Engineering geological and petrological characterization of paleoweathered rock in the K1/J2 contact zone in the Ordos Basin, China

Various geological processes (mineral composition, structure, tectonics, weathering, etc.) affect the physical–mechanical properties of rock. Petrological and engineering geological characteristics of paleoweathered rock (PWR) from the K1/J2 contact zone are described in detail via field investigation and experimental testing. This PWR exhibits mainly sandy grains and mud structures, layered and massive strata, and calcareous and argillaceous cements; fissures are developed and often filled with argillaceous and detrital materials; nine minerals and seven oxides are present, and quartz is present in each sample. Long-term weathering results in a consistent bulk density and high total porosity due to the transformation of primary minerals into secondary clay minerals, forming PWR that undergoes argillization in water. The axial point load strength (PLS) is the largest among the tested PLSs, followed by the diametral PLS, and the irregular PLS. The uniaxial compressive strength (UCS) varies widely, but the results are reliable. The mineralogical, physical and mechanical properties of the PWR are compared to predict one parameter from another and study their mutual influence. The PLS and UCS of the PWR are negatively correlated with the elastic mineral group (EMG) content, weathering alteration indexes, water content, and total porosity and positively correlated with the quartz content, brittle mineral group (BMG) content, bulk density, real density, and longitudinal wave velocity. The UCS and the PLS, axial (diametral) PLS and irregular PLS are positively correlated. These results provide a theoretical basis for physical and mechanical property prediction of PWR masses and rapid estimation of UCS in engineering.


Introduction
The Ordos Basin is currently the largest coal-producing area in China, and the total amount of coal buried less than 2 km from the surface of the basin is about 2 trillion tons, which accounts for more than 40% of the country's total and is projected to be the country's main energy supply production area over the next 50-100 years (Wang 2017;Zhu et al. 2021). In recent years, large-scale coal mining in some mines in the Ordos Basin has caused the deformation (failure) of overlying strata, a decline in impermeable capacity, the leakage of Cretaceous water bodies, water-sand inrush accidents, and damage to the ecological environment (Guo et al. 2020;Lu et al. 2018;Zhu et al. 2020); and there has been a phenomenon of mining water-sand inrush only occurs in some mines or some working faces of the same mine. Through our statistical analysis of borehole data in the mining area of the Ordos Basin and a large number of field geological surveys, we found that paleoweathered rock (PWR) in the K 1 /J 2 contact zone generally exists in the central part of the Ordos Basin, serving as the key aquifuge directly below the Cretaceous water body; the deformation and destruction of PWR led to the loss of water bodies in the Cretaceous system. The PWR may become a new material source for mine water-sand inrush when encountering argillization and disintegration . The behavior of rock under stress is studied in engineering geological research, and the quantification of engineering geological and petrological characteristics is very useful in the interpretation of rock behavior. Rock properties are actually affected by various geological processes, such as mineral composition and content, structure, tectonics and weathering (Pappalardo et al. 2016;Bieniawski 1989). Therefore, a detailed description of the engineering geological and petrological characteristics of PWR in the K 1 /J 2 contact zone in the Ordos Basin can provide a deep understanding of the properties of PWR and their behavior under stress. It is of great significance to scientifically explain the occurrence of water-sand inrush in some mines (working faces) of the Ordos Basin, as well as the safety of coal mines and the prevention and control of water hazards.
Some physical and mechanical properties of rock depend on geological characteristics, which causes the rock to show inhomogeneity, discontinuity and anisotropy (Douma et al. 2017;Vikram and Ruchika 2012). There are many studies on the geological characteristics of rocks worldwide, mainly focusing on petrography, petrochemistry, structure, physical mechanics, hydrogeology and other characteristics (Zhang et al. 2013;Ulyasheva et al. 2016;Marques et al. 2017;Menningen et al. 2018;Vonto et al. 2020;Han and Bai 2020). Many scholars have been searching for potential relationships between certain geological characteristics and rock mechanical properties (Chatterjee and Mukhopadhyay 2002;Tamrakar et al. 2007;Sousa et al. 2005;Liu et al. 2020a). For example, the mineral composition and contents, density, total porosity, water content and wave speed of rock will affect its mechanical properties and lead to the anisotropy of the rock (Meng and Pan 2007;Cantisani et al. 2013;Undul 2016;Fereidooni 2016;Sun et al. 2017;Wang et al. 2019). Many scholars have carried a considerable amount of research on the relationship between rock point load strength (PLS) and uniaxial compressive strength (UCS) (D'Andrea et al. 1965;Broch and Franklin 1972;Gunsallus and Kulhawy 1984;Hawkins 1998;Kahraman 2001;Quane and Russell 2003;Palchik and Hatzor 2004;Sabatakakis et al. 2008;Basu and Kamran 2010;Heidari et al. 2012;Xiang 1981;Wei 1982;Li and Wong 2013;Wong et al. 2017;Liu and Zhang 2019;Liu et al. 2020b). The above studies have improved the understanding of the macro-and microproperties of rocks. However, so far, there are no reports on PWR in the K 1 /J 2 contact zone. Therefore, this paper has carried out research on the petrological and engineering geological characteristics of PWR in the K 1 /J 2 contact zone to deeply understand the properties of PWR and their behavior characteristics under stress conditions.
In this work, PWR samples were collected from the K 1 /J 2 contact zone in the Ordos Basin to test the mineral composition and contents, chemical element composition and contents, water content, density, total porosity, longitudinal wave velocity, free swelling rate, PLS and UCS of the PWR. The aim is to study the petrological and engineering geological characteristics of the PWR in the K 1 /J 2 contact zone. Through the regression analysis method, the relationship between each feature data type and the degree of influence of each feature data type on the engineering characteristics of PWR are studied. The results of this research prove the possibility of PWR in the K 1 /J 2 contact zone as a new material source for mine water-sand inrush, which is of great significance to the safety of coal mining and ecological environment protection in the Ordos Basin.

Geological setting and sampling site
The Ordos Basin is a multicycle superimposed basin developed on the North China Craton and currently located in the western North China Craton (Xu et al. 2013). In the middle of the Yanshan tectonic movement, during the Late Jurassic to Early Cretaceous, the Ordos Basin developed considerable thrust nappe structures, forming a basin pattern of uplift in the east and subsidence in the west, resulting in the Jurassic Anding Formation and the overlying Cretaceous Zhidan Group (Luohe Formation) being in unconformable contact (Zhang et al. 2007;Jia et al. 2005). The Upper Jurassic strata were intermittently deposited for approximately 20 million years (Huang 2019), and PWR is preserved on the top of the Jurassic Anding Formation. According to the drilling data of the Yingpanhao mining area, PWR is widely present at the K 1 /J 2 contact zone, in Shenmu County (①), Jingbian County (②), the Ansai district of Yan'an city (③), and Ganquan County (④) (Fig. 1a). All outcrops of PWR are found in the K 1 /J 2 contact zone (Fig. 1b). The investigation shows that the PWR is characterized by purple-red to gray coloring and is generally paleoweathered sandstone, sandy mudstone and mudstone. These sedimentary characteristics consistently indicate the arid and hot sedimentary climate in the area. This is consistent with the characteristics of the arid climate reflected by the sporopollen, the specialized combination of Psilunio, and the ostracod Timiriasevia-Darwinula genera found in the research area (Wang 2011).
In this work, the PWR samples of the K 1 /J 2 contact zone were collected from core drilling in the Yingpanhao mining area and field geological survey sampling. The 17 groups of samples are from 5 regions. Each group of PWR samples was tested to determine the mineral composition, chemical element composition, density, total porosity, water content, longitudinal wave velocity, free swelling rate, PLS and UCS. Notably, the diametral and axial loading PLS test specimen diameter was nearly 50 mm, and the lengths were nearly 30 mm and 70 mm, respectively; the size of the test pieces for the irregular lump testing met the following requirements: the shortest side length was 30-80 mm, the ratio of Page 3 of 18 173 the distance between the loading points (D) to the average width of the smallest load surface passing through the two loading points (W) was 0.5-1.0, and the distance from the loading point to the free end (L) was greater than 0.5D. The UCS sample diameter and length dimensions were approximately 50 mm and 100 mm, respectively. A total of 342 PWR samples were prepared for strength testing, but only 306 valid samples were recorded, including 19 samples for the UCS testing (2 failed), 19 samples for the diametral testing (2 invalid), 18 samples for the axial testing (1 invalid) and 286 samples for the irregular lump testing (31 invalid). This paper studies the basic engineering geological properties of the PWR in the K 1 /J 2 contact zone of Ordos Basin, and discusses the potential relationship between mineralogy and physical mechanics, which is of great value and significance to the study of water-sand inrush mechanism of the thick Cretaceous water body damaged by coal mining in Ordos Basin.

SEM
The scanning electron microscope model used in this work is an FEI Quanta TM 250; microstructure and composition

XRD
The X-ray diffractometer model used in this work to perform diffraction analysis of the PWR samples is an X-Ray Diffraction from D8 Advance. The main performance indicators of this instrument were as follows: measurement accuracy: angle reproducibility of ± 0.0001°; radius of the goniometer: ≥ 200 mm; diameter of the angle measuring circle continuously changed; minimum step length: 0.0001°; angle range (2θ): − 110 ~ 168°; temperature range: 20 ~ 1200 °C; maximum output: 3 kW; stability ± 0.01%; and tube voltage 20 ~ 60 kV (1 kV/1 step). Semiquantitative mineralogical analysis of PWR diffraction data was performed using MDI Jade6 diffraction analysis software. The determination of the mineral phase in each sample was achieved by comparison with the standard spectrum of various mineral phases. The semiquantitative analysis of minerals was performed with MDI Jade6 software according to the steps of background deduction, smoothing, peak search and calculation; for each sample, the contents of various minerals were calculated by the K value method, and the relevant values were provided by the PDF card in MDI Jade6 software ). The semiquantitative K value method is as follows: suppose the mixture contains two phases, No. 1 and No. 2, and the characteristic peak intensities of 100% of their relative intensities are measured as I 1 and I 2 ; check the standard card library to determine their K values (K = I/I α -Al 2 O 3 ), which are K 1 and K 2 , respectively; then, 1% =

XRF
The XRF spectrometer model used in this paper is an X-Ray Fluorite Spectroscopy S8 Tiger and was used to analyze the main and trace element types and contents of the PWR samples. The main performance indicators of the instrument are as follows: scanning method: sequential scanning; hardware indicators: power 4 kW, maximum voltage: 60 kV; maximum current: 170 Ma; element detection range: Be(4)-U(92); and detection limit: PPM-100%. In recent years, the chemical index of alteration (CIA), chemical index of weathering (CIW) and plagioclase index of alteration (PIA) have been widely used to reflect the source area degree of weathering and are defined as follows: (Shaldybin et al. 2019;Elena et al. 2015;Farkas et al. 2018).

Test methods of engineering geological properties
The physical and mechanical properties of PWR in the K 1 /J 2 contact zone are tested in accordance with the "Standard for test methods of engineering rock mass" (China EC 2013). The tested physical and mechanical properties of PWR include the water content, bulk density, real density, total porosity, longitudinal wave velocity, free swelling rate, PLS and UCS. Rocks exhibit different engineering properties under different water content states (Majeed and Bakar 2018). To gain a better understanding of the original properties of PWR, this paper tested the water content of the PWR samples in their natural state and calculated it by Eq. (1): where w (%) is the water content of the rock, m o (g) is the sample mass before drying, and m s (g) is the sample mass after drying.
Density, defined as mass divided by volume, is the basic property of rock (Miller 1965) and is closely related to the geotechnical properties of the rock. The volume measurement includes or excludes the voids inside the rock, referred to as the bulk and real density, respectively. The bulk density is tested by the wax sealing method and calculated according to Eq. (2): where ρ bluk (g/cm 3 ) is the bulk density, m s (g) is the drying mass of the bulk sample, m 1 (g) is the mass of the sealed test piece in air, m 2 (g) is the mass of the sealed test piece in water, ρ w (g/cm 3 ) is the density of water (0.998 g/cm 3 at 20 e, and ρ p (g/cm 3 ) is the density of paraffin wax.
The real density is determined with the pycnometer method and is calculated according to Eq. (3): where ρ r (g/cm 3 ) is the real density; m s (g) is the drying mass of the powdered sample; m 1 (g) is the total mass of the bottle and test solution; m 2 (g) is the total mass of the bottle, test solution and rock powder; and Ρ WT (g/cm 3 ) is the density of the test solution, which is the same as the test temperature.
Porosity is one of the important physical properties that control the mechanical properties of rock strength and deformability (Palchik and Hatzor 2002;Sabatakakis et al. 2008;Pappalardo 2015). The total porosity (n) is the ratio of pore volume to sample volume and is calculated according to Eq. (4): where n (%) is the total porosity, ρ bluk (g/cm 3 ) is the bulk density, and ρ r (g/cm 3 ) is the real density. The speed at which ultrasonic waves propagate in the rock depends on the density of the rock and the pores and cracks in the rock (Khandelwal and Ranjith 2010). A UTA-2000 intelligent ultrasonic detector measuring instrument was used to test the longitudinal wave velocity V p of the PWR; the sampling frequency was 10 MHz, and the timing accuracy was 0.1 s. During the test, butter was applied to both ends of the rock sample to better couple the acoustic sensor with the sample. V p was determined by dividing the length of the sample by the time required for the pulse to pass through the sample and was calculated according to Eq. (5): where v p (m/s) is the longitudinal wave velocity, t p (s) is the propagation time of the longitudinal wave in the direct transmission method, and t 0 (s) is the zero delay of the instrumental system.
Rock free swelling refers to the free swelling of rock volume with time under the action of external factors. There are many external factors that affect rock swelling: water penetration, reduction in rock external force, chemical substances (such as sulfide), frost action, etc. (Sun et al. 2013). The PWR in the K 1 /J 2 contact zone studied in this paper is located under a thick Cretaceous water body; the thickness is mainly due to the free swelling of the rock caused by the penetration of water. The free swelling rate of the PWR was investigated through free swelling rate testing of the rock and was calculated according to Eq. (6) (GBT-23516 2010): where V H (%) is the axial free swelling rate of the rock, △H (mm) is the axial deformation of the specimen, and H (mm) is the original height of the specimen. The point load test equipment used is a YXDZ-10 rock point load tester (maximum pressure of 10 kN) and a vernier caliper (Fig. 2). The sample was collected and prepared to avoid cracks. The size of each irregular block specimen was 50 mm ± 35 mm, and the ratio of the distance between the two loading points to the average width of the loading point was 0.3-1.0. In the test, the direction of the minimum size of the test piece was selected as the loading direction. First, the instrument was checked to ensure accurate alignment, then the center of the sample was placed close contact with the loading cone. The pressure was adjusted to zero, and within 10-60 s, a load was applied at a constant speed until the specimen broke. The pressure gauge reading F at the time of failure was recorded, and the size of the broken surfaces of the specimen were measured.
According to the standard procedure of ASTM (1995), the formula for calculating the PLS of rock without size correction is as follows: where P (kN) is the applied load at failure and D e (mm) is the equivalent diameter defined. For the diametral test, the calculation formula of equivalent core diameter D e is as follows: where D (mm) is the distance between two loading points and D' (mm) is the distance between loading points at the moment of specimen failure after penetration of the upper and lower cone ends. For axial and irregular lump tests, the calculation formula of equivalent core diameter D e is as follows: where W (mm) is the average width of the minimum section through two loading points. When the equivalent core diameter is not 50 mm, the PLS index of rock should be corrected. When there are many experimental data and the equivalent core diameter in the same group of samples has multiple sizes not equal to 50 mm, the relationship curve between D e 2 and failure load P should be drawn based on the experimental results, and the corresponding P 50 value when D e 2 is 2500 mm 2 should be found from the curve. The PLS of the rock was calculated as follows: where I s(50) (MPa) is the PLS index of the rock with an equivalent core diameter of 50 mm and P 50 (kN) is the corresponding P value when D e 2 is 2500 mm 2 , as calculated from the P-D e 2 relationship curve. Figure 2 shows the definitions of L, D, D', W 1 and W 2 (the widths at the upper and lower ends of the cross-section). Note that the average width W is defined as W = (W 1 + W 2 )/2. The dimension L is measured from the loading point to the nearest free face. The shape of the irregular lump samples strictly followed the ASTM (1995) standard, which suggests that the D/W ratio should be between 0.3 < D/W < 1 and that L should be ≥ 0.5D. If the measured L, D and W do not meet this requirement, the test is invalidated, and the data are discarded. In addition, if the failure section does not pass through the loading points, the specimen is invalidated. Furthermore, all the samples must be checked to have an equivalent size greater than ten times the mineral grains; otherwise, the test is also invalidated.
The experimental instrument used in this test was a D-1000 electro-hydraulic servo universal testing machine, with a maximum axial load of 1000 kN (Fig. 3). During each test, the test piece was placed in the center of the pressure plate of the testing machine, the ball seat was adjusted, and the two ends of the test piece were in even contact with the upper and lower pressing plates of the testing machine; then, loading at the rate of 0.5-1.0 MPa/s was performed until failure. The failure load (P) and the phenomena that occurred during the loading process were recorded. The UCS of the rock was calculated according to the failure load and the section area of the test piece. The calculation formula is as follows: where R c (MPa) is the rock UCS, P (kN) is the failure load, and A (mm 2 ) is the cross-sectional area of the rock specimen.

Petrological characterization
Through numerous surveys of PWR outcrops in the K 1 /J 2 contact zone, a preliminary understanding of the macrostructure characteristics of PWR has been obtained. The color of PWR is mainly light red to purple-red, light gray to gray, and light green. The structure is dominated by gravel, fine grains, silt grains and pelites, and a few are cryptocrystalline (Fig. 4e, f). The tectonic activity mainly formed layered and massive strata, a few of which are earthy (Fig. 4a-d). The cements are mainly calcareous and argillaceous, with sparse iron cements (Fig. 4a-c). Joints and fractures are developed, often filled with mud and clastic material. The microstructure characteristics of PWR were also observed through SEM images. Paleoweathered siltstone grains are cemented together to form flocculent structure; there are micro cracks between flocs of different sizes, almost no karst caves and holes are developed, and the structure is dense; the flocs are in concave convex contact to form a particle-supported support structure (Fig. 4n). Paleoweathered muddy sandstone grains are mainly flocculent, scattered with small debris particles; pores and fissures are relatively developed, and occasionally karst caves and holes are found, and the structure is relatively dense; flaky debris particles are interspersed between the flocs, mainly line contact, a few are concave convex contact, forming a particle-supported support structure (Fig. 4o). Paleoweathered marl grains are mainly flake particles, with very few floc particles; the pores between the particles are obviously increased, and the karst caves and holes are also obviously developed, and the structure is loose; the flocs are surrounded by flake debris particles, dominated by point contact, with very few line contacts, debris particles contact each other to form a support structure (Fig. 4p). Paleoweathered mudstone grains are mainly flake-like fine particles, occasionally slightly larger ones; the pores between the particles are well developed, and the karst caves and holes are also developed, but they are filled with fine particles and the structure is loose; the fine particles intersect the matrix mixed together, the particles are in point-like contact, forming a support structure (Fig. 4q). The XRD semiquantitative analysis results are shown in Fig. 5, reflecting the mineral composition of PWR in the K 1 / J 2 contact zone in the Ordos Basin. Clearly, all the PWR collected from outcrop sections contains quartz. This is because quartz is the most stable mineral among the detected mineral types; quartz is also one of the most stable minerals on Earth's surface (Sun et al 2013). The remaining detected minerals (calcite, dolomite, albite, muscovite, kaolinite, illite, montmorillonite, and chlorite) vary depending on the sampling location. For example, the calcite of the AS-1 and GQ-2 groups has been weathered and decomposed into other secondary minerals, and the calcite and dolomite of the SM-1 and SM-2 groups have been weathered into other secondary minerals. The rock-forming minerals listed above were identified and described according to the "Geotechnical Investigation and Design Manual" (Lin 1996) and SEM images. Quartz is kidney-shaped or irregular (Fig. 4j), hard and brittle, and has strong resistance to weathering. Calcite often forms crystal clusters and granular or nodular shapes (Fig. 4k) and is brittle. Dolomite is often granular or massive (Fig. 4l) and brittle, with curved surfaces and stripes. Feldspar is often platy or columnar (Fig. 4m) and brittle, with stripes visible on the cleavage surface. Muscovite is flaky or scaly, stacked and elastic. Kaolinite is generally lumpy, flaky, or earthy, with a slippery feel, easily absorbs water, and has a plastic viscosity when wet. Illite is generally earthy, with a greasy feel, and is weaker than muscovite. Montmorillonite is often earthy or cryptocrystalline, with a slippery feel, and swells significantly after being immersed in water. Chlorite is scaly, has a slippery feel, is flexible, and has poor elasticity.
XRF was used to analyze the main elemental composition of the PWR samples, and the results are shown in Fig. 6. The PWR mainly contains 7 kinds of oxides; on the outcrop profile, SiO 2 is the oxide with the largest proportion in most sample groups. Notably, the outcrop sections contain a large amount of Fe 2 O 3 , but XRD analysis of some samples corresponding to these groups (JB-1 to JB-5, JB-7, AS-1, GQ-1, GQ-2) did not detect chlorite, which may have been decomposed into amorphous iron. In Fig. 6, the changes in CIA, CIW and PIA of PWR are also shown. High CIA and CIW values reflect relatively strong weathering in warm and humid climates; conversely, low CIA values reflect relatively weak weathering in cold and dry climates. PIA is suitable for judging the presence of only plagioclase in the host rock; in terms of the degree of weathering in provenance areas without potassium feldspar, the larger the PIA value is, the stronger the degree of weathering (Xu and Shao 2018;Zhao et al 2019). Figure 6 shows that the values of CIA, CIW, and PIA are in the ranges of 6.83-64.64%, 7.01-70.15%, and 3.82-20.38%, respectively; the range variations indicate that the weathering degrees of the PWR samples obtained at different outcrops were quite different.

Physical-mechanical characterization
According to the above testing methodology, we obtained the physical and mechanical properties of the PWR in the K 1 /J 2 contact zone ( Table 1). The water content of the PWR from the different outcrops ranges between 3.86 and 10.23%, with an average of 7.66%; where "mean" represents the average of the experimental test values, and "times" represents the number of experimental tests. The bulk density is between 2.36 and 2.57 g/cm 3 , with an average of 2.43 g/ cm 3 ; the real density is between 2.61 and 2.69 g/cm 3 , which is relatively uniform, with an average of 2.64 g/cm 3 . The total porosity is between 4.11 and 10.27%, and the average is 8.22%. The total porosity is relatively high, which may be due to weathering and internal structure; and the microscopic images and descriptions of the internal structure of PWR samples are shown in Fig. 4j-q and Sect. 4.1, which also reflect the physical characteristics of high porosity. The  longitudinal wave velocity is between 0.78 and 3.82 km/s, and the average is 1.95 km/s. The free swelling rate of PWR is between 12.1 and 51.8%, and the average is 32.9%. According to the experimental results of the irregular sample PLS, the P-D e 2 relationship curve was drawn, and the P-D e 2 linear regression fitting curve formula of each group of irregular samples is shown in Table 2, which also shows the linear regression correlation coefficient r, the determination coefficient r 2 , and the significance F value of the F test. Mathematical statistics theory (Chen et al. 2014) suggests that the correlation coefficient r expresses the linear correlation degree between X and Y as two random variables, − 1 ≤ r ≤ 1: when − 1 ≤ r < 0, X and Y are negatively correlated; when r = 0, X and Y are not correlated; and when 0 < r ≤ 1, X and Y are positively correlated. The coefficient of determination r 2 indicates the degree of fit of a straight line and indicates how well the fitted straight line can reflect the fluctuation in Y, 0 < r 2 ≤ 1: an r 2 value closer to 1 indicates a better fit. The F test was used to determine the linear significance of all independent variables X to Y as a whole; the significance F value is generally less than 0.05, and the smaller the value, the more significant it is (0.05 is actually the significance level, which was artificially set). In Table 2, the JB-1 group data show r = 0.95 > 0, indicating that P and D e 2 are positively correlated; r 2 = 0.9, which is close to 1, indicating a good degree of fit; and the significance F = 5.29E − 8 < 0.05, indicating that for all the samples, D e 2 is linearly significant for P overall. Then, the P 50 value corresponding to D e 2 = 2500 mm was calculated according to the linear regression fitting formula for each group (Table 2), and the PLS index I s(50)axi of each group of irregular samples was calculated according to Eq. (10) ( Table 1). The obtained irregular sample PLS is between 1.13 and 6.61 MPa, with an average of 2.64 MPa.
According to Eqs. (7)-(9), the axial and diametral PLSs were calculated (Table 1). The axial loaded PLS is between 2.65 and 13.41 MPa, with an average value of 5.97 MPa; the diametral loaded PLS is between 1.78 and 8.38 MPa, and the average value is 3.96 MPa. Table 1 shows that for the same group of samples with the same lithology, I s(50)axi > I s(50)dia > I s(50)irr because the direction of the axial point load is approximately perpendicular to the sedimentary layer of the sample, and the loading direction of the diametral point load is approximately parallel to the sedimentary bedding surface, which results in I s(50)axi > I s(50)dia . This result is consistent with the research results of Basu and Kamran (2010). The diametral and axial PLS tests are performed in the dry state, and the irregular sample PLS is tested in the natural moisture state. The PLS of the dry sample is higher than that of the water-containing sample (Jeng et al. 2004;Majeed and Bakar 2018), and the experimental results are consistent with the research results of Hawkins (1998). According to Eq. (11), the UCS of the PWR was calculated (Table 1) to be between 13.65 and 160.69 MPa. The degree of variation in UCS is large, which may be caused by the variation in lithology, cement and degree of weathering; the average UCS is 73.61 MPa. By observing the specimens after uniaxial compression failure, three failure modes can be summarized from the propagation direction of the cracks: shear failure mode (Fig. 3a), compression failure mode (Fig. 3b), and mode in which shear failure and compression failure coexist (Fig. 3c).

Correlations between engineering geological and petrographic properties of PWR
Rocks are composed of mineral aggregates (including crystalline and amorphous minerals) with a certain structure. Therefore, the mechanical properties of fresh rock mainly depend on the mineral composition and relative content of the rock (Liu et al. 2020b). Some scholars believe that rock strength is linearly related to mineral composition and content (Fereidooni 2016;Wang et al. 2019;Pappalardo et al. 2016), while others believe that rock strength is exponentially related to mineral composition and content (Meng and Pan 2007;Pappalardo et al. 2016). As shown in Fig. 5, each group of samples contains quartz, while the other minerals present depend on the sampling location; this variability is Table 2 The P-D e 2 regression equations and coefficient of determination Sample groups P-D e 2 regression equation caused by the different degrees of weathering in different locations. This work attempted to analyze the relationship between PLS, UCS and quartz content of PWR by linear regression and exponential regression. The results show that the correlation coefficient of linear regression is higher than that of exponential regression; the linear regression formula is shown in Table 3, and the PLS and UCS of PWR are positively correlated with the content of quartz, where Qu represents quartz. According to the description of their petrological characteristics, calcite, quartz, dolomite, and albite are brittle and high in hardness and are collectively referred to as the brittle mineral group (BMG); while muscovite, clay minerals, and chlorite minerals are elastic and low in hardness and are collectively referred to as the elastic mineral group (EMG). We analyze the correlation between the strength of the PWR and the BMG and EMG contents, and the results are shown in Table 3. The PLS and UCS of the PWR are positively correlated with the BMG content and negatively correlated with the EMG content. We also tested the free swelling rate of the PWR, and the content of clay minerals in the rock determines the PWR free swelling rate. The free swelling rate of the PWR is linearly positively correlated with the content of the clay minerals, where FSR is the free swelling rate and CM is clay minerals (Table 3). When the rock undergoes weathering, primary minerals will transform into secondary minerals; at the same time, changes in the chemical composition and structure of the rock will lead to the gradual weaken of the rock. The higher the degree of weathering of the rock is, the more serious the degree of destruction, and the worse its mechanical properties. The main chemical elements of the PWR were analyzed by XRF, and three weathering alteration indexes were calculated (CIA, CIW, and PIA) (Fig. 6). We also analyzed the correlation between the strength of PWR and CIA, CIW, and PIA, and the results are shown in Fig. 7. The PLS and UCS of the PWR are negatively correlated with the three weathering alteration indexes, and the correlations between the PLS and the three weathering alteration indexes are higher than those between the UCS and the three indexes.

Correlations between the mechanical and physical properties of PWR
The mechanical properties of rock are affected by its water content. Jeng et al. (2004) studied the influence of water content on the strength of sandstone and found that water saturation and wetting will cause the strength of sandstone to decrease. Majeed and Bakar (2018) studied the influence of water content on the strength of sedimentary rocks and found that the UCS of saturated rock is 40-50% lower than that of dry rock. Wei et al. (2020) studied the influence of water content on the strength of gypsum and found that an increasing water saturation had a weakening effect on the strength of gypsum. The results of the correlation analysis of the strength and water content of the PWR in this paper are shown in Fig. 8. The PLS and water content of the PWR are negatively exponentially correlated (Fig. 8a), UCS is negatively linearly related to the moisture content (Fig. 8f), and an increasing water saturation reduces the strength of the PWR. Chatterjee and Mukhopadhyay (2002) studied the linear correlation between UCS and dry density of reservoir rocks in Italy. Fereidooni (2016) studied eight types of hornfelsic rocks collected from the southern and western parts of the city of Hamedan in western Iran, and found that UCS and I s (50) were linear with density. Wang et al. (2019) studied the exponential correlation between UCS and bulk density of Jurassic weakly cemented sedimentary rocks in western China. In this paper, the correlation analysis results of the PWR strength and the bulk density and real density are shown in Fig. 8. The PLS is positively exponentially correlated with the bulk density and real density (Fig. 8b, c), and the UCS is positively linearly correlated with the bulk density and real density (Fig. 8g, h). Porosity is one of the important parameters that controls rock strength (Pappalardo 2015). The PLS and total porosity of the PWR are negatively exponentially correlated (Fig. 8d), and the UCS is negatively linearly related to total porosity (Fig. 8i). These findings are consistent with previous research results (Chatterjee and Mukhopadhyay 2002;Fereidooni 2016;Wang et al. 2019;Dincer et al. 2004). Some scholars have studied the relationship between rock strength and longitudinal wave velocity, finding that some relationships are linear (Fereidooni 2016;Pappalardo et al. 2016) while others are exponential (Wang et al. 2019). In this paper, there is a positive exponential correlation between the PLS and the longitudinal wave velocity  . 8e), and the UCS has a positive linear correlation with the longitudinal wave velocity (Fig. 8j).

Correlation between the PLS and UCS of PWR
This section describes the regression analysis conducted on the PLS and UCS data of the PWR in the K 1 /J 2 contact zone and the relationship between them, providing a theoretical basis with which engineers can use point load tests to quickly estimate the UCS of PWR in practical engineering applications. There are many studies on the correlation between rock PLS and UCS. Most scholars believe that UCS and PLS are linearly related (D'Andrea et al. 1965;Broch and Franklin 1972;Gunsallus and Kulhawy 1984;Hawkins 1998;Kahraman 2001;Palchik and Hatzor 2004;Sabatakakis et al. 2008;Basu and Kamran 2010;Xiang 1981;Wei 1982;Li and Wong 2013;Liu and Zhang 2019), and a few scholars believe that UCS and PLS are exponentially related (Quane and Russell 2003). We conducted a linear regression analysis on the relationships between the UCS and the PLS, axial PLS, diametral PLS and irregular PLS, and the results are shown in Fig. 9; all the relationships show a positive linear correlation. Whether the UCS obtained from the transformation of the PLS test is accurate and reliable is discussed next. In this paper, the relative error between the UCS obtained from the transformation of the PLS test and the UCS of standard laboratory rock samples is used for verification. The definition of the relative error is as follows (Wang 2015): where R c is the UCS obtained from PLS test conversion and σ c is the UCS of the standard laboratory rock sample. The calculated relative errors of UCS obtained by the PLS relation and ISRM method are shown in Table 4. Using the method described in this paper, the relative error ranges between the UCS values estimated by the PLS testing of samples (irregular, diametral, and axial) and the measured values obtained by standard laboratory rock UCS testing are 5.33-118.99%, 2.24-224.08%, and 1.91-168.77%, respectively; the average values are 43.77%, 69.01%, and 49.13%, respectively. Using the ISRM method, the relative error range between the UCS of PWR samples estimated by the PLS testing of samples (irregular, diametral, and axial) and the measured values obtained by the laboratory standard rock UCS testing are 23. 48-74.65%, 0.48-344.19%, and 17.11-208.15%, and the average values are 55.83%, 98.14%, and 73.63%, respectively. By comparison, the method in this paper is more reasonable than the ISRM method, and the error of the estimated UCS is smaller, which is more suitable for the transformation between the PLS and UCS values of the PWR in the K 1 /J 2 contact zone of the Ordos Basin.