Strength Of Sandstone Research Articles

Study on dynamic characteristics of red sandstone under cyclic impact

In order to study the dynamic characteristics of red sandstone under cyclic impact, the cyclic impact test of red sandstone at the same incident velocity was carried out by E-SHPB test device. Through the analysis and summary of the test data, the influence of cyclic loading times on the dynamic compressive strength of red sandstone and the failure process of red sandstone under the impact of 1000v loading voltage are discussed. The test results show that under the impact of 1000v loading voltage, the peak stress of the specimen decreases linearly with the increase of the number of impacts. The dynamic compressive strength of the specimen under the fifth cyclic impact loading is about 9MPa lower than that under the first impact, and the resistance to deformation is weakened. With the increase of the number of impacts, the cracks in the specimen are continuously generated and expanded, and the specimen is mainly split failure.

Experimental study of volumetric sand production with gas flow

The presence of sand in a production stream has been a common issue for wells drilled in high permeability sandstone formations. In the case of gas producing reservoirs, sand production can be particularly hazardous due to the high gas velocities. It can among others lead to erosion of downhole components and surface equipment and to significant production downtime. A comprehensive experimental study was conducted to investigate the effects of gas flow on sand production. This was accomplished by comparing gas flow tests to tests with oil or water flow. In these tests, hollow cylinder sandstone specimens, initially wet or at ambient humidity conditions, were isotropically compressed under simultaneous fluid injection. One-phase as well as two-phase flow experiments were carried out to simulate important processes encountered in gas fields, like water capillary flow or water-cut. The results showed that sand onset was delayed in the gas flow experiments, which agrees with experimental observations in the literature. The delayed sand onset, i.e., higher sand onset stress, was related to water evaporation due to gas flow, termed flow-through drying, which strengthens the rock. The water-sensitive strength of sandstones was also examined by completing a series of uniaxial compression tests at various water saturations. The analysis of the volumetric sand production data and the X-ray CT-scans of the tested specimens showed that the decreased capillary bonds between grains when only one fluid is present in the pores, e.g., one-phase water or gas flow, results in continuous sand production of individual grains or small-sized flakes, creating large voids in the vicinity of the hole. Under such conditions, the constantly enlarging failure zone eventually causes the total collapse of the specimen. In contrast, specimens with higher capillary cohesion due to a water-oil or water-gas interphase show post sand onset stability and lower sand rate where, due to higher grain to grain cohesion, chunks of failed rock material remain in the hole and provide additional support that prevents the rapid collapse of the specimen even as the applied stress increases.

Strength characteristics and damage constitutive model of sandstone under hydro-mechanical coupling

Abstract To study the mechanical properties of saturated sandstone, experiments were conducted under hydro-mechanical coupling on saturated sandstone. A damage constitutive model was established to describe the response of saturated sandstone under pore pressure, and its validity was verified using the results of the triaxial tests. The results indicate that the peak strength (σ p), effective peak strength (σ p′), residual strength (σ r), effective normal stress (σ n′), effective shear strength (τ n′), elasticity modulus (E), and rupture angle (θ) of sandstone are positively correlated with the confining pressure (σ 3) and negatively correlated with the pore pressure (P). Conversely, Poisson’s ratio (μ) exhibits an opposite relationship. The model parameters exhibit non-linear relationships with the confining pressure (σ 3), with the parameter m decreasing gradually as the confining pressure increases, and the parameter F 0 increasing with higher confining pressure (σ 3). Moreover, the pore pressure (P) and the confining pressure (σ 3) significantly affect the damage variables (D), with the stress value at the damage initiation point increasing with increasing confining pressure (σ 3), while the strain value at the damage initiation point decreasing with increasing pore pressure (P), indicating that pore pressure induces damage development in rocks.

Influence of dynamic load and water on energy accumulation and dissipation in sandstone

In various engineering projects such as mineral extraction, hydropower resource utilization, railway construction, and geological hazard mitigation, rock engineering is often encountered. Furthermore, dynamic loads and moisture content exert notable influence on the energy transformation processes within rocks. Yet, the specific interplay of dynamic loading and water's impact on the energy conversion mechanism within the sandstone remains unexplored. To address this gap, this study conducted impact loading experiments on sandstone, elucidating the rock’s mechanical response under these conditions and unraveling the underlying energy conversion mechanisms. It was observed that the strength of sandstone exhibits a direct correlation with impact velocity. Moreover, employing energy calculation principles, we established a connection between moisture content and the sandstone’s internal energy conversion properties. The study also delved into the microscopic fracture mechanisms within the sandstone, ultimately concluding that both water content and dynamic loading have a significant impact on these microscopic fracture mechanisms.

Prediction model for sandstone strength based on Weibull distribution of micro-element strength and power-law distribution of crack length

It is of the great significance to construct the strength prediction model that considers the influence of the macro and micro defects in the rock in an overall manner to ensure the construction of smart mines and the safety of underground personnel and equipment. Based on the Weibull distribution of rock micro-element strength and the power-law distribution of crack length and the discrete element calculation model, the prediction model for strength of damaged rock specimens were established by numerical simulation and theoretical derivation respectively. Then the rationality of the model was verified by the calculated results. The results show that: 1) The weibull distribution of the micro-element strength and the power-law distribution of the crack length in the PFC2D calculation model are realized by programming, and the quantitative corresponding relationship between the macro, micro and micro damage in the rock and the corresponding distribution parameters is analyzed. 2) 400 sandstone specimens with macro, micro and micro damage are numerically established and loaded to achieve statistical analysis of the relationship between micro element strength, pre-crack information and rock strength. According to the simulation results, the four-dimensional space scatter points of uniaxial compressive strength of sandstone specimens are constructed, and the flow law of compressive strength of sandstone specimens under the influence of multiple damage parameters is obtained. 3) Combined with Mori Tanaka method and rock damage probability distribution theory, a 12 parameter rock strength prediction model is established. The model can both describe the influence of the micro-element strength and macroscopic crack information on the rock strength, and the model calculation results are highly consistent with the simulated results, with the correlation coefficient up to 0.991.

Research and analysis of the impact of the pore structure on the mechanical properties and fracture mechanism of sandstone

Rock pore structure, including porosity, pore size, and particle size, plays a crucial role in determining rock mechanical properties. This study investigates the impact of pore structure on rock mechanical properties through laboratory experiments and numerical simulation methods on sandstones with varying porosity and pore size. The pore structure characteristics of sandstone were determined using XRD, SEM, and NMR microscopic techniques. Additionally, the influence of rock porosity on rock mechanical properties was analyzed by combining Uniaxial compression test with DIC technology, revealing the fracture mechanism caused by porosity in rocks. Numerical models were constructed to simulate sandstones with different porosities and pore diameters, followed by uniaxial compression simulation tests to explore the influence of varying pore diameters on rock mechanical properties and the fracture mechanism. The study reveals the presence of four distinct pore types in the sandstone: micropores in the matrix (0–0.002 µm), intergranular pores (0.002–0.2 µm), dissolution pores (0.2–4 µm), and fracture pores (4–30 µm). Among these, intergranular pores and dissolution pores are the predominant types, accounting for approximately 92–96% of the total pore volume in the sandstone. It is observed that an increase in porosity leads to a decrease in the mechanical strength of sandstone and an increase in Poisson's ratio while keeping the pore size constant. Similarly, when the porosity remains constant, an increase in pore size results in a decrease in the mechanical strength and an increase in Poisson's ratio. Additionally, the study also finds that as the porosity and pore diameter of sandstone increase, the area of internal equivalent stress expands, leading to a shorter crack initiation time and accelerated crack penetration speed, ultimately resulting in a decline in the mechanical properties of sandstone. Numerical simulation experiments further demonstrate that large pores exhibit higher stress concentration compared to small pores, thereby exerting a more significant influence on the mechanical properties of sandstone.

Reactivation of variably sealed joints and permeability enhancement in geothermal reservoir rocks.

The online version contains supplementary material available at 10.1186/s40517-023-00271-5.

Simulation Experimental Investigations into the Mechanical Response and Failure Mechanisms of Coal–Rock Combinations

The stability of the composite structures formed by coal pillar and roof rock is of great significance to safe production and sustainable development of coal mines. In order to explore the failure and instability mechanisms of coal–rock combinations (CRCs) with varying rock-to-coal height ratios, uniaxial compression tests of CRCs with varying rock-to-coal height ratios were performed via laboratory tests and numerical simulation of particle flow tests, and the mechanical response and failure mechanisms of CRC were comprehensively investigated with regard to their strength, failure characteristics, crack and energy evolution. The results show that the stress thresholds for the crack initiation, uniaxial compressive strength, and elastic modulus of CRCs rose with the decreasing coal-to-rock height ratio, and the fragmentation degree of the coal samples increased with rock-to-coal height ratio. The instability and failure of CRCs are the result of the interaction between the strength of sandstone and coal at the interface and the strength of sandstone and coal far from the interface region; in addition, they are influenced by the distribution range of microfractures during the loading process. The point effect and slip effect formed by coal failure cause sandstone split failure and shear failure, respectively. The number of cracks, macrocrack length, total input energy, elastic strain energy, and dissipated strain energy all reduce first and then increase as the coal thickness reduces. CRCs still have a certain load-bearing capacity in the post-peak stage, mainly due to their strong load-bearing skeleton structure and the friction between particles in the fracturing area, which can resist external forces.

Experimental Study on the Dilatancy Characteristics and Permeability Evolution of Sandstone under Different Confining Pressures

It is of practical significance to investigate the dilatancy and seepage characteristics of tight sandstone gas under different confining pressures for its efficient development. Therefore, fluid–solid coupling triaxial loading experiments with gas-bearing sandstone were conducted. The results showed that the gas-bearing sandstone exhibited brittle characteristics with tensile–shear composite failure. The dual logarithmic model can better characterize the sandstone strength (R2 = 0.9952), whereas the fitting effect of the linear Mohr–Coulomb criterion is poor (R2 = 0.9294). The dilatancy capacity of sandstone was negatively correlated with confining pressure, and the dilatancy index decreased by 38.4% in the form of its convex power function with the increasing confining pressure. The sandstone underwent significant damage dilatancy during the yielding stage, resulting in a significant permeability recovery, with an increase of 67.0%~70.4%, which was greater than the decrease of 9.6%~12.6% in the elastic stage. In view of the different dominant factors of permeability reduction induced by pore compaction and recovery induced by crack development, the permeability model was established with volumetric strain and radial strain as independent variables, which could better reflect the whole process of permeability evolution.

Mohr–Coulomb and Modified Hoek–Brown Strength Criteria of Layered Sandstone Considering the Unloading Effect and Anisotropy

The Mohr–Coulomb (M-C) and Hoek–Brown (H-B) strength criteria are widely used in various engineering fields, such as mining engineering, tunnel engineering and so on. To investigate the M-C and H-B strength criteria considering the unloading effect and anisotropy, series of triaxial loading (unloading) tests on layered sandstone were conducted. The results revealed that the peak strength was significantly affected by the unloading effect. Moreover, the cohesion and internal friction angle had a significant nonlinear relationship with the bedding angle. Additionally, the M-C and modified H-B strength criteria were established considering the unloading effect and anisotropy. Then, according to the strength criteria established, the peak strength could be estimated theoretically. Furthermore, compared to the M-C strength criteria, the modified H-B strength criteria were more appropriate for accurately estimating the triaxial compressive strength of layered sandstones. The conclusions obtained could provide certain references for the stability control of deep excavation engineering.

Numerical Simulation of Uniaxial Compressive Strength and Failure Characteristics of Non-Uniform Water-Bearing Sandstone.

As complex and heterogeneous materials, the mechanical properties of rocks are still in need of further investigation regarding the mechanisms of the effects of water. In engineering projects such as goaf foundation treatment and ecological restoration, it is particularly important to describe the fracturing process of non-uniform water-containing sandstone media. The study utilized the theory of continuum mechanics to adopt an elastoplastic strain-softening constitutive relationship and develop a numerical model for analyzing the uniaxial compressive strength and failure characteristics of non-uniform water-containing sandstone. The results indicate that, compared with the reference rock sample, the shorter the capillary path of water entering the rock sample's internal pores or the larger the contact area with water, the shorter the time required for the rock sample to be saturated. Increasing the water content causes a rapid decline in the rock sample's elastic modulus and intensifies its brittleness. Group D2 and D3 samples exhibited a decrease in average peak strength to 70.4% and 62.1%, respectively, along with a corresponding decrease in the elastic modulus to 90.78% and 76.55%, indicating significant strain softening. While the failure mode of the rock sample remains consistent across different water contents, the homogeneity of failure shows significant variation. Increasing volumetric water content raises the likelihood of interconnecting cracks between rock samples, resulting in a progressive decline in macroscopic mechanical properties such as peak strength, critical strain, and elastic modulus. This research is significant in advancing the theory and construction technology for ecological restoration in goaf areas.

Degradation of physico-mechanical properties and damage mechanisms of sandstone under the combined action of freeze–thaw cycles, chemical solution, and compressive stress

Rocks in cold regions subjected to freeze–thaw cycles are often affected by the surrounding hydro-chemical solutions and external load. In this study, the evolution of physical and mechanical characteristics and the damage mechanism of sandstone under the combined action of freeze–thaw cycles, chemical solution, and compressive stress were investigated. A series of quick cyclic freeze–thaw tests in different chemical solutions and stress levels were conducted. The dry mass, wave velocity, and compressive strength decrease as the number of freeze–thaw cycles increases. The variations in dry mass, wave velocity, and rock appearance indicate that lower stress levels (<0.5σ0, σ0 is the saturated uniaxial compressive strength of the original specimen) can limit the effect of repeated freeze–thaw cycles and chemical corrosion, whereas higher stress levels (>0.5σ0) can exacerbate the combined effect on rock damage. In addition, a modified decay model is proposed that incorporates the initial properties and residual integrity of the rock to describe the evolution of rock strength and wave velocity. Both the residual strength and wave velocity of sandstone are constants that are independent of stress level and chemical solution. The degradation rate of compressive strength increases abruptly at higher stress, whereas that of wave velocity generally decreases with increasing stress level. The continuous action of the cyclic frost-heaving force, hydrolysis and chemical corrosion, and external compressive stress promote generation and propagation of pores and microcracks, causing deterioration of the mass, wave velocity, and compressive strength.

Experimental Study of the Mechanical and Acoustic Emission Characteristics of Sandstone by Using High-Temperature Water-Cooling Cycles

In order to study the physical and mechanical properties of sandstone under high-temperature water-cooling cycling conditions, an RMT-150B electrohydraulic servo rock testing system and a DS-5 acoustic emission detection and analysis system were used to conduct uniaxial compression acoustic emission tests on sandstone after high-temperature water-cooling cycles. The deformation, strength, and acoustic emission characteristics of sandstone were analyzed under different temperatures and cycle times. The results show that the high-temperature water-cooling effect caused changes in the physical properties of sandstone. The volumetric expansion rate of the rock samples first decreased, then increased in temperature, and the strength first increased, then decreased, whereas the number of cycles had less of an impact on the physical properties. At 200 °C, with increased cycle number, the elastic modulus increased by 20.1%, and the compressive strength increased from 63.9 MPa to 71.46 MPa. At 300–600 °C, the elastic modulus and compressive strength of sandstone gradually decreased with increases in the temperature and cycle number, with reductions of 6.04%, 7.24%, 28.7%, 35.57%, 17.6%, 18.2%, 20.4%, and 60.5%, respectively. With increased temperature and cycle times, the acoustic emission ringing counts increased, ringing counts and cumulative energy appeared earlier, the rock samples entered elastic deformation earlier, the yield stage length increased, and the samples showed a tendency to transition from brittle to ductile damage.

Study on Brittleness Characteristics and Fracturing Crack Propagation Law of Deep Thin-Layer Tight Sandstone in Longdong, Changqing

Tight-sandstone oil and gas resources are the key areas of unconventional oil and gas resources exploration and development. Because tight-sandstone reservoirs usually have the characteristics of a low porosity and ultralow permeability, large-scale hydraulic fracturing is often required to form artificial fractures with a high conductivity to achieve efficient development. The brittleness of rock is the key mechanical factor for whether fracturing can form a complex fracture network. Previous scholars have carried out a lot of research on the brittleness characteristics of conglomerate and shale reservoirs, but there are few studies on the brittleness characteristics of sandstone with different types and different coring angles in tight-sandstone reservoirs and the fracture propagation law of sandstone with different brittleness characteristics. Based on this, this paper carried out a systematic triaxial compression and hydraulic fracturing experiment on the tight sandstone of Shan 1 and He 8 in the Longdong area of the Changqing oilfield. Combined with CT scanning cracks, the brittleness characteristics and fracturing crack propagation law of different types and different coring angles of sandstone under formation-confining pressure were clarified. The results show that there are great differences between different types of sandstone in the yield stage and the failure stage. The sandstone with a quartz content of 100% has the highest peak strength and a strong brittleness. Sandstones with a high content of natural fractures and dolomite have a lower peak strength and a weaker brittleness. There are also differences in the peak strength and fracture morphology of sandstone with different coring angles due to geological heterogeneity. The sandstone with a comprehensive brittleness index of 70.30 produces a more complex fracture network during triaxial compression and hydraulic fracturing than the sandstone with a comprehensive brittleness index of 14.15. The research results have important guiding significance for on-site fracturing construction of tight-sandstone reservoirs.

Direct tensile mechanical properties and damage fracture mechanisms of thermally damaged coal measures sandstone under high strain rate loading

The direct tensile mechanical properties of highly thermally damaged rock under high strain rate loads are a key basic mechanical problem that must be solved for the stability and effective control of surrounding rock stability in the combustion control area of an underground coal gasification project. In this paper, a two-dimensional equivalent grain-based model (GBM) unit and Split Hopkinson Tension Bar (SHTB) numerical model for thermally damaged coal-measures sandstone were constructed using particle flow code (PFC). The comparison with the experimental results shows that the numerical method can accurately describe the dynamic direct tensile behavior of thermally damaged sandstone. The following conclusions are drawn: The dynamic tensile strength of thermally damaged sandstone shows a significant strain rate-strengthening effect. With the increase in thermal damage temperature, the dynamic tensile strength of sandstone increases first and then decreases. The generation and development of hot cracks in a high-temperature environment is the fundamental reason for the change in macroscopic mechanical properties. The dynamic tensile failure process of thermally damaged sandstone can be divided into four stages: the dynamic damage initiation, the dynamic damage development, the damage crack penetration, and the sample dynamic fracture. With the increase in impact velocity, the initial kinetic energy, elastic strain energy, dissipated energy, and elastic strain energy ratio in the failure process of thermally damaged sandstone gradually increase. In contrast, the dissipated energy ratio gradually decreases. As the heat treatment temperature increases, the elastic strain energy and the ratio of elastic strain energy increase first and then decrease.

Numerical analysis on mechanical difference of sandstone under in-situ stress, pore pressure preserved environment at depth

Deep in-situ rock mechanics considers the influence of the in-situ environment on mechanical properties, differentiating it from traditional rock mechanics. To investigate the effect of in-situ stress, pore pressure preserved environment on the mechanical difference of sandstone, four tests are numerically modeled by COMSOL: conventional triaxial test, conventional pore pressure test, in-situ stress restoration and reconstruction test, and in-situ pore pressure-preserved test (not yet realized in the laboratory). The in-situ stress restoration parameter is introduced to characterize the recovery effect of in-situ stress on elastic modulus and heterogeneous distribution of sandstone at different depths. A random function and non-uniform pore pressure coefficient are employed to describe the non-uniform distribution of pore pressure in the in-situ environment. Numerical results are compared with existing experimental data to validate the models and calibrate the numerical parameters. By extracting mechanical parameters from numerical cores, the stress-strain curves of the four tests under different depths, in-situ stress and pore pressure are compared. The influence of non-uniform pore pressure coefficient and depth on the peak strength of sandstone is analyzed. The results show a strong linear relationship between the in-situ stress restoration parameter and depth, effectively characterizing the enhanced effect of stress restoration and reconstruction methods on the elastic modulus of conventional cores at different depths. The in-situ pore pressure-preserved test exhibits lower peak stress and peak strain compared to the other three tests, and sandstone subjected to non-uniform pore pressure is more prone to plastic damage and failure. Moreover, the influence of non-uniform pore pressure on peak strength gradually diminished with increasing depth.

Dynamic response and energy evolution of sandstone under combined dynamic and static loading

Impact disturbance and bedding angle have a substantial effect on the mechanical response of sandstone under prestressed loading. Therefore, in this paper, a combined 1D static and dynamic loading test system is employed for examining the compression of sandstone at various bedding angles under a pre-applied axial pressure of 25 MPa. Under these conditions, the strength, stress-strain curves, energy usage ratio, particle size and deformation of sandstone are obtained. The results are as follows. (1) Strain rebound easily occurs in high-strength sandstone under low impact pressure. (2) The peak strength of sandstone is positively correlated with the impact pressure. The peak strength and combined dynamic‒static strength of sandstone change in a "v" shape. (3) The rock's failure particle size is controlled by the bedding plane at low impact pressure. (4) We propose a new energy calculation method in which the energy utilization rate presents an approximately inverted "v" shape. (5) The sandstone with different bedding angles has different bursting liabilities at an identical impact pressure. (6) The impact pressure is proportional to the crack growth rate of sandstone.

Experimental and numerical investigation on the dynamic shear failure mechanism of sandstone using short beam compression specimen

In this study, a novel testing method is proposed to characterize the dynamic shear property and failure mechanism of rocks by introducing the short beam compression (SBC) specimen into the split Hopkinson pressure bar (SHPB) system. Firstly, the stress distribution of SBC specimen is comprehensively analyzed by finite element method (FEM), and the results show that the optimal notch separation ratio of SBC specimen is C/H = 0.2 to achieve successful dynamic simple-shear tests. Then, dynamic shear tests are conducted on sandstone using the SBC-SHPB method. Via careful pulse shaping technique, the dynamic force balance is guaranteed for SBC specimens, and the testing results show that the dynamic shear strength of sandstone is significantly rate-dependent. Combining the results of dynamic compression and tension tests, the failure envelopes of sandstone under different loading rates are obtained in the principle stress plane. It is found that the failure envelope of sandstone constantly expands outwards with increasing loading rate. Moreover, the energy partition of SBC specimen is quantified by virtue of high-speed digital image correlation (DIC) technique. The results show that the kinetic energy portion is non-negligible, and the shear fracture energy increases with increasing loading rate. In addition, the microscopic shear cracking mechanism of SBC specimen is analyzed by the thin section observation: the intra-granular (TG) fracture of minerals dominates the dynamic shear failure of sandstone, and the portion of TG fracture increases with increasing loading rate. This study provides a convenient and reliable method to measure the dynamic shear property and failure mechanism of rocks.

Study on microscopic failure mechanism and numerical simulation of sandstone under different saturated pressure

X-ray diffraction and SEM scanning are conducted to examine the alterations in sandstone under different saturation conditions to reveal the water-rock softening effect on sandstone from the Qilicun tunnels in China under varying saturation pressures. The mechanisms underpinning the strength softening of sandstone are analyzed using uniaxial compression tests. The experimental results demonstrated that after immersion in water, the internal cementing material within the sandstone dissolves, and the mineral particles fragment or disintegrate, increasing porosity. In the presence of water, the macroscopic compressive strength of sandstone exhibits a declining trend. Concurrently, as the saturation pressure escalates, the compressive strength diminishes by approximately 10%, the elastic modulus decreases by about 30%, and Poisson's ratio incrementally falls by about 25%. The sandstone's failure is characterized by both axial multiple splitting surface failure and shear failure surface. Finally, a strain-softening numerical model is employed to simulate the failure behaviors of sandstone under various saturation pressures. The findings indicated that the sandstone sample exhibits plastic failure characteristics under high saturation pressure.

Effect of Physical Properties on Mechanical Behaviors of Sandstone under Uniaxial and Triaxial Compressions.

Mechanical properties of sandstone, such as compressive strength and young's modulus, are commonly used in the design of geotechnical structures and numerical simulation of underground reservoirs using models such as the digital groundwater, equivalent porous medium, and Discrete Fracture Network (DFN) models. A better understanding of the mechanical behaviors of sandstone under different loading conditions is imperative when assessing the stability of geotechnical structures. This paper highlights the effect of the physical properties (i.e., porosity, mean grain size) and environmental conditions (i.e., water content and confining stress) on uniaxial compressive strength, triaxial compressive strength, and young's modulus of sandstone. A series of uniaxial and triaxial compression experiments are conducted on sandstone formations from Wyoming. In addition, experimental data on sandstones from the literature are compiled and integrated into this study. Prediction equations for the compressive strengths and young's modulus of sandstone are established based on commonly available physical properties and known environmental conditions. The results show that the mean Uniaxial Compressive Strength (UCS) decreases as the porosity, water content, and mean grain size increase. Furthermore, a predictive empirical relationship for the triaxial compressive strength is established under different confinements and porosity. The relationship suggests that the mean peak compressive strength increases at a higher confinement and decreases at a higher porosity. The results and recommendations provide a useful framework for evaluating the strength and deformation of most sandstone.