The exploitation of natural resources, the development of geothermal resources, and the construction of underground engineering projects, among other activities, can affect rock properties and, consequently, lead to engineering disasters. The mechanical properties of rocks subjected to high temperatures differ from those observed at room temperature. The mechanical property changes induced by physicochemical processes within the rocks following high-temperature exposure are closely related to temperature.
Currently, research on the mechanical properties of rocks subjected to high-temperature action is primarily focused on the impact of temperature on the static and dynamic mechanical properties of rocks. The influence of temperature on the mechanical properties of rocks in static and dynamic loads is a key area of investigation. The results of the tests demonstrate that Meng1 et al. conducted uniaxial and triaxial compression tests on limestone subjected to high temperatures ranging from 20 to 800 ℃. Shi2 conducted uniaxial compression tests on sandstones at varying temperatures and with differing stratigraphies to ascertain the impact of test temperature and stratigraphy on the physical and mechanical properties of the sandstones. Li3et al. observed that above 600°C, granite specimens exhibited a considerable number of conspicuous large cracks and volume expansion, accompanied by a rapid decline in the coefficient of thermal conductivity. Wang4 et al. employed a modified split Hopkinson compression bar to conduct dynamic compression tests on granite samples at temperatures between 20 and 500°C. This allowed for a detailed examination of the effects of heating at varying temperatures and impact rates on the mechanical behavior of the granite specimens. Furthermore, a statistical damage ontology model for rocks based on the Weibull distribution was developed, and the factors influencing the model parameters were analysed. The findings indicate that there is a notable influence of strain rate on the augmentation of dynamic compressive strength at elevated temperatures. Wong5 et al. conducted dynamic uniaxial compression tests on marbles at high temperatures ranging from room temperature to 750 ℃ using a modified Hopkinson Pressure Bar (SHPB) device, which is equipped with a high-temperature oven and can be heated. The results demonstrated that the peak stresses of the heated specimens exhibited a negative correlation with the heating temperature. Shu6 et al. conducted a cyclic impact loading test on granite at temperatures between 25 and 800 ℃. The aim was to study the thermal effects of dynamic cyclic loading under the action of rock energy dissipation. The Hopkinson pressure bar (SHPB) experimental system was used to carry out the test on heat-treated rocks. The relationships between energy dissipation, energy dissipation rate, impact time, damage mode, and temperature were examined. Mao7 et al. investigated the mechanical properties of mudstone under the influence of different loading rates, from room temperature to 400°C. A series of experiments was conducted by Ping8,9,10,11to investigate the effects of high-temperature cycling on sandstone specimens. The experiments employed eight distinct strain rates and a dynamic single-axis compression test. Moreover, the influence of elevated temperatures, spanning a range of 25 to 1000°C, on sandstone was examined through the utilization of shock compression tests. The objective of this study was to elucidate the effects of peak stress, strain, and elastic properties on sandstone under thermal conditions. The damage sustained by the model and the test pieces was found to be dependent on the rate at which they were loaded. Six discrete loading rates were employed for the evaluation of sandstone specimens at temperatures ranging from 25 to 800°C. A one-dimensional dynamic combination loading was employed to test the limestone specimens at different strain rates, to investigate their fracture mechanics performance. The objective of the analysis was to identify the characteristics of the tensile fracture mechanics and energy consumption of the specimens subjected to a pre-applied static load. Furthermore, the analysis sought to examine the correlation between the mechanical properties and the temperature history of the limestone specimens, which were subjected to six distinct levels of shock pressure following heating to 200, 400, and 600°C.
Furthermore, Zhang12 examined the internal mineral composition and microstructural alterations of rocks at elevated temperatures by analyzing the physico-mechanical characteristics, energy dissipation, and damage modes of muddy sandstones at diverse temperatures in both air-dried and saturated states. This was accomplished through the use of the RMT-150B Rock Mechanics apparatus and the Split Hopkinson Pressure Bar (SHPB) device. Furthermore, Jin13 conducted SEM and EDS tests to examine the microstructure of sandstone. Their research employed magnetic resonance imaging, scanning electron microscopy, and uniaxial testing to investigate the micro-composition and mechanical properties of sandstone under different temperatures and cooling modes. Their findings revealed the change rule of sandstone’s mechanical properties under water cooling and natural cooling modes. Li14examined the damage behavior of sandstone by subjecting it to heat treatment at varying temperatures. Subsequently, they developed a comprehensive, coupled model to elucidate the underlying damage process. Furthermore, scanning electron microscopy (SEM) and X-ray diffraction (XRD) analyses demonstrate that elevated temperatures induce phase transformations of quartz within the rock, thereby imparting substantial alterations in the physical and mechanical properties of the rock material15,16,17.
The aforementioned studies have not yet addressed the variability of mechanical properties of red rocks under static and dynamic loading conditions,, nor have they considered the impact of internal mineral composition changes following high-temperature exposure. This paper employs a combination of X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques to investigate the mineralogical composition and chemical reactions of red sandstone subjected to various temperatures. The combined analysis of mass loss rate, volume expansion rate, and longitudinal wave velocity loss rate of mechanical parameters of red sandstone after high-temperature action reveals the damage mechanism law of high temperature on the mechanical properties of red sandstone. This provides a specific theoretical basis for the exploitation of deep natural resources, the development of geothermal energy resources, and the construction of underground engineering.
Specimen Preparation
In this paper, the experimental red sandstone was sourced from Jiaozuo City, Henan Province, in accordance with the recommendations of the International Society of Rock Mechanics18. This sandstone was used for impact tests on cylindrical specimens, with a diameter close to 50mm and a height ranging from 25mm to 50mm. The cylindrical core sizes adopted for the red sandstone specimens were Ф50 × 100mm and Ф50 × 25mm. These were obtained using a rock coring machine, slicer, and double-end smoothing machine, among other equipment.
Firstly, large rock cores were drilled vertically using a drilling machine. Subsequently, the columnar cores were cut to the approximate test sizes using a slicing machine. Finally, the specimen end faces were ground using a double-end smoothing machine to ensure that the unevenness of the two end faces was less than 0.05mm and that the end face was perpendicular to the specimen axis with an error of less than 0.25°. This ensured that the machining accuracy met the test requirements. The test specimens were all taken from the same batch of rock blocks, and care was taken to avoid any additional damage to the samples.
Use the brushing method to remove dust, mud, and other impurities on the surface of the sample. After cleaning, use clean paper towels to gently dry the sample surface to avoid leaving water residue. Place the cleaned sample in a well-ventilated place without direct sunlight to dry naturally. After drying, the sample should reach a constant weight, i.e. the weight no longer changes with time.
Pack and seal the sample using a ziplock bag. During the packaging process, make sure that the samples are not subject to mechanical damage such as collision. Uniquely identify and number each sample, and store the sealed samples in a dry, cool, well-ventilated area. Ensure the consistency and comparability of the red sandstone test block samples in the experimental process, to improve the reliability and repeatability of the experimental results.
Experimental equipment
In order to minimize the effect of the discrete physical and mechanical properties of the rock on the test results, the OLYMPUS 5077PR ultrasonic pulse tester was used to test the rock samples at similar longitudinal wave velocities by the relevant provisions of the Standard for Testing Methods for Engineering Rocks (GB/T50266-2013)19, 2013.
The test was performed using a type OLYMPUS 5077PR ultrasonic pulse tester with NI LabVIEW2020 software, probe frequency 0.1~20MHz, 35MHz wideband receiver, maximum average power of 500mW, and pulse voltage of 400V. Equation(1) is the formula for calculating the wave velocity, and rock samples with similar longitudinal wave velocity were selected.
$${\text{V=}}\frac{{\text{d}}}{{\text{t}}}$$
(1)
Where V is the wave velocity, d is the sample length, and t is the acoustic signal time interval.
The wave velocity of the test rock sample ranges from 2530 to 2640m/s.
Zhengzhou Bona Thermal Furnace Co., Ltd. BR-12N muffle furnace on the red sandstone samples of high-temperature heating, in order to make the specimens heated uniformly, inside and outside the temperature of the same specimens to leave a certain gap evenly placed.Test set to 10 ℃ / min rate of temperature rise, to be the studio temperature to reach the preset temperature of 500, 600, 700, 800, 900, 1000 ℃, respectively, after a constant temperature of 4h, and the temperature of the studio is not changed.
The temperature range of 500 ~ 1000°C is a common heating condition of red sandstone, covering the complete process from mild thermal damage to severe degradation of red sandstone, including strength reduction, brittleness increase, crack extension, and so on. The high temperature has a significant effect on the mechanical properties of the rock, which is of strong practical significance. Temperatures higher than 1000°C and lower than 500°C were not involved due to the practical considerations of the study and the limitations of the experimental conditions. At 200 ~ 500℃, the red sandstone mainly undergoes thermal expansion and slight dehydration, and the degradation of mechanical properties is small. Above 1000°C, the rock may melt and the degradation mechanism turns to liquid or semi-liquid behavior. The difficulty of testing increases at extreme temperatures. Although a wider temperature range is not covered, the results in the range of 500 ~ 1000°C are of high reference value for the degradation mechanism of the properties of rock materials.
As shown in Fig.1. The maximum temperature inside the furnace is up to 1200°C. The chamber size is 300mm x 300mm x 400mm.
Muffle furnace.
The static load uniaxial compression test was carried using by a YNS600 microcomputer-controlled electro-hydraulic servo universal testing machine with DH3814 static strain collector in the mechanic’s laboratory after high-temperature action, as shown in Fig.2, and the controlled loading rate was 0.3MPa/s.
The uniaxial compressive impact loading test adopts the pneumatic separated Hopkinson press bar device of the Impact Mechanics Laboratory of Henan University of Science and Technology to carry out the dynamic impact test on the red sandstone specimen, as shown in Fig.3. The impact rod, incident rod and transmission rod of the SHPB test device are all made of the same kind of high-strength alloy steel, and the incident rod end is equipped with a waveform shaper, and the impact strength is controlled by the ordinary nitrogen pneumatic pressure controller during the test.
The impact rod, incident rod, transmission rod, and absorption rod of the SHPB test device are all fabricated from the same high-strength alloy steel, with lengths of 400, 2400, 1200, and 1000mm, material density of 7800kg/m3, the elastic modulus of 210 GPa, Poisson’s ratio of 0.3, and longitudinal wave speed of 5190m/s. The impact rod is equipped with a waveform shaper at the end of the incident rod, and an ordinary nitrogen pneumatic controller is used to control the impact strength during the test.
Electro-hydraulic servo universal testing machine.
Diagram of pneumatic split Hopkinson lever device.
In order to comparatively analyse the influence of high temperature on the dynamic properties of the red sandstone specimens, the SHPB impact compression test should be carried out under the same loading conditions, i.e. the specimens should be loaded with the same incident wave. Before the impact test on each specimen, the impact stroke of the impact bar is strictly controlled to achieve the same impact velocity and load waveform when the same impact air pressure is used for the test, thus ensuring the consistency of the applied impact load.
According to the basic principle of the SHPB test20, the dynamic stress σ(t), strain Ɛ (t), and strain rate Ɛ (t) of the red sandstone specimen can be obtained by adopting the three-wave method for data processing21. The formulae are
$$\sigma (t)=\frac{{E{A_0}\left( {{\varepsilon _I}+{\varepsilon _R}+{\varepsilon _T}} \right)}}{{2{A_s}}}$$
(2)
$$\dot {\varepsilon }(t)=\frac{{{C_0}\left( {{\varepsilon _I} - {\varepsilon _R} - {\varepsilon _T}} \right)}}{{{L_s}}}$$
(3)
$$\varepsilon (t)=\frac{{{C_0}}}{{{L_s}}}\,\int_{0}^{t} {\left( {{\varepsilon _I} - {\varepsilon _R} - {\varepsilon _T}} \right)dt} $$
(4)
Where: A0 and AS are the cross-sectional areas of the specimen and the compression bar, respectively; E is the modulus of elasticity of the compression bar; C0 and LS are the ultrasonic velocity and length of the compression bar, respectively; and Ɛ I, Ɛ R and Ɛ T are the incident, reflected and transmitted elastic waves, respectively.
The instrument used for the XRD test was a SmartLab rotary-target X-ray diffractometer, with the test accelerating voltage set at 20kV, the scanning speed at 10°/min, and the scanning angle ranging from 10°to 80°. Random samples were taken from the crushed specimens, which were then ground using a ball mill, screened through a 200-mesh sieve, and finally, the samples were evenly spread on a tray to start the test, and the diffraction patterns of the samples were obtained and analysed.
Analysis of experimental results
Stress-strain curve
The static and dynamic peak strengths of the red sandstone specimens were tested by electro-hydraulic servo universal testing machine and SHPB test system respectively after different temperatures. Figure4 shows the static stress-strain curve of the red sandstone specimens after different temperatures. Figure5 shows the dynamic stress-strain curve of the red sandstone specimen after different temperatures.
As shown in Fig.4, the static typical full stress-strain curves at each temperature are basically divided into four stages: compression, elasticity, yielding and damage. It is shown in Fig.5 that the dynamic typical full stress-strain curve at each temperature is basically divided into 3 stages of elasticity, yielding and damage. It can be found that different temperature changes have certain effects on rocks under static and dynamic loading.
With the growth of temperature, the deformation of the red sandstone gradually increases, and the compaction stage of the red sandstone under static loading gradually becomes longer, and the red sandstone is thermally damaged under the action of high temperature, so that the internal mineral composition and structure of the rock undergoes significant changes. In the temperature range of 700 ~ 1000 ℃, the stress-strain curve and 600 ℃ before the change in the magnitude of the larger, this is because of the high temperature of 600 ℃ in the internal structure of the rock has undergone a large change in the primary cracks caused by the expansion of the pore space increased. In the compression stage, new cracks start to sprout and develop gradually in the red sandstone, which is shown by the approximately linear relationship of stress-strain curves.
Static stress-strain curves of specimens after different temperature treatments.
Compaction stage: in this stage, it does not need a lot of stress to produce large deformation, which is related to the original pores and cracks inside the rock in a short time compaction; With the growth of temperature, the pressure-dense stage of sandstone also gradually becomes longer, and the resulting deformation is also larger. This indicates that the sandstone has undergone thermal damage under the action of temperature, which has caused significant changes in the internal mineral composition and structure of the rock.
In the elasticity stage, the internal fissures and micropores of the red sandstone were continuously extruded, the microtissues were not closed in time, and the pores and pores were continuously contracted, resulting in the red sandstone being continuously extruded and compacted. At the same time, with the increase in temperature, the internal structure of the rock was gradually destroyed, and the strength of the cement and mineral particles was reduced, and the slope in the elasticity stage showed a significant decrease, reflecting the effect of high temperature on the rock samples leading to the weakening of the deformation resistance.
In the yield stage, the internal cracks of the rock gradually expand, new cracks continue to be generated, the slope of the curve gradually decreases, and after reaching the yield point, as the internal cracks continue to expand and extend, the main cracks through the specimen are eventually formed. In which the stress acting on the red sandstone specimen by the impact load is lower than the yield strength of the red sandstone, forming an elastic stress wave, the stress at this stage varies linearly with the strain.
In the destructive stage, after the rupture of the rock specimen occurs, the overall bearing capacity decreases rapidly with the increase of strain, and the rock specimen is completely destroyed and loses its bearing capacity. In this stage, the stress of the red sandstone specimen decreases rapidly from the peak state, and the compressive strength of the red sandstone specimen is not enough to resist external force and damage. At 1000 ℃, the strength of the red sandstone specimen is lower, compared with the strength of the red sandstone specimen at 25 to 800 ℃, there is a significant decrease.
From the static and dynamic stress-strain curves of the red sandstone, it can be seen that with the increase in temperature increases the internal damage of the rock samples, resulting in the slope and peak point of the elastic phase of the reduced, these two values reflect the deformation resistance and load-bearing capacity of the rock under static and dynamic loading.
In order to understand the effect of high temperature on the static and dynamic deformation resistance and bearing capacity of rocks, the evolutionary characteristics of peak stress and deformation modulus need to be further analysed.
Stress-strain curves of specimens under impact loading after different temperature treatments.
Peak stress
Figure6a shows the graph of dynamic load peak stress data of red sandstone after different temperature effects; Fig.6b shows the graph of static load peak stress data of red sandstone after different temperature effects. According to the experimental and variance data in the figure, it can be clearly seen that near the temperature of 500 ~ 600℃, the variance becomes larger and the specimen dispersion increases. About 900 ~ 1000℃, the variance again becomes significantly larger and the specimen dispersion increases. This phenomenon reflects that there is a significant difference between the different temperature groups of red sandstone, and these two intervals are the key temperature points for various damage mechanisms, such as mineral phase transformation, melting, dehydration or decomposition, triggered by high temperature.
Use the average of the two data as the peak stress value. Figure6c shows the comparison of the peak strength patterns of red sandstone specimens under static and dynamic loading after different temperatures. The peak strengths of the two loading cases both decrease significantly with the increase in temperature, and the relationship is basically linear.
The peak stress can be used to characterize the maximum bearing capacity of the rock. As the temperature increases, the static and dynamic peak values of the rock show a decreasing trend. Under static loading conditions, the peak stress reached 131.09MPa at room temperature, decreased to 127.1MPa after heating treatment at 500°C, and reached 84.3MPa after continuous heating to 1000°C, with a decrease of 35.6%. Under dynamic loading, it reaches 83.93MPa at room temperature, the peak stress decreases to 61.07MPa after heating treatment at 500°C, and reaches 44.45MPa after continuous heating to 1000°C, with a decrease of 47%.
During the process of temperature increase, the attached and bound water within the rock volatilizes at different temperatures, and the corresponding mineral particles and cementation undergo swelling damage.
Plot of peak stress versus temperature in red sandstone after different temperature treatments. (a) Peak dynamic load stress data at different temperatures. (b) Peak static load stress data at different temperatures. (c) Comparison of peak stresses for dynamic and static loads.
Modulus of elasticity
Figure7a shows the dynamic load elastic modulus data of red sandstone after different temperatures, and Fig.7b shows the static load elastic modulus data of red sandstone after different temperatures. According to the experimental and variance data in the figure, it can be clearly seen that, similar to the case of peak stress near 500 ~ 600℃ and 900 ~ 1000℃, the variance becomes significantly larger and the specimen dispersion increases. Both reflect the internal changes of the red sandstone after suffering from different temperatures have obvious differences.
Taking the average data of both as the elastic model value. The temperature dependence of the modulus of elasticity of the red sandstone under static and dynamic loading after different temperature treatments is shown in Fig.7c. The mentioned modulus of elasticity is the maximum value of the stress-strain ratio in the stress-strain curve of the red sandstone after treatment with the corresponding calibrated temperature, which is expressed as the deformation-resisting ability of the red sandstone in the test.
With the increase of heating temperature, the elastic modulus of red sandstone treated at high temperature showed an overall decreasing trend. Under static loading conditions, the elastic modulus decreased to 70 GPa after heating treatment at 500°C and reached 22.5 GPa after continuous heating to 1000°C. Comparing 500°C, the decreased rate reaches 71.1%, and the elastic modulus from 500 to 1000°C were 70, 55, 33, 30, 23, and 22.5 GPa, respectively. Under dynamic loading, the modulus of elasticity decreased to 12.74 GPa after heating treatment at 500°C, and reached 6 GPa after continuous heating to 1000°C, with a decrease of 53%. The modulus of elasticity was 12.75、10.87、9.93、8.43、7.85 and 6.09 GPa from 500°C to 1000°C, respectively.
The linear modulus of elasticity is minimal when the temperature is 1000°C. This is mainly caused by the thermal damage effect and its degree of damage increases with the increase of temperature. This reflects that high-temperature treatment gradually destroys the main load-bearing structures such as mineral particles and cement structure within the red sandstone, and the microcracks within the specimen gradually increase, resulting in the degradation of its deformation resistance. Therefore, thermal damage can change the dynamic mechanical properties of red sandstone.
Plot of elastic modulus versus temperature for red sandstone after different temperature treatments. (a) Modulus of elasticity for dynamic loads at different temperatures. (b) Modulus of elasticity for static load at different temperatures. (c) Comparison of modulus of elasticity for dynamic and static loads.
Physical properties of red sandstone after high temperature
Changes in specimen appearance characteristics
The apparent color of the rock is related to the internal mineral composition of the rock, when the red sandstone is treated with different temperatures, its internal composition will undergo a certain transformation, which will lead to changes in the apparent color of the red sandstone. Generally, quartz is gray-white, orthoclase is generally flesh-red, light yellow-red, light yellow-white, plagioclase is milky-white, and calcite is generally white or milky-white. It changes as the temperature rises, and when the temperature exceeds 500°C, the color changes to light brown. When the temperature increases from 25 to 200°C, the uniformity of the sandstone grains remains unchanged, and no obvious microcracks appear on the surface.
Apparent colour of static loaded red sandstone specimens after high-temperature treatment.
Apparent colour of dynamically loaded red sandstone specimens after high-temperature treatment.
Damage fragmentation diagram of red sandstone specimen under static loading after high-temperature action.
Damage fragmentation diagram of red sandstone specimen under dynamic loading after high-temperature action.
The damage characteristics of high-temperature sandstone can also reflect its strength characteristics. Figure8 shows the apparent color of static-loaded red sandstone specimens after high-temperature treatment, Fig.9 shows the apparent color of dynamically-loaded red sandstone specimens after high-temperature treatment, Fig.10 shows the experimental damage morphology of the red sandstone at room temperature under static load conditions and after different high-temperature treatments, and Fig.11 shows the experimental damage morphology of the red sandstone at room temperature under dynamic load conditions and after different high-temperature treatments.
The color of the red sandstone is greyish-white at room temperature. Upon exposure to temperatures over 25°C, the intergranular voids and particle separation that occur as a result of the temperature increase lead to the formation of prominent granular properties. At temperatures between 500 and 700°C, the surface of the red sandstone assumes a white-red hue. At temperatures exceeding 600°C, pronounced microcracks emerge on the surface of the sample. As the temperature continues to increase, reaching 800 ~ 1000°C, pyrite reacts with oxygen to form hematite. This reaction causes the color of the red sandstone to gradually change from brownish red to bright red.
The degree of crushing under pressure, both under static and dynamic loading, is closely related to temperature. The degree of fragmentation of the red sandstone specimen subjected to static loading increases gradually with the temperature, accompanied by a conical shape of the shear surface and the presence of powdery material on the shear rupture surface, along with clear friction traces. Additionally, part of the specimen displays a longitudinal fracture. Cracks are observed to align with the direction of loading, and the damage morphology of the specimen becomes increasingly complex with the increase in temperature. It is observed that as temperature increases, specimen damage becomes more severe, and the resulting fragmented rock is smaller in size, exhibiting a powdery and crumbly texture. The damage pattern of specimens under dynamic loading becomes increasingly complex with increasing temperature.
The degree of crushing of the specimens under dynamic loading demonstrated a tendency to decrease and then gradually increase with the temperature rise. At a temperature of 25°C, the red sandstone specimen exhibited a cleavage surface along its axial direction and subsequently fractured into multiple pieces. At temperatures of 500°C and 800°C, the rupture degree of the specimen did not diminish; conversely, the specimen’s dynamic compressive strength increased.
Therefore, the specimen by the impact of the degree of fragmentation with the increase in the action of the temperature shows the trend of the first decrease and then gradually increase. The temperature of 900 ℃ or more, the emergence of axial cleavage surface, specimen damage began to intensify, 1000 ℃, the specimen broken into smaller pieces.
Effect of high temperature on specimen mass, volume and longitudinal wave velocity
Mass loss rate, volume expansion rate and longitudinal wave velocity attenuation rate of specimen after high temperature versus temperature. (a) Mass loss rate as a function of temperature. (b) Volume expansion versus temperature. (c) Longitudinal wave attenuation rate versus temperature.
The application of elevated temperatures results in the evaporation and loss of diverse water types within the rock. This occurs at a specific temperature and is accompanied by phase transformation and the decomposition, dehydroxylation, and other physicochemical reactions of minerals. These changes impact the quality, volume, and density of the rock, influencing its mineral composition and pore space development. Consequently, the longitudinal wave velocity of the rock undergoes alteration. Consequently, the extent of damage to red sandstone following exposure to high temperatures can be gauged by examining the fluctuations in mass loss rate, volume expansion rate, and longitudinal wave velocity. As illustrated in Fig.12, the mass loss rate, volume expansion rate, and longitudinal wave velocity attenuation rate of the specimen subjected to high temperatures are presented about the temperature.
The mass loss rate of the red sandstone specimen increases at a relatively slow rate between 500 and 700°C, reaching a value of 1.81% at 700°C. This is due to the evaporation of free and bound water within the red sandstone, which results in a reduction in the specimen’s mass. At temperatures between 700 and 1000°C, the rate of mass loss accelerates significantly. During this phase, the mass loss rate increases from 1.81 to 5.76%. This rapid growth stage is characterized by a more complex mass reduction process. In addition to the decomposition of calcite to produce CO2 and facilitate escape, there are also processes of mineral decomposition, phase change, and dehydroxylation, including mineral detachment, phase change of quartz, and dehydroxylation reaction of kaolinite, among others.
The volumetric expansion of red sandstone specimens in the 500 to 1000°C stage with increasing temperature is due to the differences in the coefficients of thermal expansion of the different mineral compositions within the red sandstone. This results in the generation of thermal cracks, which subsequently expand the volume. In the temperature range of 500 to 800 degrees Celsius, the volume expansion rate of red sandstone exhibits a relatively gentle increase, reaching approximately 1.5% with each degree Celsius rise. However, as the temperature continues to increase, the volume expansion rate accelerates significantly, reaching 3.5% at 1000 degrees Celsius. As the temperature rises, the water vapor pressure inside the rock gradually increases, which in turn accelerates the expansion of the cracks. This process results in a rapid increase in volume. Additionally, the process of mineral phase change also accelerates the shedding of mineral particles. Concurrently, during the cooling phase, the cracking phenomenon will result in the formation of additional microfractures, thereby increasing the volume of the red sandstone.
The longitudinal wave attenuation rate of red sandstone exhibits a linear increase between the temperatures of 500 and 1000°C. The change in the rate is also approximately linear, with a decrease from 35% at 500°C to 76.92% at 1000°C. This indicates that the velocity of the wave decreases gradually as the temperature rises. Following the application of high temperatures, a series of physical and chemical reactions, including dehydration, phase change, melting, crack development, and differential mineral expansion, occur within the rock. These reactions result in alterations to the rock’s density, mineral composition, and pore development, which in turn affect the longitudinal wave velocity of the rock.
High temperatures can cause thermal expansion of red sandstone grains, resulting in tiny gaps between otherwise tightly packed grains, thus increasing the overall porosity of the rock. In addition, high temperatures may cause phase changes or decomposition of minerals within the rock, creating new pores or cracks and further increasing porosity.
Increased porosity means an increase in the number of fluid passages within the rock, thus increasing the permeability of the rock. The connectivity of the pores and cracks inside the rock increases. Therefore, the increase in porosity of red sandstone at high temperatures directly leads to an increase in its permeability.
Under the action of high temperature and stress loading, the rock is more prone to volume expansion and plastic deformation during the loading process due to the increase in porosity and volume expansion rate. This deformation leads to a reduction in the bearing capacity of the rock and makes it more susceptible to damage.
Under the effect of high temperature and osmotic pressure, the enhancement of permeability of red sandstone can make it easier for fluids to flow inside the rock, thus accelerating the creep process of the rock. This may result in rocks being more susceptible to deformation and damage under long-term loading.
Therefore, the influence of these factors on the mechanical behavior of rocks needs to be fully considered in rock engineering in high-temperature environments to ensure the safety and stability of the project.
Mineral composition of specimen
X-ray diffraction patterns of red sandstone at different temperatures.
X-ray diffraction waterfall.
Under heat-treatment conditions, the periodicity of the crystals is somewhat disrupted, generating additional phase differences that lead to incomplete phase-length interference under Bragg-compliant conditions. As a result, the diffraction intensity changes. According to the results of X-ray diffraction experiments, the X-ray diffraction patterns of red sandstone at room temperature and in the range of 500℃~1000℃ are plotted, as shown in Fig.13 The main mineral compositions of the red sandstone used in this experiment are quartz, sodium feldspar, and a small amount of clay and so on. Figure14 shows the X-ray diffraction information of the red sandstone after the action of different temperatures. The diffraction peaks of zeolite disappeared before heating to 500°C. Pyrite reacted with oxygen to form hematite at 600°C ~ 1000°C, which led to a gradual change in the color of the red sandstone to brownish red and bright red. Plagioclase pyroxene and the diffraction peak disappear at 700℃, montmorillonite disappear at 900℃, while quartz, sodium feldspar, hornblende, etc. are relatively stable.
- (1)
The chemical composition and structure of square zeolite (\(\:\text{N}\text{a}\text{A}\text{l}{{\text{S}\text{i}}_{2}\text{O}}_{6}\bullet\:{\text{H}}_{2}\text{O}\)) varies according to species but usually contains elements such as silicon, aluminum, oxygen, etc. The zeolite in the red sandstone of this experiment is square zeolite. Its diffraction peak disappears when the temperature rises to 600 ℃, indicating that the decomposition of square zeolite occurs at a certain temperature before 600℃. When the decomposition is completed before 600 ℃, its decomposition generates silica, aluminum oxide, oxide Na, and other substances, the equation is:
$${\text{NaAlS}}{{\text{i}}_{\text{2}}}{{\text{O}}_{\text{6}}} \cdot {{\text{H}}_{\text{2}}}{\text{O }} \to {\text{ 2Si}}{{\text{O}}_{\text{2}}}{\text{ + A}}{{\text{l}}_{\text{2}}}{{\text{O}}_{\text{3}}}{\text{ + N}}{{\text{a}}_{\text{2}}}{\text{O + }}{{\text{H}}_{\text{2}}}{\text{O }}$$
(5)
Square zeolite loses its water of crystallization at high temperatures, leading to changes in its structure. This in turn produces microcracks or pores within the rock, thus affecting the mechanical properties of the rock.
- (2)
Plagioclase (\(\:{\left(\text{M}\text{g},\text{F}\text{e}\right)}_{2}\left[{\text{S}\text{i}}_{2}{\text{O}}_{6}\right]\)) is a silicate mineral whose chemical formula can be expressed as MgSiO3. decomposition reaction can occur at high temperatures, in the experiment plagioclase can still be observed at 600 ℃ diffraction peaks, diffraction peaks disappeared at 700 ℃, indicating that in the temperature interval, the decomposition of plagioclase occurs, and its decomposition generates olivine, silica, siderite, and other and other substances, whose equations are:
$$M{g_2}S{i_2}{O_4} \to {\text{M}}{{\text{g}}_{\text{2}}}{\text{Si}}{{\text{O}}_{\text{4}}}{\text{+Si}}{{\text{O}}_{\text{2}}}$$
(6)
$$F{e_2}S{i_2}{O_6} \to 2Si{O_2}+2FeO$$
(7)
Plagioclase pyroxene undergoes reactions such as thermal expansion, thermal decomposition or phase transformation at high temperatures. The creation of microcracks or pores within the rock leads to stress concentrations within the rock, which reduces the strength and modulus of elasticity of the rock.
In addition, the coefficient of thermal expansion of plagioclase may be different from that of the surrounding minerals, leading to the generation of thermal stresses inside the rock, further aggravating the damage to the rock.
- (3)
Montmorillonite (\(\:\text{C}\text{a}{\text{A}\text{l}}_{4}{\text{S}\text{i}}_{8}{\text{O}}_{20}{\left(\text{O}\text{H}\right)}_{4}\bullet\:\text{n}{\text{H}}_{2}\text{O}\))is a layered silicate clay mineral, which is mainly composed of silicon, aluminum, oxygen and other elements, and contains a small amount of water molecules and exchangeable cations. Calcium montmorillonite is found in the red sandstone in the experiments, and the first heat-absorption valley occurs between 80 and 250°C to shed interlayer water and adsorbed water; the second heat-absorption valley occurs Between 600~700℃,de-structured water; the third heat absorption valley at 800 ~ 935 ℃, the lattice is destroyed, the equation is:
$$ CaAl_{4} Si_{8} O_{{20}} \left( {OH} \right)_{4} \cdot nH_{2} O \to CaO + 2Al_{2} O_{3} + 8SiO_{2} + {\text{ }}nH_{2} O{\text{ }} $$
(8)
Montmorillonite is a layered silicate mineral with strong hydrophilicity. At high temperatures, montmorillonite undergoes dehydration, leading to changes in its interlayer structure and a decrease in the interlayer distance, which reduces the densification of the rock and produces more microcracks and pores inside the rock, thus affecting the mechanical properties of the rock and showing that dehydrated montmorillonite is more susceptible to crushing.
In addition, the expansion of montmorillonite at high temperatures may also lead to cracks or pores inside the rock, reducing the strength and elastic modulus of the rock.
- (4)
Feldspar (\(\:\text{N}\text{a}\text{A}\text{l}{\text{S}\text{i}}_{3}{\text{O}}_{8}\)) is an aluminosilicate mineral with a stable crystal structure, and kaolinite (\(\:{\text{A}\text{l}}_{4}{\text{S}\text{i}}_{4}{\text{O}}_{10}{\left(\text{O}\text{H}\right)}_{8}\)) feldspar, common pyroxene, and other aluminosilicate minerals are formed by weathering and have good refractory properties, and the diffraction intensity decreases consistently between 500°C and 1000°C due to the effect of loss of water in the structure and the chemical equations, respectively:
$$NaAlS{i_3}{O_8} \to N{a_2}O+A{l_2}{O_3}+3Si{O_2}$$
(9)
$$A{l_2}S{i_2}{O_5}{\left( {OH} \right)_4} \to A{l_2}{O_3}+2Si{O_2}+2{H_2}O$$
(10)
Sodic feldspar undergoes thermal decomposition reactions at high temperatures to produce products such as alumina, silicon oxide, and sodium oxide. The physical and chemical properties of these products are different from those of sodium feldspar, which may lead to changes in the internal structure of the rock, thus affecting the mechanical properties of the rock. In addition, the coefficient of thermal expansion of sodium feldspar may also be different from that of the surrounding minerals, leading to thermal stresses within the rock.
Kaolinite is a layered silicate mineral that undergoes dehydration at high temperatures, leading to changes in its structure. In particular, when the temperature reaches 470~520°C, kaolinite will shed the (OH) in the outer layer of its structure, and when the temperature reaches 540°C, the (OH) in the inner layer of the structure will also be shed, resulting in serious damage to the structure of kaolinite. This dehydration may lead to changes in the internal pore structure of the rock, thus reducing the strength and elastic modulus of the rock.
Dehydrated kaolinite may be more susceptible to chemical reactions, such as replacement reactions with surrounding silicate minerals, to produce new mineral phases, which may have lower strength and elastic modulus.
- (5)
Pyrite (\(\:\text{F}\text{e}{\text{S}}_{2}\))decreases slowly at 600 ~ 1000°C, when pyrite reacts with oxygen to form hematite, thus gradually changing the color of the specimen to brownish red and bright red. The chemical equation is:
$$ 4FeS_{2} + 11O_{2} \to 2Fe_{2} O_{3} + 8SO_{2} $$
(11)
Pyrite undergoes oxidation at high temperatures to produce products such as iron oxide and sulfur dioxide. This oxidation may lead to changes in the chemical composition and structure within the rock, thereby affecting the mechanical properties of the rock. At the same time, gases such as sulfur dioxide produced by oxidation may escape through microcracks in the rock, further exacerbating the damage to the rock. In addition, the oxidation of pyrite may produce volume expansion, leading to cracks or pores within the rock.
In addition, the two Si-O chemical bonds in the α-quartz structure are at an angle of 150°. When the quartz sand is heated to 573°C the α-quartz is transformed into β-quartz, and the two Si-O chemical bonds in the β-quartz structure are at an angle of 150°, and the value of the diffraction intensity is still lower than that of the initial temperature, which indicates that the temperature action also has a damaging effect on the crystal structure of the quartz, which produces irreversible changes, as shown in Fig.1515.In addition, at 500°C, OH- and H- will separate from the mineral skeleton, and the loss of component water and water of crystallization will lead to further damage to the mineral crystal structure22. At this time, the internal microcracks of the red sandstone specimen increase and the internal volume increases, resulting in changes in the microstructure and macroscopic physical and mechanical properties of the rock.
Schematic diagram of the variation of α-β quartz bond angle.
Rock is composed of a variety of mineral particles and aggregates. The mechanical properties of rocks are inevitably affected by the group of rock minerals, structure, this is due to the rocks in the temperature under the influence of its internal structure changes, this change has physical changes, such as melting, mineral phase transition, mineral fracture, etc.; There are also chemical changes, such as thermal decomposition of minerals and other reactions. Thus, the red sandstone will generate stress concentration between the mineral particles, the internal mineral structure changes, the extension of the cracks. Because the internal cracks of red sandstone always develop along the tip of the pores, through the internal pores and eventually form large cracks.
Combining the SEM results of related scholars on the evolution of cracks in red sandstone after high-temperature action and the XRD test of red sandstone after high temperature conducted in this paper, it is found that, as shown in Figs.16 and 17, the internal mineral particles of the heated and cooled rock cooled and shrunk, and the cracks connected and expanded, and the cracks became bigger after cooling and shrinking, and the minerals and cementation materials were thermally decomposed or dissolved. The crack contraction phenomenon occurs at 500~600℃, where thermal stress plays a major role in this temperature range, and thermal reactions appear. When the temperature rises from 500 to 1000°C, the escape of structural water will change the lattice structure, which in turn produces intergranular cracks. Different minerals are subjected to uneven thermal expansion by temperature, and fissure expansion and penetration occur around the mineral crystals, and the damage gradually increases.
The XRD test pointed out that the diffraction peaks of zeolite, plagioclase and montmorillonite gradually disappeared at this stage, and the different coefficients of thermal expansion of various minerals further aggravated the microscopic damage of the red sandstone. Meanwhile, the change of diffraction information caused by the phase transformation of quartz at this temperature also promoted the rapid development of cracks. In addition, with the increase of temperature, the thermal stress is also gradually enhanced, and the above-combined effects lead to the rapid development, growth, and penetration of cracks and pores in the red sandstone at this temperature interval, especially at 800~ 1000 ℃, the cracks expand particularly rapidly, resulting in a significant reduction in the macroscopic compressive strength of the red sandstone at this stage.
Schematic diagram of the microstructure of the specimen at 25°C.
Schematic diagram of the microstructure of the specimen after high temperature.
Theoretical model
To be able to construct theoretical models capable of describing quantitative relationships between temperature, mineral composition changes and mechanical properties, it is assumed that (1) all minerals are subjected to the same strain. (2) The individual mineral properties Ei and σfi are usually regarded as constants. (3) The overall properties are linear combinations of the properties of the components. The Voigt model is introduced.
Modulus of elasticity at different temperatures:
$${E_0}=\sum\limits_{i} {{V_{i}}{E_i}} $$
(12)
Where E0 is the overall modulus of elasticity; Ei is the modulus of elasticity of component i ; and Vi is the volume fraction of component i, which is the mass percentage according to the XRD test results. The volume fraction Vi can be calculated from the mass and mineral density:
$${V_{i}}=\frac{{\frac{{{w_i}}}{{{\rho _i}}}}}{{\sum\nolimits_{j} {\frac{{{w_j}}}{{{\rho _j}}}} }}$$
(13)
Where: wi he mass percentage of mineral i (obtained by quantitative XRD analysis); ρi the density of mineral i ;
The Voigt model is commonly used to estimate the undamaged properties of a material, i.e. assuming that the material is free of cracks or other defects. is a theoretical value in an ideal state. The Voigt model can be modified for high temperature environments:
$${E_0}=\sum\limits_{i} {{V_{i}}(T){E_i}} $$
(14)
Where, Ei(T): ideally, should vary with temperature, but in practice is often simplified to take the room temperature value. Vi(T): dynamic volume fraction. In red sandstone, the minerals that play a major strength role are quartz and feldspar. The decomposition or phase transformation of the two minerals at high temperatures is expressed by the weight function transformation fraction fi(T) (0 ≤ fi≤ 1), which is defined as follows according to the XRD data:
$${f_{quartz}}(T)=\left\{ {\begin{array}{*{20}{c}} {0,\,T<573^\circ C} \\ {1,\,T \geqslant 573^\circ C} \end{array}} \right.$$
(15)
$${f_{feldspar}}(T)=\left\{ {\begin{array}{*{20}{c}} {0,\,} \\ {\frac{{T - 500}}{{500}},} \\ {1,\,} \end{array}\,\begin{array}{*{20}{c}} {T<500^\circ C} \\ {500^\circ C \leqslant T<1000^\circ C} \\ {T \geqslant 1000^\circ C} \end{array}} \right.$$
(16)
Volume fraction of mineral i as a function of temperature
$${V_i}(T)={V_{i0}}\left[ {1 - {f_i}(T)} \right]+{V_{i,new}}{f_{i}}(T)$$
(17)
Vi0:
volume fraction of mineral i in the initial state.
Vi, new:
volume fraction of the new phase, indicating the volume fraction of mineral i completely transformed into the new phase.
This is further combined with the damage variable D(T) (reflecting the cumulative effect of microcracks and porosity, 0 ≤ D ≤ 1).
Assumptions (1) Mechanical properties (σ and E) vary with temperature and damage. (2) Temperature change is a quasi-static process, and dynamic effects are ignored. Then, according to the damage mechanics, the modulus of elasticity after damage by high temperature action:
$$E(T)={E_0}(T)(1 - D(T))$$
(18)
$$D(T)=1 - \frac{{E(T)}}{{{E_0}(T)}}$$
(19)
$$D(T)={D_{crack}}(T)+{D_{min}}(T)$$
(20)
Where, D(T): includes thermal crack damage and mineral transformation damage. Thermal crack damage Dcrack(T) is caused by thermal expansion mismatch. Mineral transformation damage Dmin(T) is caused by mineral decomposition or phase transformation. If D > 1, take D = 1.
Cracks expand rapidly from 800°C to 1000°C, and coupled with the crack expansion rate, the damage increases nonlinearly:
$${D_{crack}}(T)={k_1}{(\frac{{T - 20}}{{780}})^n}$$
(21)
Dcrack : Crack rate at different temperatures T, derived from acoustic emission, DIC or high-speed camera.
k1:
scale factor, a combination of inherent material properties and experimental conditions;
n:
the degree of nonlinearity of crack extension velocity with temperature. k1, n were fitted by experimental data in the interval from 800°C to 1000°C.
780°C is the critical point where the internal structure of red sandstone changes from “microdamage accumulation” to “rapid crack expansion”.
Mineral transformation leads to damage increment:
$$\Delta {D_{i}}={k_{2i}}{f_i}(T)$$
(22)
$${D_{min}}(T)=\sum\limits_{i} {{k_{2i}}{f_i}(T)} =D(T) - {D_{crack}}(T)$$
(23)
k2i:
damage contribution factor for mineral i. The damage variable at temperature T can be obtained according to the formula.
Therefore, the damage variable at temperature T can be obtained according to the above equation:
$$D(T)={k_1}{\left( {\frac{{T - 20}}{{780}}} \right)^n}+{k_{2i}}{f_i}(T)$$
(24)
Cumulative damage variables at temperature T:
$$D(T)=\int_{{20}}^{T} {{k_1}{{\left( {\frac{{T - 20}}{{780}}} \right)}^n}+{k_{2i}}{f_i}(T)dT} $$
(25)
Peak Stress:
$${\sigma _{f0}}=\sum\limits_{i} {{V_{i}}{\sigma _{fi}}} $$
(26)
Where σf0 is the overall strength and σfi is the stress per unit volume of component i.
The Voigt model can be modified for high temperature environments:
$${\sigma _{f0}}=\sum\limits_{i} {{V_{i}}(T){\sigma _{fi}}} $$
(27)
Where σfi(T): ideally, it should vary with temperature, but in practice it is often simplified to take the room temperature value.
The free expansion strain for thermal crack damage is:
$${\varepsilon _{{\text{th}}}}={\alpha _{}}{\text{\varvec{\Delta}}}T$$
(28)
$$\Delta T=T - {T_0}({T_0}=20^\circ C)$$
(29)
The coefficient of thermal expansion, α, is a characteristic parameter of a material’s length or volume expansion in response to a change in temperature, and each mineral attempts to expand at different rates when the temperature rises. Mineral particles are constrained from expanding freely by cements or other particles restraining each other. This constraint results in an expansion mismatch that translates into internal stresses.
Hence, thermal stresses:
$${\sigma _{fi}}={E_i}{\alpha _i}\Delta T$$
(30)
E: local modulus of elasticity;
α: coefficient of thermal expansion
$${\sigma _{f0}}(T)=\sum\limits_{i} {{V_i}(T)} \cdot {E_i} \cdot {\alpha _i} \cdot \Delta T$$
(31)
According to damage mechanics:
Peak Stress and Modulus of Elasticity
$${\sigma _f}(T)=\sum\limits_{i} {\left[ {{V_{i0}}(1 - {f_i}(T))+{V_{i,new}}{f_{i}}(T)} \right]} {E_i}{\alpha _i}\Delta T\left[ {1 - {k_1}{{\left( {\frac{{T - 20}}{{780}}} \right)}^n}+{k_{2i}}{f_i}(T)} \right]$$
(32)
$$E(T)={E_0}(T)\left[ {1 - {k_1}{{\left( {\frac{{T - 20}}{{780}}} \right)}^n}+{k_{2i}}{f_i}(T)} \right]$$
(33)
The model systematically reveals the micro-mechanism of the degradation of mechanical properties of red sandstone under high temperature and connects temperature, mineral change and mechanical properties through quantitative relationships, providing a theoretical basis for the study of rock behavior under high-temperature environments.