1 Introduction

More than 90% of open-pit coal capacity comes from cold climate regions above 38° North latitudes, such as Xinjiang, Inner Mongolia, North of Shaanxi Province and etc. Goal resources’ safe and efficient mining faces enormous challenges under cold winter temperatures. There are two major influence factors. One is the water content in coal and rock masses. Drought risks are most likely to occur in North and Northwest areas with less precipitation and uneven distribution of groundwater system (Takarli et al. 2008; Guo and Shen 2016; Hu et al. 2019; Shen et al. 2020). Local springs or groundwater runoff are common during the open-pit mining process. At this point, the water contents of the open pit slope rock mass will significantly increase with uneven distributions (Li et al. 2014, 2021a; Zhang et al. 2021). In the low temperature in winter, the rock masses have different physical and mechanical properties in different water-bearing areas under the effects of freezing or frost heaving (Kodama et al. 2013; Wang et al. 2019a). The other is the high-strength mining blasting disturbance. A single blasting can yield 100 tons of coal resources for 10-million-ton open-pit mines. The high-intensity blast-induced stress waves have significant disturbance impacts on coal and rock mass (Navarro Torres et al. 2018; Chi et al. 2019; Shen et al. 2020; Azizi and Moomivand 2021). Therefore, the study on the mechanical properties of frozen sandstones and the damage and fracture mechanism under impact loads is essential to efficiently ensure the safe and efficient mining of open-pit coal mines in winter. The blasting mining of coal seams can be realized by reasonably designing blasting parameters. On the other hand, it can provide references for the design of control parameters of the stability of the slope coal and rock masses. Besides the large-scale open-pit coal mines, such problems also occur in other engineering in winter in northwestern and northern China, such as tunnel excavation, foundation excavation of large buildings, etc. (Cui et al. 2020; Jiang et al. 2021).

Water is one of the fundamental environmental factors faced by rocks (Cai et al. 2020b). Rocks will undergo weathering and decomposition after long-term exposure to air under natural environmental conditions, which will cause changes in physical and mechanical properties that are stable in a short period (Shang et al. 2004; Qi et al. 2009; Jaques et al. 2020). However, soaked in water or aqueous state, the clay mineral particles in rocks will show significant swelling. In addition, some mineral components readily soluble in water dissolve in water. This can cause remarkable changes in the internal structures of rocks and, in turn affect the macroscopic physical and mechanical properties. Such changes are more evident for sedimentary rocks such as coal-measure strata (Hale and Shakoor 2003; Deng et al. 2016; Kim and Changani 2016). The low-temperature environment is one of the essential factors affecting the mechanical properties of water-bearing rocks. Water can change from the liquid phase into solid phase as the temperature changes from room temperature to below 0 °C. The volume growth will result in significant changes in the microstructure characteristics of rocks (Al-Omari et al. 2015; Huang et al. 2021). When the water content is within a specific range, rocks are frozen and their mechanical properties will be strengthened, due to the contraction of particles and loads of pore ice (Zhou et al. 2021; Ming et al. 2021). When the water content exceeds the maximum value of the range, rocks will undergo frost heaving. Their physical and mechanical properties are significantly affected during water migration and accumulation in freezing zones. Huang et al. (2018) have pointed out that rocks with water contents of over 9% will experience significant frost heaving. There are plentiful research results on the static mechanical properties of rocks in the low-temperature environment (Bayram 2012; Bai et al. 2020; Deprez et al. 2020). Scholars have systematically studied mechanical characteristic parameters of different types of rocks, such as failure intensity, elastic modulus, macro failure characteristics and etc. (Feng et al. 2018b; Zhang et al. 2018; Wang et al. 2019a). The variations of mechanical properties of rocks with temperature and water content have also been discussed (Dwivedi et al. 2000; Kodama et al. 2013; Jia et al. 2020).

The problems of rock dynamics are gradually increasing in the low-temperature environment with the increase of geotechnical engineering in cold regions, which restrict the safe and efficient development of engineering. Scholars have conducted research on the rock mechanics characteristics under low-temperature environment by using the split-Hopkinson pressure bar (SHPB) test system and the corresponding low-temperature loading devices (Wang et al. 2016a; Yang et al. 2019; Weng et al. 2020). The results indicated that as the loading rate increased, the mechanical strength and dynamic elastic modulus of rocks increased significantly under fixed temperature and physical properties, which are the same as the research results at room temperature (Ma et al. 2018; Ke et al. 2018). The temperature loading conditions are one of the critical factors in researching rock dynamic characteristics under low-temperature environments. In the natural water-bearing state dynamic mechanical properties of rocks occur temperature strengthening as the environmental temperature increases, and the degree of temperature strengthening is related to the type of rocks (Wang et al. 2019b; Yang et al. 2019; Weng et al. 2020). It is worth noting that the current research focuses on the dynamic mechanical characteristics of rocks under freeze–thaw cyclic loading (Luo et al. 2020; Li et al. 2021b). The research results showed that as the number of freeze–thaw cycles increased, rock’s dynamic strength and dynamic elastic modulus would decrease. This was mainly caused by the changes in rock pore structures under freeze–thaw cycles (Zhang et al. 2018; Seyed Mousavi et al. 2019; Zhou et al. 2020b). In order to explore meso-mechanism of rock macroscopic and dynamic mechanical properties under low-temperature environments, many mesoscopic test methods have been adopted, such as NMR, CT technology, mercury intrusion, etc. (Zhou et al. 2015; Chen et al. 2021). Moreover, the establishment of some theoretical models and the analysis of energy dissipation mechanisms can also provide theoretical support for the study of macroscopic and dynamic mechanical properties change of rocks under low temperature environment (Wang et al. 2016b, 2017; Wang et al. 2019c).

The safety of engineering construction in coal regions is of great significance in winter. As shown in Fig. 1, the rock-soil masses are in freezing period for nearly 1/3 of the year (120 days). Therefore, the key to efficient open-pit coal mining in winter is to clarify the mechanical response characteristics of frozen rocks under the blast and impact loadings. Meanwhile, clarifying the damage and fracture mechanism of frozen rocks under the blasting disturbance is the key to slope safety protection during the blasting mining process. As shown in Fig. 2, open-pit mining may encounter water-rich areas such as springs. The rock mass has saturated water content in the spring areas. The water content will gradually decrease because it is far from the spring area. The change in the water content is the major reason for different rock dynamic mechanical response under low temperature environment. Taking the winter blast mining of Beitashan Pasture Coal Mine in Xinjiang as the research background and the average winter temperature of − 20 °C as the test temperature, this paper will carry out experiments on mechanical properties of sandstone specimens with various water contents under different impact loads by using the LT-SHPB test system. Then based on the energy dissipation theory, it will study the mechanical properties of frozen sandstone under impact loads, the mesoscopic fracture mechanism and the energy dissipation mechanism of macroscopic failure using the SEM test system. The research results are aimed to provide references for open-pit mining in cold regions, blasting and construction of similar geotechnical engineering and the design of rock-soil mass protection parameters.

Fig. 1
figure 1

Temperature variation characteristics of Beitashan Pasture Coal Mine in Xinjiang, China, in 2018 (north latitude 44° 59′ 20″–45° 33′ 20″ and east longitude 90° 16′ 45″–91° 11′ 48″)

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Fig. 2
figure 2

Characteristics of frozen rock-soil mass around the open-pit mine slope spring

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2 The testing scheme

In this testing, the real-time low-temperature SHPB (LT-SHPB) test system was adopted to perform real-time impact compression tests on sandstone specimens with different saturations under low-temperature conditions. There were two processes. Firstly, the processed sandstone specimens were treated with different saturations. Then the impact loading tests were conducted in low temperature environment.

2.1 Specimen preparations

2.1.1 Sandstone specimen preparation

In this testing, the sandstones were taken from the southern slope of Beitashan Pasture Coal Mine in Xinjiang. By X-ray diffraction analysis technology, the main mineral components are quartz (54.6%), muscovite (29.3%), Kaolinite (8.9%), borated muscovite (2.9%) and montmorillonite (4.3%). According to the recommendations on rock dynamics test from the International Society for Rock Mechanics (ISRM), sandstones were processed into cylindrical samples with the dimension of 50 × 50 mm after coring, cutting and grinding, which could meet the requirements of flatness (≤ 0.05 mm) and parallelism (≤ 0.02 mm) at both ends (Zhou et al. 2012; Zhang and Zhao 2014). The basic physical and mechanical parameters of the standard specimens are shown in Table 1.

Table 1 Basic physical and mechanical properties of sandstone samples
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2.2 Treatment of water saturation in specimens

The definition of saturation (water saturation) is given as follows (Liu et al. 2020b):

$$S = \frac{{m_{{\text{s}}} - m_{{\text{d}}} }}{w} \times 100\%$$
(1)

where S is the saturation of the specimen; ms is the specimen mass under various water contents; md is the mass of dry specimens; w is the water content of a fully saturated specimen, which can be calculated by Eq. (2).

$$w = \frac{{m_{{\text{f}}} - m_{{\text{d}}} }}{{m_{{\text{d}}} }} \times 100\%$$
(2)

where mf is the mass of a fully saturated specimen.

The sandstone specimen saturation treatment process is specified in relevant regulations of ISRM on rock saturation test. Firstly, the specimens shall be wholly dried to eliminate the uneven water content of the specimens. Secondly, the dried specimens are completely saturated. Finally, the saturated specimens were prepared into specimens with various saturations. In this testing, the specific process is as follows (Liu et al. 2020b; Huang et al. 2021):

  1. 1.

    Drying treatment: The DHG9076 electric constant-temperature drying oven was used for dying of specimens at 105 °C for 24 h. After 24 h, the specimen was weighed every 1 h until the weight difference was less than 0.02 g. Next, all dried specimens were taken out and put into dryers. The specimens were cooled to room temperature and sealed with bags.

  2. 2.

    Saturation treatment: The dried specimens were put into the negative vacuum pressure air extracting devices. The vacuum pumping was performed for 6 h at an air pressure of − 0.09 MP. Then the distilled water was injected with the negative pressure in the sealed tank. The injection stopped until the distilled water level was higher than the specimen. In the beginning, a large number of bubbles floated on the surface of the specimen. After standing for some time, the bubbles disappeared. At this point, the air pressure in the container was adjusted to the atmospheric pressure. After soaking for 6 h, the moisture on the surface was dried every half an hour. The specimen was difference until the weight difference between two weighings was less than 0.02 g. Finally, the specimens were wrapped in plastic and put into sealed bags.

  3. 3.

    Saturation treatment: According to Eqs. (1) and (2), the average saturation of the sandstone specimens in fully saturated states could be calculated. Then the specimen mass could be obtained under the saturations of 25%, 50% and 75%, respectively. Finally, the processed specimens were dried in a drying box at a temperature of 50 °C. The mass ms was weighed every 1 min. The drying of the entire group of specimens was completed when ms reached the target saturation level.

The prepared specimens with various saturation were wrapped in plastic wrap, sealed with tape and put into the curing box for the impact test (Weng et al. 2021).

Figure 3 shows the process flow of the specimen saturation treatment and low-temperature treatment.

Fig. 3
figure 3

Process flow of the specimen saturation treatment and low-temperature treatment

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2.3 The system and principles of low-temperature impact testing of sandstones

The real-time LT-SHPB was adopted for the impact test, as shown in Fig. 4. The whole system is mainly composed of low-temperature loading, impact loading and drive, pressure bar, data acquisition and processing, and energy absorption systems.

Fig. 4
figure 4

Real-time low temperature rock dynamic mechanics test system

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The low-temperature loading system can provide low-temperature loads for specimens, which can be impacted under real-time low-temperature conditions. The low-temperature loading system contains the low temperature controller, liquid nitrogen container, heating wire, low temperature sensor and low temperature environment room. The aluminum silicate needle blanket was adopted in the low temperature environment room to form the insulating layer, which could ensure the minimum temperature of − 50 °C. During the test, the liquid nitrogen in the container was vaporized into nitrogen under the action of the thermocouple, and flowed into the low-temperature chamber to reduce the temperature of the specimen. The heating wire stopped working when the room temperature detected by the low-temperature sensor reached the preset value. The process was automatically controlled by the solenoid valve. The thermocouple could automatically restart when the room temperature exceeded the preset value. The test results indicated that the room temperature could stay at the preset value, and the temperature difference was within ± 0.2 °C.

Except for the low-temperature loading system, the composition and functions of the other four systems were the same as those of the conventional SHPB test system. During the test, specimens were installed between the incident bar and the transmitted bar according to the test plan. The low-temperature environment room was adjusted to the corresponding temperature, which was kept for 6 h. Then the impact loading was conducted according to the plan. The high-pressure nitrogen drove the striker to hit the incident bar during impact loading. Thus the incident waves were generated and transmitted to the specimen along the incident bar. Part of the incident waves was reflected to the incident bar to form the reflected waves, and the other part was transmitted through the specimen to the transmission bar to form the transmitted waves. In the process, the strain signals were collected by the strain gauge, transmitted to ultra-dynamic strain gauge, and finally saved to the computer.

According to the one-dimensional theory of stress waves, the specimen’s stress σ, strain ε and strain rate \(\dot{\varepsilon }\) could be calculated by the three-wave method, as follows (Lifshitz and Leber 1994; Xia and Yao 2015; Xu and Dai 2018):

$$\left\{ {\begin{array}{l} {\dot{\varepsilon } = \frac{{C_{{\text{s}}} }}{{L_{0} }}\left[ {\varepsilon_{{\text{I}}} (t) - \varepsilon_{{\text{R}}} (t) - \varepsilon_{{\text{T}}} (t)} \right]} \hfill \\ {\dot{\varepsilon } = \frac{{C_{{\text{s}}} }}{{L_{0} }}\int {\left[ {\varepsilon_{{\text{I}}} (t) - \varepsilon_{{\text{R}}} (t) - \varepsilon_{{\text{T}}} (t)} \right]dt} } \hfill \\ {\sigma = \frac{{A_{{\text{s}}} }}{{2A_{0} }}E_{{\text{s}}} \left[ {\varepsilon_{{\text{I}}} (t) - \varepsilon_{{\text{R}}} (t) - \varepsilon_{{\text{T}}} (t)} \right]} \hfill \\ \end{array} } \right.$$
(3)

where Cs is the propagation velocity of the stress wave in the compression bar; εI (t), εR (t) and εT (t) refer to the strain signals of the incident wave, the reflected wave and the transmitted wave, respectively. Es is the elastic modulus of the pressure bar; As is the cross section area of the pressure bar; A0 is the cross sectional area of the sample; L0 is the original length of the sample.

The test temperature was set at − 20 °C to simulate the average winter temperature in Xinjiang. Five groups of specimen saturation were set, that is 0%, 25%, 50%, 75% and 100%. Five groups of impact loads were designed, that is 0.3 MPa, 0.4 MPa, 0.5 MPa, 0.6 MPa and 0.7 MPa. During the test, the saturation and impact load were taken as change factors, and the orthogonal experiment was carried out.

During the test, in order to ensure that test could satisfy two assumptions, the rubber sheet was used as the waveform shaper (Yin et al. 2015; Lin et al. 2021). The improved waveforms are shown in Fig. 5. It could be seen that the superposition of the incident wave and the reflected wave coincides with the transmitted wave, indicating that the test could satisfy the assumption of uniformity. Then the incident wave was stable and the growth time was long, which could provide enough time for the constant stress of two ends inside the specimen. Finally, the three groups of waveforms presented the shape of half sine waves. The waveforms were relatively smooth without obvious transverse oscillations. The test could better meet the one-dimensional stress wave propagation hypothesis (Li et al. 2016, 2017).

Fig. 5
figure 5

Waveforms in the impact loading test

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The laser velocimeter obtained the change laws of the striker impact velocity v with loaded impact pressure P for different specimens during the testing, as shown in Fig. 6. The striker impact velocity has nothing to do with the states of rock specimens. In Fig. 6, the loading and output of the overall equipment were relatively stable. As P increased, v increased rapidly and linearly. As P increased from 0.3 to 0.7 MPa, v increased from 6.82 to 8.98 m/s. According to Eq. (6), the change laws of strain rates \(\dot{\varepsilon }\) with the impact pressure P and the saturation S were obtained under different conditions, as shown in Fig. 7. In Fig. 7a, as P increased, \(\dot{\varepsilon }\) increased rapidly and linearly, and the slope of the line gradually changed with the increase of S. When S increased from 0 to 75%, the linear slope continued to increase, indicating that the sensitivity of \(\dot{\varepsilon }\) to P gradually enhanced. When S increased from 75 to 100%, the linear slope was greatly reduced, and the sensitivity of \(\dot{\varepsilon }\) to P decreased rapidly. With the increase of saturation, \(\dot{\varepsilon }\) first increased and then decreased. When S was 75%, \(\dot{\varepsilon }\) reached the maximum value, as shown in Fig. 7b. Figure 7 showed that the saturation significantly impacted the strain rate, which was directly related to the freezing and frost heave of specimens with different water contents in low-temperature environments.

Fig. 6
figure 6

Variation curves of impact velocity with the impact pressure

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Fig. 7
figure 7

Variation curves of strain rates with the impact pressure and saturation

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In the following analysis, the change in the mechanical properties of sandstones will be analyzed with the strain rate as an independent variable. The failure characteristics and energy dissipation mechanism are related to the energy input, that is, the initial velocity of the striker. Therefore, the striker velocity will also be taken as an independent variable for relevant conclusion analysis (Wang et al. 2020b).

3 Dynamic mechanical response characteristics and microscopic mechanism of frozen sandstones with different saturations

3.1 Dynamic stress–strain curve change characteristics of frozen sandstones

The complete stress–strain curves of frozen sandstone specimens with different saturations at different strain rates were obtained through an impact loading test, as shown in Fig. 8a–e. In order to further compare the influence of saturation on the dynamic stress–strain curves of frozen sandstones, the dynamic stress–strain curves with different saturations at similar strain rates were given, as shown in Fig. 8f. The strain rates were similar, so the loading strain rates were assumed to be the same in the analysis.

Fig. 8
figure 8

Dynamic e stress–strain curves of frozen sandstones under different conditions

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Based on the characteristics of each stress–strain curve in Fig. 8, a typical stress–strain curve of frozen sandstone was obtained under a high strain rate, as shown in Fig. 9. It could be seen that the deformation of the frozen sandstone at low temperatures underwent the compaction stage, elastic deformation stage, plastic deformation stage and post-peak attenuation stage under the action of high strain rate loads. In Fig. 8a–e, with the same saturation, the stress–strain curves of frozen sandstone with different strain rates indicated that the changes in strain rate didn’t change the basic deformation characteristics of the curves, but could significantly change the characteristic dynamic parameters of sandstones, such as peak strain, peak stress and dynamic elastic modulus. In Fig. 8f, under the same strain rate, the stress–strain curves of the frozen sandstones with the saturation of 0 and 100% experienced remarkable compaction stage, In contrast, the other three sets of curves’ compaction stages were shorter or did not exist (Wang et al. 2019a). Additionally, the saturation significantly changed the dynamic mechanical parameters of frozen sandstones.

Fig. 9
figure 9

Dynamic stress–strain curves of frozen sandstones

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3.2 Variation laws of dynamic mechanical characteristic parameters of frozen sandstones

In Figs. 8 and 9, both the strain rate and saturation of specimens significantly impacted the mechanical properties of sandstone. The quantitative analysis was conducted to clarify the specific changes. According to the complete stress–strain curves, the variation laws of the sandstone dynamic compressive strength (peak strength) σs, dynamic elastic modulus Ed and peak strain εs were obtained and illustrated, respectively.

3.2.1 Dynamic compressive strength change characteristics

Figure 10 shows variation laws of frozen sandstone’s dynamic peak strength σs with the strain rate \(\dot{\varepsilon }\) under different saturations S. Under various S, as \(\dot{\varepsilon }\) increased, σs increased rapidly and linearly, showing significant strain rate strengthening. Under five sets of saturations, when \(\dot{\varepsilon }\) increased from the minimum to the maximum, σs increased by 30.56% (S = 0%, σs from 74.24 to 96.93 MPa), 33.19% (S = 25%, σs from 82.25 to 109.54 MPa), 44.43% (S = 50%, σs from 83.37 to 120.41 MPa), 55.45% (S = 75%, σs from 94.55 to 146.98 MPa) and 22.83% (S = 100%, σs from 67.44 to 82.84 MPa), respectively. The overall growth rate firstly increased and then decreased. With S of 75%, σs was mostly affected by the increase of \(\dot{\varepsilon }\). The scope of \(\dot{\varepsilon }\) was different during the loading process, so it is not objective to use the variation amplitude to judge the effects of the saturation on the compressive strength. Therefore, the relationships between dynamic compressive strength and strain rate were linearly fitted, as shown in Fig. 10. It could be found that as S increased, the linear slope first increased and then decreased. When S was 75%, the linear slope was the largest. The linear slope represented the sensitivity of the dynamic compressive strength of frozen sandstones to the strain rate. Within the same strain rate change range, the larger the slope, the greater the increasing amplitude of the dynamic compressive strength, the greater the sensitivity of dynamic compressive strength to the strain rate. It is particularly noteworthy that, within the same strain rate range, when S increased from 0 to 75%, σs gradually increased. While S increased from 75 to 100%, σs was greatly reduced. With S of 100%, σs was much smaller than that under other saturations. The change in the dynamic compressive strength was the same as the change in the sensitivity, which was mainly affected by the internal cracks of frozen sandstone with different saturations and ice.

Fig. 10
figure 10

Variation curves of the dynamic compressive strength of frozen strength

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3.2.2 Variation characteristics of dynamic elastic modulus

According to the slopes of the complete stress–strain curves at the elastic stage, frozen sandstone’s dynamic peak strains were obtained under different conditions. Figure 11 gives variation curves of the dynamic peak strain rates. The variation law of the dynamic elastic modulus was consistent with the compressive strength, presenting great strain rate strengthening. Specifically, under five sets of S, Ed increased by 47.31% (S = 0%, Ed from 10.71 to 15.78 GPa), 57.64% (S = 25%, Ed from 13.07 to 20.60 GPa), 53.43% (S = 50%, Ed from 18.45 to 28.30 GPa), 61.76% (S = 75%, Ed from 22.23 to 35.96 GPa) and 47.29% (S = 100%, Ed from 9.89 to 14.57 GPa), respectively. Meanwhile, the comparison between Figs. 7 and 8 indicated that the effects of saturation on the dynamic elastic modulus and dynamic compressive strength of frozen sandstones were the same. The sensitivity of dynamic elastic modulus to the strain rate increased first and then decreased with the increase of saturation. The changing trend was also true with the same range of strain rate. When S was 75%, Ed and σs were the highest. The change characteristics of the dynamic elastic modulus of frozen sandstones were also closely related to internal cracks of frozen sandstones with various saturations.

Fig. 11
figure 11

Variation curves of the dynamic elastic modulus of frozen sandstones

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3.2.3 Variation characteristics of the dynamic peak strain

According to the coordinates of the peak points of the stress–strain curves, the dynamic peak strain εs of frozen sandstones were obtained under different loading conditions and saturations. Figure 12 shows the change curves of the dynamic peak strain with the strain rate. The change characteristics were the same as those of the former two parameters. As \(\dot{\varepsilon }\) increased, εs increased linearly and rapidly. Under five sets of saturations, εs increased by 28.85% (S = 0%, εs from 12.27 to 15.81‰), 28.13% (S = 25%, εs from 11.59 to 14.85 ‰), 47.05% (S = 50%, εs from 9.84 to 14.47‰), 70.56% (S = 75%, εs from 8.90 to 70.56‰) and 27.27% (S = 100%, εs from 12.91 to 16.53‰), respectively. The comparison of curves indicated that within the exact scope of \(\dot{\varepsilon }\), as S increased, εs decreased first and then increased. When S was 75%, εs was the smallest, opposite to the changes of σs and Ed. The relationships between the dynamic peak strain and the strain rate were fitted. After fitting, the linear slope first increased and then decreased with the increase of saturation. The maximum slope was at 75% saturation, indicating that the sensitivity of εs was the strongest at this point. The value of εs was related to the entire deformation process before the peak. Therefore, internal cracks were the main reason for the difference in the dynamic peak strain.

Fig. 12
figure 12

Variation curves of the dynamic peak strain of frozen sandstones

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3.3 Characteristics of dynamic brittle-ductile transition of frozen sandstones

Sandstone is a typical brittle material. It will exhibit significant ductility characteristics under external loads and environmental conditions (Liu et al. 2020a; Walton 2021). Compared with brittleness, ductility refers to the rock material having prominent plastic deformation characteristics before failure. Therefore, the ratio of the peak and yield strain could be used as the dynamic brittle-ductile parameter of frozen sandstone. The specific equation is as follows (Ai et al. 2016; Tarasov and Potvin 2013):

$$\lambda = \frac{{\varepsilon_{s} }}{{\varepsilon_{c} }}$$
(4)

where λ is the dynamic brittle-ductile parameter; εs is the peak strain, and εc is the yield strain.

Equation (4) could be used to determine the value of λ. The most critical issue was determining the stress–strain curve’s yield point. According to the characteristics of the complete stress–strain curve of the frozen sandstone, the method in Fig. 13 was adopted to fix the yield point. Firstly, the fitting straight line (Line I) was fixed at the linear elastic stage. The peak point was taken as the reference point. Line II was parallel to Line I, intersecting the abscissa at point A. Secondly, according to the coordinates of point A, the values of εd could be obtained. Finally, taking the abscissa 0 points as the starting point, and εd as the gauge length, Line l was made parallel to the ordinate axis. The intersection of Line I and the stress–strain curve was the yield point, corresponding to the yield strain of εc and the yield stress of σc.

Fig. 13
figure 13

Method of determining yield point of the dynamic stress–strain curve of frozen sandstone

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In Fig. 13, according to the characteristics of the stress–strain curve, the frozen sandstone entered the plastic deformation stage before the yield point. The strain from the end of the elastic stage to the yield point was the initial compaction strain. After the yield point, the frozen sandstone entered the microcrack propagation stage. According to statistics, the ratio of sandstone yield strain to peak strain was between 73 and 78% under various conditions, so 75% of the peak stress was uniformly taken as the yield point. According to Eq. (4), λ was 1.33 in a completely brittle state.

According to the stress and strain data, λ could be obtained under various conditions. Figure 14 shows the change curves of λ with the saturation. The discrete value of λ was dynamic, corresponding to each saturation. It could be seen that the strain rate slightly affected λ. Therefore, the average dispersion value could be taken as λ. Std. was the discrete and average values’ standard deviation. Std./s=75 refers to the standard deviation between λ and the average value under various strain rates and S of 75%. In Fig. 14, the sandstones with different saturations exhibited significant toughness under impact load under low temperature environment. As S gradually increased, λ decreased first and then increased. As S increased from 0 to 75%, λ decreased from 2.71 to 2.09, with a decreasing amplitude of 22.88%. The brittleness of frozen sandstone was enhanced. As S increased from 75 to 100%, λ increased from 2.09 to 4.29, increasing by 1.05 times. At this point, the dynamic toughness of frozen sandstone was quickly strengthened. Meanwhile, the standard deviation and saturation were positively correlated. With the increase of S, the standard deviation gradually increased, proving that strain rate’s influence on ductile–brittle characteristics was gradually increasing (Xue et al. 2014).

Fig. 14
figure 14

Variation curves of the dynamic ductile–brittle coefficient with the saturation

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3.4 The mesoscopic mechanism of dynamic mechanical response characteristics of frozen sandstone

3.4.1 The micromechanical behavior of water-bearing sandstone in low-temperature environment

The change laws of the mechanical properties of frozen sandstone indicated that there were apparent strain rate strengthening effects under the same saturation, which is the same as the conclusions of a large number of existing studies (Yang et al. 2019; Weng et al. 2020). In fact, after fixing the environmental conditions and the rock's conditions, the rock’s mechanical properties show significant strain rate strengthening effects under the impact load (Wang et al. 2019b).

Within the same range of strain rate and under low-temperature environments, the influence of saturation on the dynamic mechanical properties of sandstone can be summarized in two stages. As S increased from 0 to 75%, the strength characteristics (peak stress) and stiffness properties (elastic modulus) showed significant saturation strengthening effects. As S increased from 75 to 100%, the saturation weakening effects existed. Figure 15 gives the reasons for such changes. In the original state, the internal microstructure of sandstone was mainly divided into the rock matrix and cracks, pre-existing cavity and free and crystal water. After completely dried, the sandstone only contained the rock matrix, cracks, and pre-existing cavity, as shown in Fig. 15a. During the saturation treatment process, clay minerals such as kaolinite and montmorillonite in the sandstone swelled with water. Thus the cracks and primary cavities were reduced in dimension (Cherblanc et al. 2016; Wang et al. 2021b). Some smaller cavities were closed, as shown in Fig. 15b. After the saturation treatment, the low-temperature treatment of sandstones had two situations: freezing enhancement and frost heave weakening of the mechanical properties. It is well known that the same water quality increased by about 9% in volume after freezing (Huang et al. 2020; Song et al. 2021). The water inside the sandstone was frozen under low saturation. The ice filled the original cracks in the sandstone and acted as the binder for the rock matrix on both sides of the cracks. Meanwhile, the freezing load could effectively reduce the internal porosity of the sandstone. In Fig. 15c, some primary pores in the matrix were filled with ice, and their mechanical properties were greatly enhanced. The enhancement efficiency gradually increased with the increase of saturation (Lin et al. 2021). Under fully saturated conditions, the volume expansion of water after freezing into ice caused extreme frost-heaving load inside the crack and the dimension of the crack increased (Tan et al. 2018; Li et al. 2018; Ke et al. 2021; Wang et al. 2021a). At the same time, new cracks occurred and penetrated the original cracks, as shown in Fig. 15d. The frost heaving caused the internal porosity of the sandstone to increase and the mechanical properties to decrease significantly.

Fig. 15
figure 15

Schematic diagrams of micromechanical behavior of sandstone in low-temperature environment (a. Primary structure of the sandstone; b. Saturation treatment; c. Mechanical behaviors under low saturation; d. Mechanical behaviors under complete saturation

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In order to further illustrate the impact of saturation on the meso-mechanical behavior of sandstone in a low-temperature environment, scanning electron microscopy (SEM) was used to observe the internal micro-structure characteristics of sandstone, as shown in Fig. 16. The observed sections were formed by mechanical cutting and were not subject to impact tests. At a magnification of 100 times, the specimens with different saturations had significant differences after being treated at low temperatures. Under arid conditions (S = 0%), there were a lot of primary defects in the sandstone, including the penetrating cracks and independent cavities free in the rock matrix (Cai et al. 2020a). There were cracks and voids when S was 25%, tbut the dimensions were smaller. Besides, crack closures due to expansion could be observed locally. Large-scale cracks were not observed with S of 20% and 75%. The internal structure of the sandstone was nearly complete, and the porosity was more minor due to the saturated expansion and the binding load of ice. When S was 100%, many frost heave cracks and regionally distributed frost heave defects were caused inside the specimens after the low temperature. Thus, the changes in internal cracks and the effects of freezing loads and frost heave loads were the fundamental reasons for the dynamic meso-mechanical changes of sandstones with different saturations in low-temperature environments (Zhou et al. 2020a).

Fig. 16
figure 16

Meso characteristics of the internal structure of sandstone with different saturation (100 times)

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3.4.2 Mesoscopic characteristics of dynamic fracture of frozen sandstone

SEM was used for frozen sandstone sections with different saturations after dynamic failure. In order to analyze the meso-fracture characteristics of the sections more clearly, the observation images magnified 2000 times were selected, as shown in Fig. 17. After impact failure, the sections of frozen sandstones with different saturations showed apparent differences. When S was 0%, the sandstone fractures were dominated by brittle cleavage steps with slight ductile slippage. There were prominent stripe zones at the upper left, which were formed by the displacement of the rock matrix on both sides under the action of impact load. When S was 25%, 50% and 75%, the sandstone fracture belonged to brittle fracture. The cleavage step entirely occupied the cross-sections of specimens. Some exposed grains were left by brittle fractures and brittle cracks with relatively flat edges. When S was 100%, the cross-sections were nearly all flexible dislocation strips. Dimples could be observed locally with elliptical shapes and superior ductility.

Fig. 17
figure 17

Microscopic morphology of impact failure of sandstone with different saturations (2000 times)

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In the process of brittle fracture, the input energy of external load was mainly used for brittle deformation, and the strength and rigidity of sandstone were high. While ductile fracture, the input energy was consumed in internal plastic deformation, leading to low overall strength and stiffness of specimens. The plastic deformation was significantly increased (Xie et al. 2011; Wang et al. 2020a).

4 Impact failure characteristics and energy consumption mechanism of frozen sandstone with different saturations

4.1 Impact failure characteristics of frozen sandstone

4.1.1 Variation laws of impact failure characteristics

After the impact loading test, the fragments of frozen sandstone under different impact velocities and saturations were collected, as shown in Table 2. The fragments of sandstone specimens were completely broken under all conditions. With the fixed saturation and at a lower impact velocity, the fragments were more significant in volume. As the impact velocity increased, the number of large fragments decreased, and the number of crushed powder particles gradually increased (Zhang et al. 1999). With the increase in impact velocity, the failure of the frozen sandstone was mainly transformed from tensile damage to comminuted compound fracture (Liu and Xu 2013). Under the fixed impact velocity, the number of fragments increased first and then decreased with the increase of saturation. The ratio of large-volume fragments was the highest when S was 75%. When the impact velocity exceeded 8 m/s, there were few large-volume fragments, and the fragments were mainly powder particles.

Table 2 Failure characteristics of frozen sandstone under different saturations and impact velocities
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4.1.2 Quantitative analysis of the impact failure

In Table 2, as the impact velocity increased, the overall dimension of the fragments gradually decreased, and the damage degree increased. At a fixed impact velocity, as the saturation increased, the change law of the damage degree was opposite to that of the mechanical parameters, showing the trend of first decreasing and then increasing. When S was 75%, the failure was the lowest, which was more evident at lower impact velocities. To quantitatively analyze the damage degree, the average particle size was used to quantify the change characteristics of the sandstone damage degree (Hogan et al. 2013).

Firstly, the classifying screen was used to screen the crushed specimens. The particle size ranges of the obtained particle were 0–6, 6–8.5, 8.5–11, 11–13, 13–15 and 15–30 mm, as shown in Fig. 18. 30 mm was the particle size of the largest fragment in this test. Secondly, the fragments in each particle size range were weighed and recorded with the number of i = 1, 2, 3, 4, 5, 6. Finally, Eq. (5) was used to calculate the average particle size of the fragments, that is, the particle size coefficient r (Li et al. 2017).

$$r = \sum\limits_{n = 1}^{6} {W_{iv} d_{iv} }$$
(5)

where Wiv represents the percentage of the mass of the i-th group of particle size fragments to the total mass of specimens; div is the average of the maximum particle size and the minimum particle size within the i-th group of a particle size range.r can be used to judge the average size of the whole fragments of the broken specimen and thus quantify the damage degree. That is, the more significant the r, the lower the damage degree of the sandstone, or vice versa (Li et al. 2017).

Fig. 18
figure 18

Characteristics of fragments after the screening

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After screening and calculations, variation laws of r with S and the impact velocity v were obtained, as shown in Fig. 19. Under the fixed S, as v increased, the average r gradually decreased, indicating that the damage degree gradually increased. With the increase of S, v increased first and then decreased, representing that the damage degree first decreased and then increased. The curve fluctuations indicated that r varied greatly with different S at lower v. The maximum r was 20.74 mm with S of 75%, and the minimum was 13.13 with S of 100%. The difference was nearly 40%. With the gradual increase of v, the overall fluctuation of the curve was more minor and tended to be flat. Mainly when v exceeded 8 m/s, the saturation no longer affected the average particle size. With v of 8.98 m/s, the difference between the largest (S = 75%, 9.62 mm) and the smallest particle size (S = 100%, 8.06 mm) was only 16%

Fig. 19
figure 19

The curved surface change of the particle size coefficient with the saturation and impact velocity

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4.2 Energy dissipation mechanism of impact failure of frozen sandstone

The impact failure of frozen sandstones is a process of energy absorption and release. The initiation, expansion, and penetration of cracks until the failure of specimens are all processes of energy dissipation, which is the essence of macroscopic impact failure (Gong et al. 2021).

4.2.1 Determination and calculation method of energy dissipation parameters

There are many energy consumption parameters in the impact failure of frozen sandstone. The dissipated energy WL and the specific surface energy λω were selected in this paper (Feng et al. 2018a; Gong et al. 2019; Gao et al. 2020).

The calculation method of dissipated energy WL was relatively simple and could be obtained by Eq. (6) using the collected strain data (Wang et al. 2018; Weng et al. 2019).

$$\left\{ {\begin{array}{*{20}l} {W_{{\text{I,R,T}}} = E_{{\text{s}}} C_{{\text{s}}} A_{{\text{s}}} \int\limits_{0}^{t} {\varepsilon_{i,r,t} (t)^{2} dt} } \hfill \\ {W_{{\text{L}}} = W_{{\text{I}}} - W_{{\text{R}}} - W_{{\text{T}}} } \hfill \\ \end{array} } \right.$$
(6)

where WI, WR, WT and WL refer to the incident energy, reflected energy, transmitted energy and dissipated energy, respectively. Es is the elastic modulus of bars of the SHPB test system; Cs is the propagation velocity of the strain wave; As is the diameter of the bar; ε is the strain signal collected on the bar. i, r and t represent the incident, reflection and transmission data, respectively.

The specific surface energy λω refers to the surface energy of sandstone fragments per unit area, which is used to characterize the energy dissipation capacity of the fragments from the matrix. It can be calculated by Eq. (7).

$$\lambda_{\omega } = \frac{{W_{L} }}{{S_{\omega } }}$$
(7)

where Sω is the surface area of all fragments after impact failure.

After the specimen was broken, it was tough to get the surface area of each fragment directly. Therefore, the equivalent transformation method was used to calculate the surface area Sω of the fragment in Eq. (7).

Firstly, the crushed sandstone fragments were screened. The total mass mi of the fragments in each particle size range could be obtained through weighing.

Secondly, the fragments in each particle size range were simplified to spheres of the average size in the particle size range, as shown in Fig. 20. Equation (8) could calculate the number of equivalent spheres in the particle size range.

$$n_{i} = \frac{{m_{i} }}{{4\pi \rho r_{i}^{3} /3}}$$
(8)

where ni is the total number of equivalent spheres in the i-th particle size range, and ri is the radius of the spheres in the i-th particle size range.

Fig. 20
figure 20

Schematic diagram of fragments transformed into spheres after failure

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Finally, the surface area of the new fragments could be calculated by Eq. (9). The first term on the right side of Eq. (9) is the surface area of all spheres, and the sum of the second term and the third term is the outer surface area of the original specimens.

$$S_{\omega } = \sum\limits_{i = 1}^{6} {4n_{i} \pi r_{i}^{2} - 2\pi rh - 2\pi r^{2} }$$
(9)

where r is the radius of the sandstone specimen in the test, and h is the height of the specimen.

By substituting Eqs. (8) and (9) into Eq. (7), the specific surface energy λω of frozen sandstone could be obtained during impact failure under different conditions.

4.2.2 Characteristics of dissipated energy of impact failure of frozen sandstone

According to the strain data collected by the ultra-dynamic strain gauge, the variation law of the dissipated energy WL with v and S could be obtained by Eq. (6) during the impact, as shown in Fig. 21. Under various saturations, as v increased, the dissipation energy increased rapidly in an approximately linear form. As v increased from 6.82 to 8.98 m/s, WL increased by 144.88%, 150.48%, 153.21%, 147.60% and 161.48%, respectively. The overall amplitude of variation was the same. After v was fixed, WL was the largest at S of 75%, and the overall change law was consistent with that of the peak strength and dynamic elastic modulus. The fluctuation of the overall curved surface remained unchanged. In Fig. 16, as S increased from 0 to 75%, the internal morphology of the sandstone specimens became dense, and the internal cracks were reduced. During the impact process, it was necessary to provide more energy to initiate and expand new cracks. Therefore, as S increased, WL was higher under the same input energy. While under fully saturated conditions, less energy was enough for crack expansion and penetration under the same loading conditions due to the existence of cracks and defects induced by the frost heave (Weng et al. 2019).

Fig. 21
figure 21

Curved surface change of the dissipated energy with saturation and impact velocity

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4.2.3 Characteristics of specific surface energy of sandstone fragments after impact failure

According to Eqs. (7), (8) and (9), the area Sω and the specific surface energy λω of all fragments of the sandstone could be obtained after the impact failure. Figures 22 and 23 give the curved surfaces of Sω and λω with S and v.

Fig. 22
figure 22

Curved surface change of the area of the fragments with the saturation and the impact velocity

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Fig. 23
figure 23

Curved surface change of the area of the fragments with the saturation and the impact velocity

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In Fig. 22, as S and v increased, the change of Sω was utterly opposite to that of the particle size coefficient r, which also could explain the change law of the damage degree of the frozen sandstone. As v increased, Sω increased gradually, and the increasing trend slowed down. When v exceeded 8 m/s, the change of Sω was nearly unaffected by S. When S was 75%, Sω was the smallest.

The variation characteristics of specific surface energy λω with S and v differed from those of other mechanical and energy parameters. In Fig. 23, as v increased, λω was different with various S. When S was 0%, 25%, 50% and 100%, the maximum values of λω were at v of 8.49 m/s. When S was 75%, the maximum λω was at v of 7.27. They were not at the place with the maximum v. This was because with a small v, the input energy was less. At this point, only those cracks that were easy to expand could absorb energy and cause visible damage to the specimen. The fragments could separate from the matrix with a small amount of energy. Thus, the specific surface energy of the whole fragments was smaller. When v and the input energy reached the maximum, a large amount of energy was consumed by lots of cracks leading to the failure of specimens. At this point, the damage degree of each fragment was even, and their consumed energy was not the highest. New cracks occurred inside the specimens when v was at an intermediate level. The dense rock matrix was not able to timely derive cracks. The fragments separated from the matrix needed more energy for complete failure. Thus the specific surface energy was relatively high. Under a fixed v, λω was the largest with S of 75%. This was also because the inside of the sandstone was dense, and more energy was needed to ensure the initiation and propagation of cracks under the same input energy.

5 Conclusions

The LT-SHPB test system was used to conduct impact loading tests for sandstone specimens with different saturations. The changes in laws of the dynamic mechanical properties of frozen sandstones were systematically analyzed. During the failure, the meso-fracture mechanism of mechanical properties and the energy dissipation mechanism were revealed. The main conclusions are given as follows:

  1. 1.

    The mechanical parameters of frozen sandstones had significant strain rate strengthening effects. Under the same strain rate, frozen sandstone’s failure strength and elastic modulus were the largest at 75% saturation, while the peak strain was the smallest. At 75% saturation, the sensitivity of the mechanical properties to the strain rate was the strongest.

  2. 2.

    Frozen sandstones showed certain toughness under the actions of impact loads. At 100% saturation, the toughness was the most striking. The meso-structure characteristics showed that the mechanical properties of sandstones with low saturations exhibited significant freeze-strengthening effects in low-temperature environment. At 100% saturation, the weakening of the frost heave could be observed, which caused changes in mechanical characteristics.

  3. 3.

    With the increase of the impact velocity, the frozen sandstone gradually transformed from tensile failure to comminuted compound fracture, and the damage degree gradually increased. The damage degree was the lowest at 75% saturation at a fixed impact velocity.

  4. 4.

    During the impact failure process, the change characteristics of dissipated energy during the failure process of frozen sandstone were consistent with those of mechanical characteristic parameters. As the impact velocity increased, the damage energy consumption gradually increased. The damage energy consumption was the largest, with the same impact velocity at 75% saturation. The change characteristics of the specific surface energy of sandstone fragments were obtained by equivalent transformation. The results indicated that the energy consumption was the largest at the intermediate impact velocity for the fragments to separate from the matrix. The specific surface energy was the largest under the same impact velocity at 75% saturation.