlong Formation, the only exposed formation on Mt. Langshan. In addition, four rock slices were created for analysis under a polarizing microscope. A detailed reconstruction of the geometry and restraint conditions of the stone pillar in place before the rockfall occurred permitted an estimation of the stress state before collapse using 3D finite-element code. The results show that the rapid retreat of soft, intercalated rock layers due to weathering can profoundly change the stress state within the rock body, causing compressive or tensile stresses to rise above compressive or tensile strengths in specific sections of a rock body, and causing partial or complete collapse.
Red beds are widespread in the eastern Sichuan Basin, SW China, and are often called “landslide prone strata”. The dip angle of these red beds is commonly less than 10°, which is much less than the angle of internal friction between the bedding planes. Thus, in theory, failure will not occur along the bedding planes in such strata. We used field methods, numerical modeling, and ring shear tests to investigate the effects of rainfall on landslides in shallow-dipping red beds, using the Qingning landslide in SW China as an example. Our results suggest that the probable mechanisms leading to failure are (1) permeation of rainfall through the cracks at the back of the landslide site that increases the hydrostatic water pressure, which adds to the sliding stress and reduces the effective stress on the failure surface, gradually destabilizing the mass. In the Qingning landslide, the maximum water pressure was as high as 21.8 m before failure. When the factor of safety decreased markedly to 1.015, the sliding mass started to slowly slide. (2) As sliding takes place, the sliding zone soil is under undrained shear and its shear strength decreases sharply to a critical value, which promotes rapid sliding. In the Qingning landslide, the shear resistance of the sliding zone soil decreased markedly to 25.9 kPa as the pore water pressure increased to 118.3 kPa. This study may provide a theoretical basis for landslide forecasting in gently inclined red beds of the eastern Sichuan Basin as well as in similar geological settings worldwide.
Firstly, the definition of damage for rock was improved according to some insufficiency or disadvantages of the definition of damage in geometric damage theory. On basis of it, rock material under stress was abstracted into two parts for failed and un-failed material; and then a new damage model had been created according to differences of two parts under force. Secondly, a statistical damage evolution equation was established by making use of statistical damage theory; and furthermore a statistical damage constitutive model of rock under a specific confining pressure has been set up. Thirdly, the model has been modified rationally by discussing the empirical relation between parameters of the model and confining pressure of rock; and then a statistical damage constitutive model applying to the condition of different confining pressures has been founded. At last, with studying physical signification of the parameters of the model, a way to find critical physical and mechanical parameters reflecting conversion between hardening and softening mutually is initially developed. It could also reflect characteristic about conversion between hardening and softening mutually; and its rationality has been shown compared with its test.
Rock materials exhibit strain softening at low confining pressure. How to accurately describe the strain softening of rock materials is very important for rock engineering. A new model, referred to as Binary Medium Model for rock matrials, is formulated under the theoretical framework of breakage mechanics for geomaterials. In the model, rock materials is conceptualized as binary medium consisting of bonded blocks and weakened bands which are idealized as bonded elements and frictional elements respectively. During the loading process the bonded elements gradually fracture and transform to be the frictional elements. The deformation properties of the bonded elements are described by ideal elastic-brittle materials and those of the frictional elements are described by hardening elasto-plastic materials. Two sets of breakage parameters, i.e., breakage ratios and strain concentration coefficients, describing the influence of rock structure on the process of failure, are introduced. The proposed model has been used to predict the behavior of sandstone sample in triaxial compression test. By making comparisons of predictions with experimental data it is demonstrated that the new model provides satisfactory modeling of many important features of the behavior of rock materials.
Based on the property that micro-cells strength is consistent with lognormal distribution function, this paper presented a new statistical damage softening constitutive model simulating the full process of strain softening for rock. Through discussing the characteristics of random distributions for rock micro-cells strength, lognormal distribution assumption is tested by Kolmogorov-Smirnov test in statistics, and the reasonable method of geometry boundary condition is selected to determine model parameters that can be easily applied to the situations under different complex conditions. Gabbro experiment comparative analyses show that the new damage softening constitutive model is rational and convenient in engineering.
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.
The recurrence of freeze-thaw processes induced by day-night and seasonal temperature changes is one of the most important reasons for damage and instability of rock engineering structures in cold regions. The study of the constitutive relationship and the damage degradation of rocks subjected to freeze-thaw weathering process is therefore of critical scientific importance to solving the stability problem of rock excavations in these regions. In this work, the stress-strain relationships of rocks subjected to different number of freeze-thaw weathering cycles were investigated in details. Experimental results show that as the number of freeze-thaw cycles increases, the compaction stage of the stress-strain curve becomes longer with more pronounced nonlinear features, while the uniaxial compressive strength, full compaction stress, tangent deformation modulus and initial deformation modulus all decrease, but the peak strain and full compaction strain all increase. A new piecewise constitutive model based on the characteristics of compaction and post-compaction stages of the stress-strain curve was proposed using a statistical compaction model in combination with the conventional statistical damage mechanics model with the strain equivalence hypothesis. Compared with the reference model, the proposed constitutive model has been demonstrated to be much more effective in describing the stress-strain behaviour of rocks having freeze-thaw damages, particularly when the number of freeze-thaw weathering cycles is significant. For all the experimental cases presented in this work, the coefficients of determination, R2, based on the proposed model are always greater than 0.93, while those of the reference model never exceed 0.85. In addition to, the model parameters have been shown to have clear physical meanings closely related to the characteristics of the measured stress-strain curve.
In this work, we shall propose a new micro-mechanical constitutive model for the estimation of effective elastic-plastic behaviors of heterogeneous rocks. A bi-potential based incremental variational (BIV) approach is developed in order to take into account non-uniform local strain fields of constituents. The studied materials are composed of a non-associated and pressure sensitive plastic matrix, elastic inclusions and/or voids. For clarity, the local behavior of matrix is first described by an elastic perfectly-plastic model. Based on the bi-potential theory to dealing with non-associated plastic flow, the solid matrix is considered as pertaining to implicit standard materials (ISMs). The effective incremental bi-potential and macroscopic stress tensor are then estimated through an extension of the incremental variational method initially established for generalized standard materials(GSMs). The accuracy of the BIV model is verified by comparing the model’s predictions with the reference results obtained from direct finite element simulations. Furthermore, by assuming that the general formulation obtained for the perfectly plastic matrix remains valid for each loading increment, the BIV model is extended to considering that the solid matrix exhibits an isotropic hardening by using an explicit algorithm. The accuracy of the extended BIV model is also validated by a series of comparisons with the reference solutions obtained by direct finite element simulations for both inclusion-reinforced composites and porous materials. Both local and macroscopic responses are compared. As an example of application, the extended BIV model is finally applied to estimating the mechanical responses of typical claystone and sandstone under different loading paths.
Red-bed soft rock covers a large area in China and is often used as filling materials for highway roadbed and embankment, while the disintegration of red-bed soft rock often causes serious settlement of the roadbed and decreased stability. To thoroughly study the disintegration properties of red-bed soft rock, a series of slake durability tests were performed using different test methods. First, the gradation of disintegrated red-bed soft rock was investigated, and the shape of the gradation curve mainly presented as reverse sigmoidal and hyperbolic. Moreover, the evolution model of the disintegration breakage of red-bed soft rock using the Morgan-Mercer-Florin (MMF) model was derived, and the model parameters were analysed. Based on the test results, the disintegration behaviours of red-bed soft rock were measured by the disintegration ratio; then, the new formula to calculate the disintegration ratio based on the concept of the traditional disintegration ratio was derived using the established model. Finally, the effect of different test methods, i.e., different test devices, drying temperatures and sizes, on disintegration breakage under cyclic wetting and drying was analysed, and the test results showed that the rate of disintegration was accelerated by the slake durability apparatus, a higher drying temperature and a larger size.
Landslides with large displacements are more dangerous than landslides with small displacements, because the first category causes more serious damages. In this paper, a new prediction method is introduced for rock planar slides with large displacements. The prediction model is not limited to a certain region but limited to a certain failure mechanism of a landslide. This case study was carried out in the red bed area, Nanjiang County, Sichuan Province, China, and validated in the red bed area of Yunyang and Fengjie Counties, Chongqing, China. The topographic factor T was proposed as a topographical indicator. The influence of the normalized rainfall R which is a combination of the duration of rainfall (D) and the average intensity (I) of rainfall was analyzed. A threshold value for rock planar sliding with large displacement was obtained by establishing a relationship between the T factor and the R factor. The primary probability factor P gives a final indication of the probability of rock planar sliding with large displacement. The prediction model is applied to the existing rock planar slides or the slopes with the presence of a number of preconditions for sliding. The prediction model obtained from Nanjiang County was validated successfully in the red bed area of the Yunyang and Fengjie Counties. It is assumed that the prediction model is suitable for other regions with a red bed structure as well.
A series of triaxial compression tests, with real-time computed tomography (CT) scanning performed in the loading process, were conducted on frozen sandstones at confining pressures of 0, 1, 2, and 3 MPa at different temperatures of −2, −6, −10, and 20 °C, respectively. The experimental results indicate that the strength of frozen sandstone increases with a decrease in temperature. The strength of frozen sandstone increases with an increase in the confining pressure at freezing temperatures. In the loading process, the evolution law of the CT value of the whole sandstone is explored, and three-dimensional reconstruction of CT images, which denote postfailure models of frozen sandstone, is also performed. According to energy dissipation theory, an isotropic damage variable is introduced. Based on the CT value of the whole sandstone, the concept of the compaction coefficient K, which describes the compaction degree, is proposed to modify the damage model obtained by Lemaitre’s strain equivalence hypothesis. The validity of the model is verified by comparing its computed results with the experimental results obtained from triaxial compression tests. The results indicated that the modified damage model can adequately predict the stress-strain relationship of the frozen sandstone.
It is of great significance to analyze and predict the deformation characteristics of rock engineering materials by establishing a universal damage constitutive model under freeze-thaw and loading conditions. Based on the study of statistical damage constitutive model founded under freeze-thaw and loading condition, analytical expressions of the model parameters and characteristic parameters in the stress-strain curves (i.e., elastic modulus, stress and corresponding strain at the peak point) were established under specific freeze-thaw cycles. Then, an attenuation model that complies with Newton's material cooling law was introduced to develop the relationship among elastic modulus, stress at peak point and freeze-thaw cycles. Thirdly, the formula of the peak strain under different freeze-thaw cycles was proposed by exploring the correlation between the peak strain of stress-strain curves and freeze-thaw cycles. Therefore, the determination method of the unified model parameters under different freeze-thaw cycles is proposed, then, statistical damage constitutive model under freeze-thaw and loading conditions is generalized, and the freeze-thaw mechanics test with marble was performed to verify the rationality of the model. The results show that stress-strain curves described by presented model under different freeze-thaw cycles have a good agreement with the experimental curves, especially at the peak strength point. The results can provide theoretical reference for the study of rock mechanical properties under different freeze-thaw cycles
The slake durability; grain quantity, size, roundness, and slake degree of red-bed mudstones are experimentally investigated using the slake durability test and the cyclic wetting and drying test. Results indicate that the complete slaking process exhibits three distinct stages. During the process, the slake durability index decreases linearly with increasing cycle number. Slight variation in grain quantity is observed. Smaller grain size fractions tend to have higher slaking degree indexes in earlier cycles. Grain roundness fluctuates. Two parameters, namely, fractal dimension and surface energy, are revealed to have the ability to represent the degree of slaking of red-bed mudstones.
An elastoplastic theory for saturated freezing soils is presented on the basis of thermoporomechanics. A saturated freezing soil considered as an open system and both Eulerian and Lagrangian formulations considering the phase transition between ice crystals and unfrozen water are given for mass conservation, momentum balance, kinetic energy theorem, first and second thermodynamics, the Clausius-Duhem inequality and conduction laws for fluid mass and heat. Using the Lagrangian saturation and considering solid-fluid interface interactions, a constitutive model for poro-elastoplastic saturated freezing soils is formulated based on the irreversible process. For isotropic linear thermo-poro-elasticity and ideal plasticity, the stress strain relationship for saturated freezing soils considering the influence of temperature and interface energy is proposed. In addition, for hardening plasticity, the general stress strain relationship is formulated under the conditions that the associated or non-associated flow rule is assumed, and a corresponding constitutive model is presented to model the cryogenic triaxal compression of saturated frozen soils. The constitutive theory proposed here provides a potential basis for modelling thermo-hydro-mechanical coupling interactions of saturated soils during the freezing process.
The freeze-thaw damage of rock is a critical problem to study rock engineering in cold regions. When water is frozen in pores, 9% volume expansion will induce damage in rock for a huge ice pressure. Thus, rock will be deteriorated and softened after freeze-thaw. Besides, loading damage produces when the inner stress exceeds the bearing capacity of rock. So it's crucial to establish a damage constitutive model under freeze-thaw and loading in order to evaluate the stability of rock engineering in cold regions. The freeze-thaw damage of rock is expressed by static elastic modulus in this paper, which can be accurately and simply predicted by damage evolution equation using P-wave velocity or compression strength proposed by Liu et al., 2015. Loading damage can be obtained by statistical theory assuming that micro-unit strength satisfies the Weibull distribution and the maximum-tensile-strain yield criterion. Then the final statistical damage constitutive equation under freeze-thaw and loading is derived, in which unknown parameters can be determined through carrying out compression experiment on rock after different freeze-thaw cycles. This developed model is validated by a previous experiment and applied to analyze the stability of a tunnel under coupled thermo-hydro-mechanical condition in cold regions. The results show that the proposed constitutive model is very suitable for rock suffering freeze-thaw cycles and it is of high accuracy and good practicality.
In this paper, a new micro-mechanics based plastic damage model is proposed for quasi-brittle materials under a large range of compressive stress. The damage is due to initiation and propagation of micro-cracks while the plastic deformation is directly related to frictional sliding along micro-cracks. The two dissipation processes are then physically coupled. With the homogenization procedure and thermodynamics framework, the macroscopic state equations are deduced and the local driving forces of damage and plasticity are defined. New specific criteria are proposed for the description of damage evolution and plastic flow. These criteria take into account the variation of material resistance to damage with confining pressure and the degradation of surface asperity of micro-cracks during the frictional sliding. An analytical analysis of macroscopic peak strength and volumetric compressibility-dilatancy transition is provided. A specific calibration procedure is further proposed for the determination of all model's parameters from conventional triaxial compression tests. The efficiency of the proposed model is verified against experimental data on three different materials and for a very large range of stress. All main features of mechanical behaviors of materials are well captured by the proposed model.
Triaxial compression tests were carried out on artificially structured soil samples at confining pressures of 25, 37.5, 50, 100, 200, and 400 kPa. A binary-medium constitutive model for artificially structured soils is proposed based on the experimental results, the disturbed state concept (DSC), and homogenization theory. A new constitutive model for artificially structured soils was formulated by regarding the structured soils as a binary medium consisting of bonded blocks and weakened bands. The bonded blocks are idealized as bonded elements whose deformation properties are described by elastic materials, and the weakened bands are idealized as frictional elements whose deformation properties are described by the Lade-Duncan model. By introducing the structural parameters of breakage ratio and local strain coefficient, the nonuniform distribution of stress and strain within a representative volume element can be given based on the homogenization theory of heterogeneous materials. The methods for determination of the model parameters are given on the basis of experimental results. Comparisons of predictions with experimental data demonstrate that the new model provides satisfactory qualitative and quantitative modeling of many important features of artificially structured soils.
Bank slope stability has become a great concern, while the impoundment of Three Gorges reservoir. The bank slope composed of red-layer soft rock has exhibited distinct deformation and failure. Therefore, a typical red-layer soft rock around Three Gorges reservoir area was selected to demonstrate the process of cyclic changes at the reservoir level and immersion-air-dry cyclic action of water-rock inside hydro-fluctuation belt. To meet the objective of this study, a series of creep tests were conducted on the rock specimens at different water-rock interaction stages. The following points were noticed based on the laboratory results: (1) the creep fracture strength and long-term strength of red-layer soft rock degraded significantly during the process of water-rock interaction. For the first three water-rock interaction circulations, the strength of red-layer soft rock degraded quickly and then gradually became stable. (2) During the creep test, the lateral expansion of red-layer soft rock increased significantly regarding to the number of cycles. (3) The creep curve includes three typical stages at failure stress level—primary (damped) stage, secondary (steady-state) stage, and tertiary (nonlinear accelerated) stage. As the number of cycles increased, the percentage of secondary stage diminished gradually. However, the tertiary stage showed a gradual increment, since the plasticity of the specimens was strengthened by water-rock interaction. (4) The shear failure characteristics of the specimens became highly considerable during the process of water-rock interaction, and there have been a gradual increment of shear rupture zone. (5) The SEM results showed that the specimen microstructure changed its state from dense to loose and porous. The findings of this research provide a good basis for long-term stability analysis of bank slope.
Breakage mechanics is a new theory different from fracture mechanics and damage mechanics. The methodology of examination for geomaterial in three levels, macro-level, meso-level and micro-level, was introduced, and the geomaterials were divided into four structural types, fragmentation structure, scatter mass structure, envelope structure and suspension structure. The principles to determine the load sharing ratio between structure bodies and structure surfaces for each structural type were discussed. At last, some meaningful conclusions were obtained for the development of breakage mechanics of geomaterial.
In this paper geomaterials are conceptualized as binary medium consisting of bonded blocks and weakened cells which are idealized as elastic-brittle element and hardening elastic-plastic element respectively. Based on the homogenization theory of heterogeneous materials, a generalized stress-strain relationship expressed in incremental form is derived. The model contains two sets of structural parameters whose evolution laws can be determined by means of 'try and error' method, i.e., breakage parameter and stress concentration coefficient of elastic-brittle element. Finally a structural clay and a sandstone specimen are taken as two examples to prove the applicability of the suggested model.
Taking red-bed soft rock along Tangkou-Tunxi section of Tongling-Huangshan expressway for example, according to the characteristics of softening and slaking with water, two representative rock samples (sandstone and mudstone) along the expressway are chosen to perform laboratory tests of slaking; and changes in grain contents of rock samples in slaking process are analyzed. On this basis, the comparative analysis of slaking characteristics of those representative samples is made; and the slaking characteristics of those samples are divided into four grades, i.e. strong slaking, medium slaking, feeble slaking and nonslaking. The results indicate that the types of red-bed soft rock and its cement, and the content of clay mineral are the main inner determinants of slaking of red-bed soft rock; the slaking characteristic gradually decreases as the grain diameter of slaking substance reduces; in order to obviously reflect the rate and degree of slaking of those samples, changes in grain contents of slaking substances greater than 5 mm and less than 0.25 mm should be selected as the evaluation objects. At last, thorough study of slaking mechanism of red-bed soft rock is made.
In order to study the water-rock interaction characteristics of red-bed rock in the Three Gorges reservoir and analyze failure process of bank slope, the distribution law of red-bed slope was obtained by statistics. According to the mineral analysis by X-ray diffraction, based on the laboratory test and scanning of microstructure, the water-rock interaction characteristics of red-bed rock was analyzed. Taking the typical bank slope in the Three Gorges reservoir as an example, the failure process of bank slope caused by water-rock interaction of red-bed rock was analyzed. The results show that hydrophilic expansibility minerals in the red-bed rock is the key of special form of water-rock interaction; the disintegration occurs along with the limitation in the rock, and in the dry-wet cycle process, not only the tension failure occurs caused by water losing shrinking, but the compression and shear failure occur, which are caused by the concentration of compressive stress in the tip of water swelling micro-fissure. The mineral in the expansibility sliding soil has no obvious change after meeting water, but the combining structure between mineral are broken. The quantity of pore and their size increase, which decreases the strength of sliding soil. It is considered that the riverside slumping mass of the second segment in Badong group in the north side from Taijitou to Jiuxianping in Badong is related with different disintegratives. The low shear strength of expansibility slide soil in red-bed and pushing effect of water pressure in the back edge results in the formation of near horizontal strata slope in Wanzhou area, whose slumping mass in the front has polyphase activities.
Rock materials exhibits strain softening at low confining pressure. How to accurately describe the strain softening is very important for rock engineering. A new model, referred to as Binary Medium Model for rock matrials, is formulated under the theoretical framework of breakage mechanics for geomaterials. In the model, rock materials is conceptualized as binary medium consisting of bonded blocks and weakened bands which are idealized as bonded elements and frictional elements respectively. During the loading process the bonded elements gradually fracture and transform to be the frictional elements. The deformation properties of the bonded elements are described by ideal elastic-brittle materials and those of the frictional elements are described by hardening elasto-plastic model. Two sets of breakage parameters, i.e., breakage ratios and strain concentration coefficients, describing the influence of rock structure on the process of failure are introduced. The proposed model has been used to predict the behavior of sandstone sample in triaxial compression test. By making comparisons of predictions with experimental data it is demonstrated that the new model provides satisfactory modeling of many important features of the behavior of rock materials.
The red-bed soft rock is widely distributed in the Three Gorges Reservoir area. The strata of red-bed soft rock generally contain one or more layers of weak interlayer. In this paper, take red-bed soft rock as our research object, considering the different thickness and saturation degree of its weak interlayer, the mechanical properties of red-bed soft rock containing weak interlayer were studied by laboratory tests and field tests based on the mineral analysis results of the weak interlayer, and a series of useful results were obtained. The research here can provide guidance for the design and construction of red-bed soft rock slope in the area of Three Gorges reservoir and western region of Hubei province, China.
Creep characteristic is one of the most important mechanical characteristics of rock. It controls the stability of rock engineering. Under step load condition, the creep test of red-bed soft rock which was collected in the seventh tunnel of Yintao water transmission engineering in Gansu is performed by using the CSS-44100 electronic servo testing machine. Based on scientific interpretation and analysis of test data, red-bed soft rock has remarkable creep characteristics and Burgers creep model can be applied to characterize the creep of red-bed soft rock. The effect of water content upon strength and creep characteristic are studied it shows that instantaneous strength decreases with increasing of water content. The higher the water content is, the more creep deformation and the time that need reaching steady state and the bigger the rate of creep are. The test results show that the creep testing curves of red-bed soft rock are coincident well with the theoretic curves and the Burgers creep model can be applied to characterize the creep properties of red-bed soft rock.
Waloddi Weibull presented three different formulations of the distribution that bears his name, a fourth began through a printer's error, and these have been followed by other formulations. Analyses in the literature depend on the particular formulation set forth by each author, causing confusion about what works with what. This article encourages practitioners to use the Weibull distribution by furnishing historical background and parallel development of the essential formulas (cumulative distribution functions, probability density functions, hazard rates, and parameter estimates) for each of five formulations.
Freeze–thaw action is a complex moisture–heat-mechanics interaction process, which has caused prevailing and severe damages to canals in seasonally frozen regions. Up to now, the detailed frost damage mechanism has not been well disclosed. To explore the freeze–thaw damage mechanism of the canal in cold regions, a numerical moisture–heat-mechanics model is established and corresponding computer program is written. Then, a representative canal in the northeast of China is taken as an example to simulate the freeze–thaw damage process. Meanwhile, the robustness of the numerical model and program is tested by some in situ data. Lastly, the numerical results show that there are dramatic water migration and redistribution in the seasonal freeze–thaw variation layer, causing repetitive frost heave and thaw settlement, and tension–compression stresses. Therefore, the strengths of soil are reduced after several freeze–thaw cycles. Further, the heavy denudation damage and downslope movement of the canal slope would be quite likely triggered in seasonally frozen regions. These zones should be monitored closely to ensure safe operation. As a preliminary study, the numerical model and results in this paper may be a reference for design, maintenance, and research on other canals in seasonally frozen regions.
Taking typical surrounding rock of the red-bed soft rock highway tunnel for example, two representative rock samples(mudstone and muddy siltstone) along the highway tunnel's surrounding rock are chosen to perform tests of compressive strength, by using the uniaxial compressive test and the point load test, the rock compressive strength characteristics under different weathering degree and water action are analyzed; The results indicate that the water sensitivity of mudstone is high and the Water sensitivity of muddy siltstone is blow. The compressive strength of the mudstone decreases with the weathering degree increases significantly.
Red bed extensively distributes in Huangshan Area of Anhui Province which belongs to category of soft rock and has the characteristics of softening and slaking with water. So the red bed soft rock cannot be used as roadbed filling directly. The feasibility of the slaking products of the red bed soft rock used as highway roadbed filling is discussed by experimental studies of the slaking of the red bed and the pavement performance of the slaking products. After the stability of the slaking of the red bed, through reasonable collocation of those parts of steady performance, the slaking products of the red bed can meet the strength and stability requirements of highway roadbed filling, and can be used as highway roadbed filling.