# Dynamic Mechanical Response and Dissipated Energy Analysis of Sandstone under Freeze-Thaw Cycles

Authors: Ke Man; Zongxu Liu; Zhifei Song; Xiaoli Liu
Journal: Geofluids
 (2021)

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## Abstract

Based on the sandstone from the slope of Baorixile open-pit mining area in Hulunbuir City, Inner Mongolia, the dynamic uniaxial compression test of sandstone with different freeze-thaw cycles has been carried out by Split Hopkinson Pressure Bar test (SHPB). The test results show that the crushing degree of sandstone becomes serious with the freeze-thaw cycle times and strain rate increases. The dynamic compressive strength increases with the raise of strain rate under the same freeze-thaw cycles, while it reduces with the increases of freeze-thaw cycles at the same strain rate. It is found that the 10 freeze-thaw cycles are an obvious inflection point. When it is less than 10 cycles, the dynamic compressive strength of sandstone specimens decreases rapidly, it is more than 10 cycles, and the strength decreases gradually. This is due to that the evolution progress of pores in sandstone is more uniform after a certain number of freeze-thaw cycles. Meantime, the effect of freezing and thawing is mostly restrained by the pore evolution. On the other hand, the dissipated energy required for sandstone failure grows up with the increase of the number of freeze-thaw cycles. It shows that more energy is needed for the engender of pores and fractures in sandstone caused by freeze-thaw cycle. This led to the deterioration of sandstone structural stability and the decrease of dynamic mechanical properties.


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## Body

## 1. Introduction

More than 70% of the land area of China is perennially frozen and seasonally frozen. Among them, some areas in the northeast and high-altitude areas in the west are permafrost regions, while north and south China are seasonal permafrost regions [1]. These frozen regions are rich in mineral resources, and the rock mass will inevitably receive dynamic loads such as impact of drilling and blasting in the process of mineral mining. In addition, the effect of temperature change on rock freezing and thawing mechanics cannot be ignored [2]. Therefore, the study of mechanical properties and failure law of rock under the combined action of freeze-thaw and dynamic load is of great significance to rock mass engineering in frozen regions.At present, the mechanical properties of rock under conventional freeze-thaw cycles have been deeply studied by many scholars [3–18]. Zhou et.al [19–21] used the NMR system to study the pore structure change and damage mechanism of granite under freeze-thaw cycle. Amitrano et.al [22] tested the failure characteristics of rock under the action of freeze-thaw cycle by acoustic emission test and found that a large number of internal cracks occurred with the progress of freeze-thaw cycle. Wu et.al [23] studied the longitudinal wave velocity, mass, and volume of marble after freeze-thaw cycle and summed up the physical and mechanical properties of marble after freeze-thaw cycle. Yang et.al [24] used uniaxial and triaxial compression tests of sandstone and coal under different temperatures and confining pressures to study the strength properties of rocks under freeze-thaw cycles. Nicholson et.al [25] carried out freeze-thaw cycle tests on fractured rocks to study the effect of primary fractures on the degree of freeze-thaw damage. Huseyin et.al [26] tested the compressive strength and other parameters of andesite after freeze-thaw cycle and obtained the deterioration law of andesite. Jihwan Park et.al [27] used CT scanning and SEM techniques to analyze the microstructure changes of rocks under freeze-thaw cycles. Bellanger et.al [28] studied the saturated water content, porosity, and permeability of limestone in northeastern France and obtained the relationship between them.Moreover, the internal damage and fracture process of rock under dynamic load will be accompanied by the transformation and dissipation of energy. Energy dissipation is the most important factor in rock failure; so, many scholars have made an indepth study on the mechanism of rock energy dissipation [29–32]. For instance, Xie et.al [33, 34] found that the internal damage and fracture of rock are caused by external energy, and the rock damage equation based on energy dissipation can better describe the damage process of rock. Gong et.al [35, 36] carried out static uniaxial compression test and Brazilian splitting test of red sandstone and found the law of linear energy storage and energy consumption in compression tension failure of rock.However, the current research on the dynamic mechanical properties of rock under freeze-thaw is relatively few. In this paper, the dynamic uniaxial compression tests of sandstone under different freeze-thaw cycles are studied in detail, and its failure mechanism is analyzed from the point of view of energy.


## 2. Samples and Test Methods

### 2.1. Sample Making

The test samples are taken from sandstone with good particle uniformity and structural integrity in Baorixile open-pit mining area in Hulunbuir City, Inner Mongolia. According to theStandard of Experimental method for Engineering Rock Mass [37], the sandstone sample is polished into a disc sample with a height of 25 mm and a diameter of 50 mm, as shown in Figure 1, and the basic mechanical parameters of the tested sandstone are shown in Table 1.Figure 1
Sandstone samples under impact loading test.Table 1
The basic mechanical parameters of the tested sandstone.
Uniaxial compressive strength/MPaLongitudinal strain/10-2Tensile strength/MPaTransverse strain/10-2Elastic modulus/GPaPoisson’s ratio28.050.843.910.093.820.14


### 2.2. Test Equipment

TDS-300 freeze-thaw cycle test machine is used in the freeze-thaw cycle test, as shown in Figure2. The temperature can be controlled by the device is -40°C-90°C, and the temperature fluctuation is ±0.05°C.Figure 2
TDS-300 freeze-thaw cycle testing machine.The impact load test of sandstone using the Split Hopkinson Pressure Bar test device (SHPB) is shown in Figure3. The device can be used to test the impact dynamic characteristics of rock, concrete, and other materials. It is mainly composed of transmitting cavity, incident rod, transmission rod, and data acquisition and processing system. The rod is made of chromium alloy steel. The diameter of the incident rod and the transmission rod is 50 mm, and the lengths are 2 m and 1.5 m.Figure 3
Split Hopkinson Pressure Bar test device (SHPB).


### 2.3. Test Scheme and Process

First of all, the sandstone samples were saturated with water, and after the samples were completely saturated, the freeze-thaw cycle test was carried out, and the single freeze-thaw cycle was set to 12 h. The samples were frozen at-20°C for 6 h and thawed at 20°C for 6 h. The experiment was divided into 6 groups according to different freeze-thaw cycles, and the freeze-thaw times were 0, 1, 5, 10, 15, and 20 times. After different freeze-thaw cycles, the Split Hopkinson Pressure Bar device was used to carry out impact loading tests on the samples with different impact pressures of 0.5 MPa, 0.6 MPa, and 0.7 MPa, and the dynamic characteristics of sandstone samples were tested.


## 2.1. Sample Making

The test samples are taken from sandstone with good particle uniformity and structural integrity in Baorixile open-pit mining area in Hulunbuir City, Inner Mongolia. According to theStandard of Experimental method for Engineering Rock Mass [37], the sandstone sample is polished into a disc sample with a height of 25 mm and a diameter of 50 mm, as shown in Figure 1, and the basic mechanical parameters of the tested sandstone are shown in Table 1.Figure 1
Sandstone samples under impact loading test.Table 1
The basic mechanical parameters of the tested sandstone.
Uniaxial compressive strength/MPaLongitudinal strain/10-2Tensile strength/MPaTransverse strain/10-2Elastic modulus/GPaPoisson’s ratio28.050.843.910.093.820.14


## 2.2. Test Equipment

TDS-300 freeze-thaw cycle test machine is used in the freeze-thaw cycle test, as shown in Figure2. The temperature can be controlled by the device is -40°C-90°C, and the temperature fluctuation is ±0.05°C.Figure 2
TDS-300 freeze-thaw cycle testing machine.The impact load test of sandstone using the Split Hopkinson Pressure Bar test device (SHPB) is shown in Figure3. The device can be used to test the impact dynamic characteristics of rock, concrete, and other materials. It is mainly composed of transmitting cavity, incident rod, transmission rod, and data acquisition and processing system. The rod is made of chromium alloy steel. The diameter of the incident rod and the transmission rod is 50 mm, and the lengths are 2 m and 1.5 m.Figure 3
Split Hopkinson Pressure Bar test device (SHPB).


## 2.3. Test Scheme and Process

First of all, the sandstone samples were saturated with water, and after the samples were completely saturated, the freeze-thaw cycle test was carried out, and the single freeze-thaw cycle was set to 12 h. The samples were frozen at-20°C for 6 h and thawed at 20°C for 6 h. The experiment was divided into 6 groups according to different freeze-thaw cycles, and the freeze-thaw times were 0, 1, 5, 10, 15, and 20 times. After different freeze-thaw cycles, the Split Hopkinson Pressure Bar device was used to carry out impact loading tests on the samples with different impact pressures of 0.5 MPa, 0.6 MPa, and 0.7 MPa, and the dynamic characteristics of sandstone samples were tested.


## 3. Test Results

The bullet velocity and strain rate of uniaxial compression test under different impact pressure are shown in Table2, and the peak dynamic compressive strength and peak strain of sandstone under different freeze-thaw cycles and strain rates are shown in Table 3.Table 2
Bullet velocity and strain rate under different pressure.
Grouping and numbering of samplesAir pressure (MPa)Bullet velocity (m/s)Average speed (m/s)Strain rate (s-1)Average strain rate (s-1)Y0-10.511.2511.0354.853.15Y1-110.4150.2Y5-111.0953.8Y10-111.1651.7Y15-111.2753.2Y20-111.0255.2Y0-20.612.8213.0975.375.07Y1-212.9870.5Y5-213.3273.8Y10-212.9377.8Y15-213.2977.7Y20-213.1975.3Y0-30.714.4114.9298.999.07Y1-315.12102.6Y5-314.7796.7Y10-315.0996.1Y15-314.8498.3Y20-315.28101.8Table 3
Dynamic uniaxial compression mechanical parameters of sandstone under different freeze-thaw cycles.
Grouping and numbering of samplesStrain rate (s-1)Compression strength (MPa)Axial strain (10-2)Y0-154.8155.540.73Y0-275.3179.110.97Y0-398.9221.031.18Y1-150.2140.280.87Y1-270.5167.991.04Y1-3102.6200.361.27Y5-153.8130.460.98Y5-273.8157.331.16Y5-396.7185.651.36Y10-151.7121.751.09Y10-277.8148.941.28Y10-396.1176.211.44Y15-153.2112.231.16Y15-277.7140.071.33Y15-398.3166.831.52Y20-155.2105.281.21Y20-275.3135.681.39Y20-3101.8158.761.59


### 3.1. Dynamic Uniaxial Compression Strength Analysis

The influence of strain rate and freeze-thaw cycles on dynamic compressive strength is as follows. Figure4 shows the dynamic compression strength curve of sandstone under different strain rates, and n is the number of freeze-thaw cycles. Figure 5 is the dynamic compression strength curve of sandstone under different freeze-thaw cycles, and s is the strain rate.Figure 4
Dynamic compressive strength of sandstone under different strain rates.Figure 5
Dynamic compressive strength of sandstone under different freeze-thaw cycles.As shown in Figure4, the dynamic compressive strength of sandstone rises with the increase of strain rate. This is due to that under the impact load of high strain rate, the sandstone with the same number of freeze-thaw cycles needs more stress, which leads to the failure of sandstone samples. The compressive strength declines with the increase of freeze-thaw cycles. It is clear that both strain rate and freeze-thaw affect the dynamic compressive strength of sandstone, but the effect of freeze-thaw is higher than that of strain rate.As illustrated in Figure5, the dynamic compressive strength of sandstone declines with the increase of freeze-thaw cycles. The reason is that repeated freeze-thaw cycles lead to repeated expansion and contraction of pores in sandstone, resulting in pores gradually developing into cracks and seriously destroying the internal structure of sandstone; so, freeze-thaw cycles will significantly reduce the mechanical properties of sandstone.


### 3.2. Variation Law of Dynamic Axial Strain

The effect of strain rate and freeze-thaw cycle on strain: Figure6 shows the dynamic axial strain curve of sandstone under different strain rates. Figure 7 shows the dynamic axial strain curve of sandstone under different freeze-thaw cycles.Figure 6
Dynamic axial strain of sandstone under different strain rates.Figure 7
Dynamic axial strain of sandstone under different freeze-thaw cycles.As it can be seen from Figure6: the dynamic axial strain of sandstone growth with the increase of strain rate, the reason is that the higher stress is needed to destroy the sandstone sample at high strain rate; so, the axial strain increases.In Figure7, the axial strain of sandstone ascends with the increase of freeze-thaw cycles. This is due to those different times of freeze-thaw cycles will destroy the internal structure of sandstone and make the internal pores growth into through fissures, resulting in the axial strain of sandstone samples will rise with the increase of the number of freeze-thaw cycles.


## 3.1. Dynamic Uniaxial Compression Strength Analysis

The influence of strain rate and freeze-thaw cycles on dynamic compressive strength is as follows. Figure4 shows the dynamic compression strength curve of sandstone under different strain rates, and n is the number of freeze-thaw cycles. Figure 5 is the dynamic compression strength curve of sandstone under different freeze-thaw cycles, and s is the strain rate.Figure 4
Dynamic compressive strength of sandstone under different strain rates.Figure 5
Dynamic compressive strength of sandstone under different freeze-thaw cycles.As shown in Figure4, the dynamic compressive strength of sandstone rises with the increase of strain rate. This is due to that under the impact load of high strain rate, the sandstone with the same number of freeze-thaw cycles needs more stress, which leads to the failure of sandstone samples. The compressive strength declines with the increase of freeze-thaw cycles. It is clear that both strain rate and freeze-thaw affect the dynamic compressive strength of sandstone, but the effect of freeze-thaw is higher than that of strain rate.As illustrated in Figure5, the dynamic compressive strength of sandstone declines with the increase of freeze-thaw cycles. The reason is that repeated freeze-thaw cycles lead to repeated expansion and contraction of pores in sandstone, resulting in pores gradually developing into cracks and seriously destroying the internal structure of sandstone; so, freeze-thaw cycles will significantly reduce the mechanical properties of sandstone.


## 3.2. Variation Law of Dynamic Axial Strain

The effect of strain rate and freeze-thaw cycle on strain: Figure6 shows the dynamic axial strain curve of sandstone under different strain rates. Figure 7 shows the dynamic axial strain curve of sandstone under different freeze-thaw cycles.Figure 6
Dynamic axial strain of sandstone under different strain rates.Figure 7
Dynamic axial strain of sandstone under different freeze-thaw cycles.As it can be seen from Figure6: the dynamic axial strain of sandstone growth with the increase of strain rate, the reason is that the higher stress is needed to destroy the sandstone sample at high strain rate; so, the axial strain increases.In Figure7, the axial strain of sandstone ascends with the increase of freeze-thaw cycles. This is due to those different times of freeze-thaw cycles will destroy the internal structure of sandstone and make the internal pores growth into through fissures, resulting in the axial strain of sandstone samples will rise with the increase of the number of freeze-thaw cycles.


## 4. Discussion

### 4.1. Energy Dissipation Law

In the impact load test of sandstone, the destruction process of sandstone must be accompanied by the absorption and dissipation of energy. Energy absorption in sandstone depends on factors such as pore space. The development and expansion of pores and fractures within the sandstone require the absorption of energy [21]. The dissipated energy required for sandstone failure can be calculated by incident energy, reflection energy, and transmission energy. The formula is as follows:
(1)WI=EoCoAo∫otεI2tdt,(2)WR=EoCoAo∫otεR2tdt,(3)WT=EoCoAo∫otεT2tdt.In the formula,WI is the incident energy, WR is the reflected energy, WT is the transmission energy, Eo is the elastic modulus of rod, Co is the longitudinal wave velocity of the rod, Ao is the cross-sectional area of the rod, εtt is the incident stress wave strain signal, εRt is the reflected stress wave strain signal, and εTt is the transmitted stress wave strain signal.The dissipated energy in the failure process of sandstone specimen is expressed byWS, and the formula is
(4)WS=WI−WR−WT.Table4 shows the energy statistics of dynamic uniaxial compression test of sandstone under different freeze-thaw cycles.Table 4
Energy statistical table.
Sample numberStrain rate/s-1WI/JWR/JWT/JWS/JY0-154.8126.3839.1036.7850.5Y0-275.3179.0761.0159.9258.14Y0-398.9230.2486.5154.5189.22Y1-150.2127.3037.9236.0253.36Y1-270.5178.8458.6447.3472.86Y1-3102.6233.0388.6244.36100.05Y5-153.8126.8438.8634.1753.81Y5-273.8180.1458.6245.6875.84Y5-396.7230.1780.2732.80117.1Y10-151.7127.9937.4431.4159.14Y10-277.8180.3762.1435.7682.47Y10-396.1232.2785.7931.87114.61Y15-153.2126.9538.6928.0160.25Y15-277.7180.2860.2532.4087.63Y15-398.3230.8181.2230.12119.47Y20-155.2126.3337.5328.1260.68Y20-275.3179.7259.4231.8488.46Y20-3101.8231.4583.1828.86119.41Figure8 shows the variation curve of four kinds of energy with the number of freeze-thaw cycles when the average strain rates are 53.15, 75.07, and 99.07. It can be seen from Figure 8 that the incident energy and transmission energy remain stable under different freeze-thaw cycles. However, the incident energy and transmission energy grow up with the increase of strain rate, and the higher the strain rate, the greater their growth. It shows that the incident energy and reflection energy are not sensitive to the number of freeze-thaw cycles. The transmission energy reduces with the increase of freeze-thaw cycles and increases at first and then declines with the increase of strain rate. The dissipated energy ascends with the increase of the number of freeze-thaw cycles, and the higher the strain rate, the greater the increase of dissipative energy.Figure 8
Four kinds of energy change curves under different strain rates and freeze-thaw cycles.
(a)
s=53.15(b)
s=75.07(c)
s=99.07


### 4.2. Failure Mechanism of Sandstone Sample

The strain rate effect of dynamic compressive strength of sandstone is analyzed from the point of view of energy. The interior of the sandstone sample is full of natural pores and fissures, and the failure process of sandstone is also the process of the development and expansion of pores and fissures. The crack rises with the increase of strain rate and so does the energy require [38]. Because the time of impact load is very short, the sample can only increase the stress to balance the external energy; so, the dynamic compressive strength of sandstone samples ascends with the increase of strain rate.Figure9 shows the curve of dissipated energy varying with the number of freeze-thaw cycles at different strain rates. It can be seen that the dissipated energy of sandstone sample rises obviously with the increase of the number of freeze-thaw cycles, and the growth rate of dissipative energy gains in with the increase of strain rate. It shows that the failure of sandstone under the combined action of freeze-thaw cycle and high strain rate impact load will absorb more energy and illustraion of the development of pores and cracks in sandstone needs higher energy. Therefore, with the increase of strain rate and the number of freeze-thaw cycles, the failure degree of sandstone specimens becomes larger and larger, as shown in Figure 10.Figure 9
The variation curve of dissipative energy with the number of freeze-thaw cycles under different strain rates.Figure 10
Failure morphology of sandstone specimens under different freeze-thaw cycles and strain rates.
(a)
n=0(b)
n=20(c)
s=53.15(d)
s=99.07


## 4.1. Energy Dissipation Law

In the impact load test of sandstone, the destruction process of sandstone must be accompanied by the absorption and dissipation of energy. Energy absorption in sandstone depends on factors such as pore space. The development and expansion of pores and fractures within the sandstone require the absorption of energy [21]. The dissipated energy required for sandstone failure can be calculated by incident energy, reflection energy, and transmission energy. The formula is as follows:
(1)WI=EoCoAo∫otεI2tdt,(2)WR=EoCoAo∫otεR2tdt,(3)WT=EoCoAo∫otεT2tdt.In the formula,WI is the incident energy, WR is the reflected energy, WT is the transmission energy, Eo is the elastic modulus of rod, Co is the longitudinal wave velocity of the rod, Ao is the cross-sectional area of the rod, εtt is the incident stress wave strain signal, εRt is the reflected stress wave strain signal, and εTt is the transmitted stress wave strain signal.The dissipated energy in the failure process of sandstone specimen is expressed byWS, and the formula is
(4)WS=WI−WR−WT.Table4 shows the energy statistics of dynamic uniaxial compression test of sandstone under different freeze-thaw cycles.Table 4
Energy statistical table.
Sample numberStrain rate/s-1WI/JWR/JWT/JWS/JY0-154.8126.3839.1036.7850.5Y0-275.3179.0761.0159.9258.14Y0-398.9230.2486.5154.5189.22Y1-150.2127.3037.9236.0253.36Y1-270.5178.8458.6447.3472.86Y1-3102.6233.0388.6244.36100.05Y5-153.8126.8438.8634.1753.81Y5-273.8180.1458.6245.6875.84Y5-396.7230.1780.2732.80117.1Y10-151.7127.9937.4431.4159.14Y10-277.8180.3762.1435.7682.47Y10-396.1232.2785.7931.87114.61Y15-153.2126.9538.6928.0160.25Y15-277.7180.2860.2532.4087.63Y15-398.3230.8181.2230.12119.47Y20-155.2126.3337.5328.1260.68Y20-275.3179.7259.4231.8488.46Y20-3101.8231.4583.1828.86119.41Figure8 shows the variation curve of four kinds of energy with the number of freeze-thaw cycles when the average strain rates are 53.15, 75.07, and 99.07. It can be seen from Figure 8 that the incident energy and transmission energy remain stable under different freeze-thaw cycles. However, the incident energy and transmission energy grow up with the increase of strain rate, and the higher the strain rate, the greater their growth. It shows that the incident energy and reflection energy are not sensitive to the number of freeze-thaw cycles. The transmission energy reduces with the increase of freeze-thaw cycles and increases at first and then declines with the increase of strain rate. The dissipated energy ascends with the increase of the number of freeze-thaw cycles, and the higher the strain rate, the greater the increase of dissipative energy.Figure 8
Four kinds of energy change curves under different strain rates and freeze-thaw cycles.
(a)
s=53.15(b)
s=75.07(c)
s=99.07


## 4.2. Failure Mechanism of Sandstone Sample

The strain rate effect of dynamic compressive strength of sandstone is analyzed from the point of view of energy. The interior of the sandstone sample is full of natural pores and fissures, and the failure process of sandstone is also the process of the development and expansion of pores and fissures. The crack rises with the increase of strain rate and so does the energy require [38]. Because the time of impact load is very short, the sample can only increase the stress to balance the external energy; so, the dynamic compressive strength of sandstone samples ascends with the increase of strain rate.Figure9 shows the curve of dissipated energy varying with the number of freeze-thaw cycles at different strain rates. It can be seen that the dissipated energy of sandstone sample rises obviously with the increase of the number of freeze-thaw cycles, and the growth rate of dissipative energy gains in with the increase of strain rate. It shows that the failure of sandstone under the combined action of freeze-thaw cycle and high strain rate impact load will absorb more energy and illustraion of the development of pores and cracks in sandstone needs higher energy. Therefore, with the increase of strain rate and the number of freeze-thaw cycles, the failure degree of sandstone specimens becomes larger and larger, as shown in Figure 10.Figure 9
The variation curve of dissipative energy with the number of freeze-thaw cycles under different strain rates.Figure 10
Failure morphology of sandstone specimens under different freeze-thaw cycles and strain rates.
(a)
n=0(b)
n=20(c)
s=53.15(d)
s=99.07


## 5. Conclusions

(1)
The dynamic mechanical properties of sandstone are significantly affected by freeze-thaw cycles and strain rate. With the increase of freeze-thaw cycles, the strength of sandstone decreases and the strain increases and the strength and strain of sandstone growth with the increase of strain rate(2)
When the number of cycles is less than 10, the dynamic compressive strength of sandstone decreases rapidly, and the image is obviously concave. When the number of cycles is more than 10 times, the strength decreases gradually, and the image shows a convex shape. 10 freeze-thaw cycles are an obvious inflection point. The reason is that after a certain number of freeze-thaw cycles, the internal pores of sandstone develop more evenly, which suppresses the effect of freeze-thaw on sandstone and slows the decrease of strength(3)
With the increase of the number of freeze-thaw cycles, the dissipative energy is required for sandstone failure growth. The reason is that the freeze-thaw cycle makes the sandstone loose, and the development of cracks aggravates. When the sandstone is destroyed by external forces, it is easy to produce more cracks, resulting in a greater degree of failure of the samples, showing a powder clastic shape



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*Source: 7724455-2021-11-10.xml*