Dynamic Tensile Failure Characteristics and Energy Dissipation of Red Sandstone under Dry–Wet Cycles

: Studying the dynamic properties of rocks in complex environments is of great signiﬁcance to the sustainable development of deep-sea metal mineral resource extraction. To investigate the inﬂuence of dry–wet cycles on the dynamic tensile properties and energy dissipation of red sandstone, a series of dynamic Brazilian disc tests was carried out through the split Hopkinson pressure bar (SHPB) apparatus. The dynamic tensile behaviors and energy dissipation distribution of the red sandstone specimens after different dry–wet cycles (0, 10, 20, 30 and 40 cycles) were analyzed in this study. The degree of dynamic tensile fragmentation and energy dissipation of red sandstone is signiﬁcantly affected by the loading rate. Speciﬁcally, when the number of dry–wet cycles remains constant, an increase in loading rate results in a signiﬁcant reduction in the average fragment size, while the energy consumption density exhibits an approximately linear increase. At a ﬁxed loading rate, the energy consumption density decreases approximately linearly with the increase in dry–wet cycles, and the higher the loading rate, the more sensitive the energy consumption density is to the dry–wet cycle. Under a ﬁxed number of dry–wet cycles, the dynamic tensile strength has an exponential relation with the increase in energy consumption density.


Introduction
There is a close relationship between deep metal mineral resource exploitation and sustainability.Deep mining enables the exploration of deeper mineral resources to meet the growing demand for metals.However, deep mining faces technical challenges and environmental risks, such as high stress, high temperature, great depth, and high rockstratum water pressure, in special environments [1].As the mining depth increases, high stress may trigger rock bursts and geological hazards, posing serious threats to personnel and equipment safety, and greatly reducing labor efficiency.To achieve sustainable development, sustainable management measures need to be taken in deep mining, such as scientific planning and design, environmental protection measures, improvements in resource-utilization efficiency, and community involvement.Technological innovation and research and development are crucial for the sustainability of deep mining, for example, the application of stratum control technology and intelligent mining equipment, to reduce environmental impact and improve resource utilization efficiency [2].Based on the engineering background of deep metal mineral resource exploitation, this paper explores the evolutionary laws of rock dynamic properties under the coupling effect of dynamic disturbance and dry-wet cycles, aiming to provide a theoretical basis for the sustainable development of deep resource exploitation.
Water-rock interactions are prevalent throughout various geological environments, spanning from subterranean depths to surface-level exposures.In the context of engineering projects such as coal mining, tunnel excavation, and dam slope construction, the periodic

Preparation of Red-Sandstone Specimen
The raw red sandstone was taken from Linyi, Shandong Province, China.The red sandstone was reddish brown, in a natural state without significant texture, and had uniform material particles.The results of X-ray diffraction tests showed that the mineral composition of red sandstone in the natural state mainly included quartz (56.4%), feldspar (23.9%), calcite (8.8%), hematite (7.4%), chlorite (2.2%) and others (1.3%).To reduce the adverse effects caused by the material heterogeneity, all the red sandstone specimens in this test were taken from the same rock (Figure 1).The flatness and verticality deviation of specimens were controlled within the allowable range of dynamic tensile tests and specifications.The size of rock specimens in the static compression test was φ 50 mm × 100 mm, and the size of the Brazilian disc used in dynamic splitting tests was φ 50 mm × 25 mm [28].The basic physical and mechanical properties parameters of the dry red sandstone are shown in Table 1.

Preparation of Red-Sandstone Specimen
The raw red sandstone was taken from Linyi, Shandong Province, C sandstone was reddish brown, in a natural state without significant texture form material particles.The results of X-ray diffraction tests showed that the position of red sandstone in the natural state mainly included quartz (56 (23.9%), calcite (8.8%), hematite (7.4%), chlorite (2.2%) and others (1.3%).adverse effects caused by the material heterogeneity, all the red sandstone this test were taken from the same rock (Figure 1).The flatness and vertica of specimens were controlled within the allowable range of dynamic tensile t ifications.The size of rock specimens in the static compression test was ϕ mm, and the size of the Brazilian disc used in dynamic splitting tests was mm [28].The basic physical and mechanical properties parameters of the stone are shown in Table 1.

Parameters
Bulk Density (kg/m

Dry-Wet Cycle Design
To evaluate the feasibility and operability of testing procedures, w method of simulating the dry-wet environment of slope rocks using natural tion at room temperature, followed by oven-drying.Specifically, red sandsto were subjected to water absorption for 24 h within a container until compl and were subsequently dried in an oven for an additional 24 h.The com cycle was carried out with the oven temperature set at 60 °C to mitigate effects of temperature on the mechanical properties of the rock specimens.U the designated number of dry-wet cycles, which were predetermined as 0, 40, dynamic tensile tests were conducted on the red sandstone specimens.Fi the dry-wet cycle of the red sandstone specimens.To evaluate the feasibility and operability of testing procedures, we employed a method of simulating the dry-wet environment of slope rocks using natural water absorption at room temperature, followed by oven-drying.Specifically, red sandstone specimens were subjected to water absorption for 24 h within a container until complete saturation, and were subsequently dried in an oven for an additional 24 h.The complete dry-wet cycle was carried out with the oven temperature set at 60 • C to mitigate any potential effects of temperature on the mechanical properties of the rock specimens.Upon reaching the designated number of dry-wet cycles, which were predetermined as 0, 10, 20, 30, and 40, dynamic tensile tests were conducted on the red sandstone specimens.Figure 2 depicts the dry-wet cycle of the red sandstone specimens.

SHPB Test Device
The split Hopkinson pressure bar (SHPB) test system with a cross-section diameter of 50 mm was used as the dynamic tensile test device.This system was mainly composed of the loading drive system, pressure bar system, energy absorption system, signal acquisition and data-processing system.Figure 3 shows the SHPB test system.The striker bar, incident bar, transmitted bar and absorption bar in the test system were made of 40 Cr alloy steel with an elastic modulus of 210 GPa and a density of 7800 kg/m 3 .The length of the incident bar and transmitted bar was 2400 mm and 1400 mm, and the diameter of the two bars was 50 mm, respectively.The striker bar was cylindrical, with a length of 290 mm and a section diameter of 36 mm.The data acquisition system adopted the DH5960 ultra-dynamic signal acquisition instrument produced by Jiangsu Donghua.
During the test, the striker was shot from the gas gun at a high velocity and impacted the front end of the incident bar, and the incident wave ( ) was first formed.When the incident wave propagated to the coincident surface of the incident bar and the specimen, a part of the incident wave was reflected by the incident bar to form a reflected wave ( ), and the remaining wave continued to propagate through the specimen to the transmitted bar to form a transmitted wave ( ).These three waves were collected by strain gauges attached to the incident bar and the transmitted bar; then, these data were recorded in the dynamic strain gauge.

Test Verification
To ensure the reliability of the experimental results, it is imperative to verify the validity of the one-dimensional assumption and the stress-uniformity assumption.Before the test, the waveform shaping technology was used in this test; that is, a square rubber sheet was pasted on the end face of the incident bar in contact with the striker (with a side length of 1 cm and a thickness of 1 mm).This step aimed to ensure the uniformity of stress transmission within the specimen, minimize the effects of dispersion, and obtain a dependable in situ stress-strain relationship.Dynamic stress balance at both ends of the specimen is an essential prerequisite to guarantee the validity of experimental results in dynamic tensile testing [29].Figure 4 displays the typical results of the dynamic stressbalance check for the specimen.It can be seen that the curve of the sum of the incident and reflected strains almost overlaps with that of the transmitted strain, which confirms that the stress on both sides of the specimen has reached equilibrium.Therefore, the effectiveness of the one-dimensional assumption and stress-uniformity assumption is verified, and the test results are effective.

SHPB Test Device
The split Hopkinson pressure bar (SHPB) test system with a cross-section diameter of 50 mm was used as the dynamic tensile test device.This system was mainly composed of the loading drive system, pressure bar system, energy absorption system, signal acquisition and data-processing system.Figure 3 shows the SHPB test system.The striker bar, incident bar, transmitted bar and absorption bar in the test system were made of 40 Cr alloy steel with an elastic modulus of 210 GPa and a density of 7800 kg/m 3 .The length of the incident bar and transmitted bar was 2400 mm and 1400 mm, and the diameter of the two bars was 50 mm, respectively.The striker bar was cylindrical, with a length of 290 mm and a section diameter of 36 mm.The data acquisition system adopted the DH5960 ultra-dynamic signal acquisition instrument produced by Jiangsu Donghua.

SHPB Test Device
The split Hopkinson pressure bar (SHPB) test system with a cross-section diam of 50 mm was used as the dynamic tensile test device.This system was mainly compo of the loading drive system, pressure bar system, energy absorption system, signal ac sition and data-processing system.Figure 3 shows the SHPB test system.The striker incident bar, transmitted bar and absorption bar in the test system were made of 40 alloy steel with an elastic modulus of 210 GPa and a density of 7800 kg/m 3 .The lengt the incident bar and transmitted bar was 2400 mm and 1400 mm, and the diameter of two bars was 50 mm, respectively.The striker bar was cylindrical, with a length of mm and a section diameter of 36 mm.The data acquisition system adopted the DH5 ultra-dynamic signal acquisition instrument produced by Jiangsu Donghua.
During the test, the striker was shot from the gas gun at a high velocity and impac the front end of the incident bar, and the incident wave ( ) was first formed.When incident wave propagated to the coincident surface of the incident bar and the specim a part of the incident wave was reflected by the incident bar to form a reflected wave and the remaining wave continued to propagate through the specimen to the transmi bar to form a transmitted wave ( ).These three waves were collected by strain gau attached to the incident bar and the transmitted bar; then, these data were recorded in dynamic strain gauge.

Test Verification
To ensure the reliability of the experimental results, it is imperative to verify the lidity of the one-dimensional assumption and the stress-uniformity assumption.Be the test, the waveform shaping technology was used in this test; that is, a square rub sheet was pasted on the end face of the incident bar in contact with the striker (with a length of 1 cm and a thickness of 1 mm).This step aimed to ensure the uniformity of st transmission within the specimen, minimize the effects of dispersion, and obtain a pendable in situ stress-strain relationship.Dynamic stress balance at both ends of specimen is an essential prerequisite to guarantee the validity of experimental result dynamic tensile testing [29].Figure 4 displays the typical results of the dynamic str balance check for the specimen.It can be seen that the curve of the sum of the incid and reflected strains almost overlaps with that of the transmitted strain, which confi that the stress on both sides of the specimen has reached equilibrium.Therefore, the fectiveness of the one-dimensional assumption and stress-uniformity assumption is v fied, and the test results are effective.During the test, the striker was shot from the gas gun at a high velocity and impacted the front end of the incident bar, and the incident wave (ε i ) was first formed.When the incident wave propagated to the coincident surface of the incident bar and the specimen, a part of the incident wave was reflected by the incident bar to form a reflected wave (ε r ), and the remaining wave continued to propagate through the specimen to the transmitted bar to form a transmitted wave (ε t ).These three waves were collected by strain gauges attached to the incident bar and the transmitted bar; then, these data were recorded in the dynamic strain gauge.

Test Verification
To ensure the reliability of the experimental results, it is imperative to verify the validity of the one-dimensional assumption and the stress-uniformity assumption.Before the test, the waveform shaping technology was used in this test; that is, a square rubber sheet was pasted on the end face of the incident bar in contact with the striker (with a side length of 1 cm and a thickness of 1 mm).This step aimed to ensure the uniformity of stress transmission within the specimen, minimize the effects of dispersion, and obtain a dependable in situ stress-strain relationship.Dynamic stress balance at both ends of the specimen is an essential prerequisite to guarantee the validity of experimental results in dynamic tensile testing [29].Figure 4 displays the typical results of the dynamic stressbalance check for the specimen.It can be seen that the curve of the sum of the incident and reflected strains almost overlaps with that of the transmitted strain, which confirms that the stress on both sides of the specimen has reached equilibrium.Therefore, the effectiveness of the one-dimensional assumption and stress-uniformity assumption is verified, and the test results are effective.

Determination of Loading Rate
Figure 5 depicts the dynamic tensile stress curve of specimen as a function of time.Prior to reaching the peak stress, a nearly linear relationship exists between the stresstime curve.The slope of this linear segment is recognized as the loading rate of the test [28].

Test Results and Analysis
In the Brazilian disc test, the calculation equation of the tensile stress at the center of the specimen can be expressed as [30]: The effective load of the compression bar at both ends of the rock specimen is denoted by P, while B represents the thickness, and D denotes its diameter.Figure 6 shows the schematic diagram of dynamic tensile loading.The effective load P of the compression bar at both ends of the rock specimen can be expressed as follows:

Determination of Loading Rate
Figure 5 depicts the dynamic tensile stress curve of specimen as a function of time.Prior to reaching the peak stress, a nearly linear relationship exists between the stress-time curve.The slope of this linear segment is recognized as the loading rate of the test [28].

Determination of Loading Rate
Figure 5 depicts the dynamic tensile stress curve of specimen as a function of time.Prior to reaching the peak stress, a nearly linear relationship exists between the stresstime curve.The slope of this linear segment is recognized as the loading rate of the test [28].

Test Results and Analysis
In the Brazilian disc test, the calculation equation of the tensile stress at the center of the specimen can be expressed as [30]: The effective load of the compression bar at both ends of the rock specimen is denoted by P, while B represents the thickness, and D denotes its diameter.Figure 6 shows the schematic diagram of dynamic tensile loading.The effective load P of the compression bar at both ends of the rock specimen can be expressed as follows:

Test Results and Analysis
In the Brazilian disc test, the calculation equation of the tensile stress at the center of the specimen can be expressed as [30]: The effective load of the compression bar at both ends of the rock specimen is denoted by P, while B represents the thickness, and D denotes its diameter.Figure 6 shows the schematic diagram of dynamic tensile loading.The effective load P of the compression bar at both ends of the rock specimen can be expressed as follows: E and A denote the modulus of elasticity and the cross-sectional area of the compression bar, respectively.When Equation ( 2) is substituted into Equation ( 1), the expression of dynamic tensile stress of the Brazilian disc can be obtained as follows: σ = 2 (3)

Analysis of Dynamic Tensile Failure Characteristics
When n = 20, the dynamic tensile failure patterns of the specimen are shown in Figure 7.It can be seen that the crushing degree of the specimen increases with the increase in loading rate.When the loading rate is small, the tensile stress in the center of the specimen is the highest; when the tensile stress exceeds the tensile strength of the rock, the first crack is generated in the center of the specimen and gradually extends to both ends; then, the main crack is formed.The specimen is finally broken into two parts after the penetration of the main crack, and the crushing area at the loading end is small, as shown in Figure 7a,b.With the continuous increase in loading rate, under the joint action of external loads, the secondary cracks at the loading end become increasingly abundant, except for the central main crack along the loading direction.As a result, the region of deformation and fracture localized at the loading end of the specimen assumes greater importance, and the central crushing area, resulting from the propagation and extension of both the primary and secondary cracks, expands.Notably, a higher loading rate correlates with a reduction in the particle size of the central crushing zone, as shown in Figure 7c-e.When the loading rate is further increased, the specimen is broken into fragments, and the average size of fragments is small, as shown in Figure 7f.When Equation ( 2) is substituted into Equation ( 1), the expression of dynamic tensile stress of the Brazilian disc can be obtained as follows:

Analysis of Dynamic Tensile Failure Characteristics
When n = 20, the dynamic tensile failure patterns of the specimen are shown in Figure 7.It can be seen that the crushing degree of the specimen increases with the increase in loading rate.When the loading rate is small, the tensile stress in the center of the specimen is the highest; when the tensile stress exceeds the tensile strength of the rock, the first crack is generated in the center of the specimen and gradually extends to both ends; then, the main crack is formed.The specimen is finally broken into two parts after the penetration of the main crack, and the crushing area at the loading end is small, as shown in Figure 7a,b.With the continuous increase in loading rate, under the joint action of external loads, the secondary cracks at the loading end become increasingly abundant, except for the central main crack along the loading direction.As a result, the region of deformation and fracture localized at the loading end of the specimen assumes greater importance, and the central crushing area, resulting from the propagation and extension of both the primary and secondary cracks, expands.Notably, a higher loading rate correlates with a reduction in the particle size of the central crushing zone, as shown in Figure 7c-e.When the loading rate is further increased, the specimen is broken into fragments, and the average size of fragments is small, as shown in Figure 7f.When Equation ( 2) is substituted into Equation ( 1), the expression of dynamic tensile stress of the Brazilian disc can be obtained as follows: σ = 2 (3)

Analysis of Dynamic Tensile Failure Characteristics
When n = 20, the dynamic tensile failure patterns of the specimen are shown in Figure 7.It can be seen that the crushing degree of the specimen increases with the increase in loading rate.When the loading rate is small, the tensile stress in the center of the specimen is the highest; when the tensile stress exceeds the tensile strength of the rock, the first crack is generated in the center of the specimen and gradually extends to both ends; then, the main crack is formed.The specimen is finally broken into two parts after the penetration of the main crack, and the crushing area at the loading end is small, as shown in Figure 7a,b.With the continuous increase in loading rate, under the joint action of external loads, the secondary cracks at the loading end become increasingly abundant, except for the central main crack along the loading direction.As a result, the region of deformation and fracture localized at the loading end of the specimen assumes greater importance, and the central crushing area, resulting from the propagation and extension of both the primary and secondary cracks, expands.Notably, a higher loading rate correlates with a reduction in the particle size of the central crushing zone, as shown in Figure 7c-e.When the loading rate is further increased, the specimen is broken into fragments, and the average size of fragments is small, as shown in Figure 7f.To quantitatively analyze the variation law of the dynamic tensile failure degree of red sandstone with loading rate, the average particle size of fragments after failure is analyzed in this section.After the dynamic impact test, the broken particles were collected, and the standard square hole sieve with a particle size of 0.25, 0.5, 1, 2, 5, 10, 15, 20 mm was selected to screen the broken particles.Subsequently, the mass of fragments retained To quantitatively analyze the variation law of the dynamic tensile failure degree of red sandstone with loading rate, the average particle size of fragments after failure is analyzed in this section.After the dynamic impact test, the broken particles were collected, and the standard square hole sieve with a particle size of 0.25, 0.5, 1, 2, 5, 10, 15, 20 mm was selected to screen the broken particles.Subsequently, the mass of fragments retained in the sieve apertures of each size fraction was determined via electronic scale measurement.Moreover, the average size of the fractured fragments was calculated by applying Equation (4).
where d represents the average size, d i represents the mean dimensions of the fragments that are captured by the sieve within the particle size interval of each group, and η i represents the percentage of fragments with an average size d i in the total mass of fragments.
As shown in Figure 8, it can be seen that, under a given number of dry-wet cycles, the average size of fragments shows a significant decreasing trend with the increase in loading rate, indicating that the crushing degree of the specimen gradually increases.This finding is also consistent with the failure pattern law analyzed above.To quantitatively analyze the variation law of the dynamic tensile failure degree of red sandstone with loading rate, the average particle size of fragments after failure is analyzed in this section.After the dynamic impact test, the broken particles were collected, and the standard square hole sieve with a particle size of 0.25, 0.5, 1, 2, 5, 10, 15, 20 mm was selected to screen the broken particles.Subsequently, the mass of fragments retained in the sieve apertures of each size fraction was determined via electronic scale measurement.Moreover, the average size of the fractured fragments was calculated by applying Equation (4).
where  ̅ represents the average size,  represents the mean dimensions of the fragments that are captured by the sieve within the particle size interval of each group, and  represents the percentage of fragments with an average size  in the total mass of fragments.
As shown in Figure 8, it can be seen that, under a given number of dry-wet cycles, the average size of fragments shows a significant decreasing trend with the increase in loading rate, indicating that the crushing degree of the specimen gradually increases.This finding is also consistent with the failure pattern law analyzed above.

Analysis of Dynamic Tensile Energy Dissipation
The rock failure under the impact load is actually the result of energy conversion.At the micro-level, the result of energy dissipation is the continuous evolution of micro-defects (such as cracks) in the rock, while, at the macro-level, the result of energy dissipation is the deformation, failure and gradual loss of the rock strength [31][32][33].According to the

Analysis of Dynamic Tensile Energy Dissipation
The rock failure under the impact load is actually the result of energy conversion.At the micro-level, the result of energy dissipation is the continuous evolution of micro-defects (such as cracks) in the rock, while, at the macro-level, the result of energy dissipation is the deformation, failure and gradual loss of the rock strength [31][32][33].According to the elastic wave theory, the energy carried by various waveforms in the system under the impact load can be calculated as follows: where W I , W R and W T represent the energy carried by the incident wave, reflected wave and transmitted wave, respectively; σ I , σ R and σ T represent the stress generated by the incident wave, reflected wave and transmitted wave in the pressure bar, respectively.
The energy carried by the incident wave is mainly converted into the following parts: the energy absorbed by the specimen, the energy reflected by the incident rod, the energy transmitted to the transmission rod, and the energy consumed by the friction between the rod and the specimen interface.Since the friction energy consumption between the interfaces accounts for a small proportion of the total, it can be ignored in the energy calculation.Therefore, the energy absorbed by the specimen can be expressed by Equation (8).
In the SHPB test, the energy that is absorbed by the specimen primarily consists of three components: the energy absorbed by the crack propagation and failure of the specimen, the energy consumed by the splash of fragments after the impact failure of the specimen, and other forms of energy consumption (such as friction energy consumption and heat energy consumption).Studies have shown that the energy used for crack propagation and rock failure generally accounts for more than 95% of the total energy, and the proportion of other energy forms is less than 5% [34].In the following studies, the energy absorbed by the specimen can be used to replace the energy consumption of the crushing.
Due to the deviation in the specimen size, the energy consumption of the crushing cannot fully reflect the response of the specimen to the stress wave.Here, the energy consumption density, i.e., the energy dissipated per unit volume, is used to reflect the average energy consumption of the specimen.The calculation function is shown as follows: where w is the energy consumption density, W s is the energy absorbed by the specimen, and V s is the volume of the specimen.The energy variation in rock specimens with the loading rate at 20 dry-wet cycles is shown in Figure 9.It is evident that as the loading rate increases all energies steadily escalate, with the transmission energy registering the slowest rate of increase.When the loading rate increases from 302 GPa•s −1 to 1204 GPa•s −1 , the incident energy, reflection energy, transmission energy and dissipative energy increase by 439.55%, 426.76%, 397.78% and 616.37%, respectively.Observations indicate that the magnitude of dissipated energy escalation surpasses that of transmitted energy amplification by a notable margin.According to the data in Table 2, the change curve of energy consumption density with loading rate under different dry-wet cycles is obtained in Figure 10.Evidently, when subjected to a constant n, the energy consumption density exhibits a near-linear increase with an augmented loading rate.Table 3 shows the fitting results of the energy-consumption density curve of red sandstone specimens at different numbers of dry-wet cycles.According to the slope of the fitting line, the influence of the number of dry-wet cycles on the loading rate sensitivity of energy consumption density can be determined.With the increase in the number of dry-wet cycles, the slope of the fitting line gradually decreases, indicating that the rate sensitivity decreases.In addition, the rate sensitivity of the non- According to the data in Table 2, the change curve of energy consumption density with loading rate under different dry-wet cycles is obtained in Figure 10.Evidently, when subjected to a constant n, the energy consumption density exhibits a near-linear increase with an augmented loading rate.Table 3 shows the fitting results of the energyconsumption density curve of red sandstone specimens at different numbers of dry-wet cycles.According to the slope of the fitting line, the influence of the number of dry-wet cycles on the loading rate sensitivity of energy consumption density can be determined.With the increase in the number of dry-wet cycles, the slope of the fitting line gradually decreases, indicating that the rate sensitivity decreases.In addition, the rate sensitivity of the non-eroded (n = 0) specimen is the strongest.To explore the relationship between energy dissipation and dynamic tensile strength, the curves of dynamic tensile strength with energy consumption densities under different dry-wet cycles are drawn, as shown in Figure 11.It can be seen that, under a given number of dry-wet cycles, with the gradual increase in energy consumption density, the tensile strength tends to increase, and the increasing trend gradually slows down.The relationship between the energy consumption density and tensile strength can be expressed as a logarithm function:   Based on the changing pattern of energy with respect to the loading rate, a quantitative relationship between the two is established via numerical fitting methodology.When the loading rate is 850 Gpa•s -1 , the variation curve of energy with the number of dry-wet cycles is drawn in Figure 12.At a given loading rate, with the increasing number of drywet cycles, the reflection energy gradually increases, and the transmission energy and the dissipation energy gradually decrease, while the incident energy fluctuates in a small range and is rarely affected by the number of dry-wet cycles.The main reason for this is that the dry-wet cycles weaken the adhesion between crystal particles, leading to the  Based on the changing pattern of energy with respect to the loading rate, a quantitative relationship between the two is established via numerical fitting methodology.When the loading rate is 850 Gpa•s −1 , the variation curve of energy with the number of dry-wet cycles is drawn in Figure 12.At a given loading rate, with the increasing number of dry-wet cycles, the reflection energy gradually increases, and the transmission energy and the dissipation energy gradually decrease, while the incident energy fluctuates in a small range and is rarely affected by the number of dry-wet cycles.The main reason for this is that the dry-wet cycles weaken the adhesion between crystal particles, leading to the gradual extension of the original cracks and the gradual increase in the volume of micropores.The cracks and pores that are generated after energy absorption appear in advance under the dry-wet cycle; thus, the required dissipation energy is relatively reduced.The increase in microcracks and holes hinders the further transmission of energy, which is reflected in the increase in reflection energy and the decrease in transmission energy.According to the fitting results in Table 5, the energy consumption density at the loading rates of 450, 650, 850 and 1050 GPa•s −1 is calculated, and the curve of energy consumption density changing with n is drawn, as shown in Figure 13.Observations reveal that, under identical loading rates, the energy consumption density demonstrates a nearlinear decrease upon increasing n.When n increases from 0 to 40 and the corresponding loading rates are 450 GPa•s −1 , 650 GPa•s −1 , 850 GPa•s −1 and 1050 GPa•s −1 , the energy consumption density decreases by 59.82%, 49.91%, 45.50% and 43.01%, respectively.This indicates that the lower the loading rate, the greater the reduction in energy consumption density.Table 5 shows the linear fitting results between the dynamic tensile energy consumption density of the red sandstone under different loading rates and the number of dry-wet cycles.It can be seen that, with the increase in loading rate, the absolute value of the linear slope gradually increases, indicating that the sensitivity of energy consumption density to dry-wet cycles gradually increases.According to the fitting results in Table 5, the energy consumption density at the loading rates of 450, 650, 850 and 1050 GPa•s −1 is calculated, and the curve of energy consumption density changing with n is drawn, as shown in Figure 13.Observations reveal that, under identical loading rates, the energy consumption density demonstrates a nearlinear decrease upon increasing n.When n increases from 0 to 40 and the corresponding loading rates are 450 GPa•s −1 , 650 GPa•s −1 , 850 GPa•s −1 and 1050 GPa•s −1 , the energy consumption density decreases by 59.82%, 49.91%, 45.50% and 43.01%, respectively.According to the fitting results in Table 5, the energy consumption density at the loading rates of 450, 650, 850 and 1050 GPa•s −1 is calculated, and the curve of energy consumption density changing with n is drawn, as shown in Figure 13.Observations reveal that, under identical loading rates, the energy consumption density demonstrates a nearlinear decrease upon increasing n.When n increases from 0 to 40 and the corresponding loading rates are 450 GPa•s −1 , 650 GPa•s −1 , 850 GPa•s −1 and 1050 GPa•s −1 , the energy consumption density decreases by 59.82%, 49.91%, 45.50% and 43.01%, respectively.
This indicates that the lower the loading rate, the greater the reduction in energy consumption density.Table 5 shows the linear fitting results between the dynamic tensile energy consumption density of the red sandstone under different loading rates and the number of dry-wet cycles.It can be seen that, with the increase in loading rate, the absolute value of the linear slope gradually increases, indicating that the sensitivity of energy consumption density to dry-wet cycles gradually increases.

Figure 2 .
Figure 2. Schematic diagram of the dry-wet cycle process.

Figure 2 .
Figure 2. Schematic diagram of the dry-wet cycle process.

Figure 2 .
Figure 2. Schematic diagram of the dry-wet cycle process.

Figure 4 .
Figure 4. Extracted signals in a typical dynamic tensile test (In: incident wave; Re: reflected wave; Tr: transmitted wave).

Figure 4 .
Figure 4. Extracted signals in a typical dynamic tensile test (In: incident wave; Re: reflected wave; Tr: transmitted wave).

Figure 4 .
Figure 4. Extracted signals in a typical dynamic tensile test (In: incident wave; Re: reflected wave; Tr: transmitted wave).

E
and A denote the modulus of elasticity and the cross-sectional area of the compression bar, respectively.

Figure 6 .
Figure 6.Loading diagram in a typical dynamic tensile test.

Figure 6 .
Figure 6.Loading diagram in a typical dynamic tensile test.

Sustainability 2023 , 15 E
15,  x FOR PEER REVIEW 6 of and A denote the modulus of elasticity and the cross-sectional area of the compression bar, respectively.

Figure 6 .
Figure 6.Loading diagram in a typical dynamic tensile test.

Figure 8 .
Figure 8. Variation in average fragment size at different dry-wet cycles versus loading rate.

Figure 8 .
Figure 8. Variation in average fragment size at different dry-wet cycles versus loading rate.

Figure 9 .
Figure 9. Energy variation with loading rate.

Figure 9 .
Figure 9. Energy variation with loading rate.

Figure 10 .Table 3 . 2 Figure 10 .
Figure 10.Relationship between energy consumption density and loading rate at different drywet cycles.Table 3. Fitting results of energy consumption density curve of red sandstone specimens at different numbers of dry-wet cycles (R 2 : correlation coefficient).Number of Dry-WetFitting Curve R2

Figure 11 .
Figure 11.Relationship between dynamic tensile strength and energy consumption density at different numbers of dry-wet cycles.

Figure 11 .
Figure 11.Relationship between dynamic tensile strength and energy consumption density at different numbers of dry-wet cycles.

Sustainability 2023 , 15 Figure 12 .
Figure 12.Energy variation with the number of dry-wet cycles.

Figure 13 .
Figure 13.Variation in energy consumption density at different loading rates versus the number of dry-wet cycles.

Figure 12 .
Figure 12.Energy variation with the number of dry-wet cycles.

Sustainability 2023 , 15 Figure 12 .
Figure 12.Energy variation with the number of dry-wet cycles.

Figure 13 .
Figure 13.Variation in energy consumption density at different loading rates versus the number of dry-wet cycles.

Figure 13 .
Figure 13.Variation in energy consumption density at different loading rates versus the number of dry-wet cycles.

Table 1 .
Physical and mechanical parameters of red sandstone specimens.

Table 1 .
Physical and mechanical parameters of red sandstone specimens.

Table 2 .
Calculation results of energy in the dynamic tensile tests.

Table 3 .
Fitting results of energy consumption density curve of red sandstone specimens at different numbers of dry-wet cycles (R 2 : correlation coefficient).
Table 4 shows the fitting results of dynamic tensile strength with energy consumption density at different numbers of drywet cycles.

Table 4 .
Fitting results of dynamic tensile strength with energy consumption density at different numbers of dry-wet cycles (R 2 : correlation coefficient).

Table 4 .
Fitting results of dynamic tensile strength with energy consumption density at different numbers of dry-wet cycles (R 2 : correlation coefficient).

Table 5 .
Fitting results of energy consumption density curve of red sandstone specimens at different loading rates (R 2 : correlation coefficient).