Study on Effects of Mineral and Pore Characteristics on Mechanical Behavior and Acoustic Emission of Sandstone

Abstract

This study conducts acoustic emission (AE) tests on five types of medium-grained sandstones under uniaxial compression coupled with analysis using nuclear magnetic resonance (NMR) and scanning electron microscopy (SEM) techniques. We systematically investigated the relationship among mineral content, pore structure (porosity and pore type), mechanical properties, damage mechanisms, and AE characteristics. The results show that the uniaxial compressive strength (UCS) and modulus of elasticity (E) of sandstones are positively correlated with the content of feldspar and other minerals, while exhibiting an inverse relationship with quartz content. Simultaneously, they are negatively correlated with the porosity and influenced by the percentage of mesopores. The AE energy and cumulative AE energy characteristics are jointly influenced by the pore structure and fracture mechanism. The correspondence between SEM fracture morphological features and the change rule of fractal dimension (D) was established based on fractal theory. Additionally, the crack classification results based on the ratio of rise time to amplitude (RA) and average frequency (AF) align with the macroscopic failure mode. However, the cumulative number of cracks and their corresponding cumulative AE energy are jointly influenced by both the pore structure and the fracture mechanism. The distribution characteristics of the AE dominant frequency are influenced by porosity and correlated with the complexity of internal fracture patterns. Furthermore, the “three-frequency synergistic growth phenomenon” occurs during macroscopic damage. The research findings provide a scientific basis for the assessment and monitoring of sandstone rock stability.

1. Introduction

Rocks, serving as natural porous materials, typically consist of an assemblage of one or more minerals. The physical properties of rocks are influenced by factors such as mineral composition, concentration, size, arrangement, and pore structure. − However, in geotechnical engineering construction, there is a frequent occurrence of rock formations with identical nomenclature but substantial differences in mechanical properties, with sandstone being the most representative example. Therefore, to ensure the safety of geotechnical engineering projects, − it is crucial to investigate the impact of mineral features and pore structure of sandstone on its mechanical properties, destructive mechanisms, and acoustic emission (AE) signals.

The investigation into the mineral composition and particle size of rocks has consistently been a focal point of interest in the field of geotechnical engineering. − Diamantis et al. conducted thin-section identification and uniaxial compression tests on 47 types of rocks, revealing that mineral grain size has a minimal impact on the mechanical characteristics of rocks. Zheng et al. investigated the influence of mineral composition and particle size distribution on the failure of marble through true triaxial tests and particle flow code (PFC) simulation. The results indicated that variations in the grain size and particle quantity have no apparent effect on the failure mode of marble. However, some scholars argue that there is a certain correlation between the mineral characteristics of rocks and their mechanical properties, deformation characteristics, and failure modes. − Han et al. conducted grain-based model (GBM) simulations to study the effects of grain size and mineral content, suggesting that material heterogeneity and mineral content jointly control the type and quantity of microcracks. Du et al. established the relationship between plagioclase content and the strength of sedimentary rocks through uniaxial compression and Brazilian splitting tests. Meng et al. proposed a connection between joint surface roughness and mineral grain size based on direct shear tests on granite. Peng et al., employing GBM modeling, investigated the influence of grain size on the strength of low-porosity, multimineral crystalline rocks, ultimately finding a positive correlation between rock strength and grain size.

AE in rocks signifies the release of localized strain energy through instantaneous elastic waves under external loads. − It encapsulates crucial information about the internal damage processes of rocks. Consequently, AE technology finds widespread application in the research field of rock mechanics. Li et al. conducted uniaxial compression tests on four types of samples, including coal, sandstone, shale, and mudstone. Through the analysis of AE parameters such as amplitude-frequency (AF) and ring-down count (RA), it was observed that coal samples exhibited primarily shear cracks during the fracture process, whereas sandstone, shale, and mudstone predominantly exhibited tensile cracks. Liu et al. investigated the impact of strain rate on granite fracture patterns and AE signals through uniaxial compression tests and impact loading experiments. The results indicated that with an increase in strain rate, tensile cracking became the predominant fracture mode in granite, accompanied by a decrease in the b-value of AE. Zhang et al. studied the mechanical properties and failure mechanisms of sandstone under different dry-wet cycling conditions, concluding that the variation in AE fractal dimension aligned with the softening coefficient of sandstone. The research suggests that traditional AE time-domain parameters (ring count, energy, and amplitude) can only provide a simplistic description of the rock’s failure process. In contrast, frequency-domain parameters carry more comprehensive information about rock fracture, making the study of AE frequency-domain parameters an increasingly focal point for researchers. − Zhang et al., following direct tensile tests on sandstone, observed a correspondence between the dispersion of tensile strength and the complexity of mineral composition. Furthermore, they established a connection between domain frequency signals and the peak strength of the specimens. ,

In summary, existing research findings indicate that the mechanical properties, failure mechanisms, and AE characteristics of rocks are influenced by the mineral characteristics. However, studies of the impact of mineral content and pore structure on the mechanical properties, failure mechanisms, and AE characteristics of sandstone are relatively limited. To address this gap, this study conducted AE experiments under uniaxial compression on five types of medium-grain sandstones. By integrating nuclear magnetic resonance (NMR) and scanning electron microscopy (SEM) techniques, we systematically analyzed the influence of mineral content and pore structure (porosity and pore types) on mechanical performance and failure mechanisms. Additionally, we examined the AE energy counts and cumulative energy counts features of different sandstones. Quantitative analysis of the AE energy using fractal theory further revealed matching patterns between AE characteristics and the internal fracture evolution process. Finally, in conjunction with RA and AF parameters and dominant frequency signal features, we investigated the complexity of microcrack variations and internal failure modes in sandstone. The research results elucidate the mechanisms through which mineral content and pore structure influence the internal fracture behavior of sandstone, providing a reliable basis for the assessment and monitoring of the corresponding rock mass stability.

2. Materials and Method

2.1. Test Material

The sandstone specimens used in this study were collected from two distinct stratigraphic units in China. One set was obtained from the Middle Devonian Tiaomachong Formation (D₂t) in Jishou City, Hunan Province, and the other was obtained from the Upper Triassic Xujiahe Formation (T₃xj) in Ya’an City, Sichuan Province. The Tiaomachong Formation typically comprises littoral to shallow-marine quartz-rich sandstones, while the Xujiahe Formation consists of terrestrial fluvial-lacustrine sedimentary sequences, thereby providing a contrast in depositional environment and initial composition. To ensure lithological consistency, all samples from each quarry were extracted from the same, continuous stratigraphic layer. A total of five types of medium-grained sandstone were selected as representative materials, encompassing variations in mineralogy and pore structure inherent to their respective geological origins.

All samples were prepared in strict compliance with the standards suggested by the International Society for Rock Mechanics and Rock Engineering (ISRM). They were processed into standard cylindrical specimens with a diameter of 50 mm and a height of 100 mm. The end faces were precision-ground to maintain flatness, with nonparallelism controlled within 0.05 mm, thereby ensuring the accuracy and reliability of subsequent uniaxial compression and acoustic emission measurements. The prepared rock specimens are shown in Figure .

1.

Rock samples used in the test.

2.2. Test Equipment

Thin-section petrographic identification was first conducted on standard rock thin sections prepared from dry sandstone samples using a ZEISS Axio Imager A2m polarizing microscope. Observations were carried out under both plane- and cross-polarized light to identify mineral species based on optical properties and to assess their relative abundances and textural relationships. The detailed workflow included: (1) preparing standard-thickness thin sections; (2) observing with the polarizing microscope under transmitted, plane- and cross-polarized light; (3) identifying minerals based on optical characteristics; and (4) estimating mineral contents visually using percentage charts for major phases (>10%), while recording presence and texture for minor phases. Mineral percentage contents and grain size distributions were obtained through visual estimation and comparison with the Chinese standard reference Manual for Identification of Transparent Minerals in Thin Section, without the use of digital image processing software. This methodology is well-established for qualitative-to-semiquantitative petrographic analysis. −

Pore structure analysis was subsequently performed by using a MacroMR12–150H–I NMR analyzer on standard cylindrical core plugs with dimensions of 50 mm in diameter and 100 mm in height. Before NMR testing, all specimens were vacuum-saturated to ensure full pore-water saturation. A CPMG pulse sequence was applied to acquire the T ₂ relaxation distribution, from which porosity and pore-size characteristics were derived.

Uniaxial compression tests were then carried out using a WAW-1000 kN servohydraulic testing system under a displacement-control loading at 0.15 mm/min. AE monitoring during loading was conducted with a PCI-2 digital AE system, using a 40 dB preamplifier gain, a 40 dB threshold, and 1 MSPS sampling frequency. Commercial petroleum jelly was applied between the AE sensor and the specimen surface to ensure proper coupling. Fracture morphology after failure was examined using an electron microscope (model: COXEM EM-30) operated at 15 kV. All instrument settings and procedures were standardized to ensure reproducibility, as shown in Figure . For each sandstone type, three parallel specimens were tested, with additional samples used when an abnormal dispersion occurred.

2.

Test systems: (a) polarization microscope, (b) NMR system (MacroMR12–150H–I), (c) loading and AE system, and (d) SEM system (COXEM EM-30).

According to the characteristics of the pore structure, the sandstones can be divided into two groups: high-porosity sandstones (Rock Nos. 1 and 2) and low-porosity sandstones (Rock Nos. 3–5). Among them, samples from Rock Nos. 3–5 were used to analyze the influence of different mineral contents on their properties.

3. Results and Analysis

3.1. Mineral Characteristics

As shown in Figure and Table , the mineral compositions of the sandstones are broadly similar, consisting mainly of feldspar, quartz, mica, siliceous lithic fragments, and clayey lithic fragments, which form the basic framework of these sandstones. Feldspar exhibits typical characteristics of moderate sorting and rounding, predominantly featuring subhedral to subangular shapes and fine-grained structures. Quartz shares similar characteristics, with interstitial materials primarily composed of brownish clayey components.

3.

Thin-section identification of different sandstones (1 mm).

1. Mineral Characteristics of Different Sandstones.

rock no.	petrographic description
1	The plagioclase grains exhibit moderate roundness and are predominantly subangular. Quartz displays moderate sorting, with a fine-grained structure interspersed with a few coarser particles. Its roundness ranges from subangular to subrounded. Siliceous rock fragments are generally subrounded and consist of cryptocrystalline to fine-grained quartz. Mudstone fragments are subrounded and composed of cryptocrystalline material. Mica appears in flake form, exhibiting parallel extinction and distinct cleavage planes. The filling material is primarily clayey and appears brown.
2	The plagioclase grains are well-sorted, exhibiting moderate roundness and a predominantly subangular shape. Quartz also demonstrates good sorting with a fine-grained structure, and its roundness varies from subangular to subrounded. Siliceous rock fragments range from subangular to subrounded and are primarily composed of cryptocrystalline quartz. The filling material mainly consists of carbonate minerals and clayey components, with the clayey portion appearing brown.
3	The plagioclase grains exhibit moderate roundness and are mostly subangular. Quartz has average sorting, characterized by a fine-grained structure, with roundness ranging from angular to subrounded. Siliceous rock fragments display subangular to subrounded shapes. Mica is present as flakes with parallel extinction and well-defined cleavage planes. Mudstone fragments are subrounded and brown. The filling material is primarily composed of carbonate minerals, with minor clayey components, which also appear brown.
4	The plagioclase grains exhibit good sorting and a fine-grained structure, with poor roundness and a predominantly subangular shape. Quartz, also fine-grained, shows poor roundness and is mostly subangular, with occasional subrounded grains. Siliceous rock fragments are primarily subangular and composed of cryptocrystalline quartz. Mica occurs in flakes, displaying parallel extinction and distinct cleavage planes. The filling material is mainly carbonate minerals, with minor clayey and iron-rich components; the iron-rich portion appears black.
5	The plagioclase grains display average sorting and a fine-grained structure, with moderate roundness, commonly appearing subangular to subrounded. Quartz exhibits average sorting, with grain sizes ranging from fine to medium, and its roundness varies from angular to subrounded. Rock fragments are primarily subangular to subrounded, with dominant lithologies including andesite-breccia and siliceous rock. The filling material varies in color from brown to black and consists mainly of clayey and iron-rich components.

In order to further quantify the mineral characteristics of the sandstone, quantitative statistics of mineral composition and grain size were obtained from petrographic thin-section analysis, and the results are summarized in Tables and . It can be observed that the mineral composition of the sandstone is essentially the same, with feldspar and quartz having particle sizes ranging from 0.1 to 0.5 mm. Therefore, the influence of mineral composition and particle size on the results is not considered in this experiment. Among them, the content of feldspar and quartz in the sandstone is the highest, with feldspar percentages ranging from 25 to 62% and quartz percentages ranging from 22 to 70%.

2. Percentage Mineral Content of Different Sandstones Based on Petrographic Thin-Section Analysis.

rock no.	feldspar (%)	quartz (%)	mica (%)	siliceous rock debris (%)	argillaceous rock debris (%)	filler (%)	opaque mineral (%)	other (%)
1	25	70	0.5	1	0.5	2	1
2	25	66		3		5	0.5	0.5
3	30	60	0.5	3	0.5	4	1	1
4	40	48	1	1		5	4	1
5	62	22		10		3	1	2

3. Mineral Grain Size Distribution of Different Sandstones Based on Petrographic Thin-Section Analysis.

rock no.	feldspar (mm)	quartz (mm)	mica (mm)	siliceous rock debris (mm)	argillaceous rock debris (mm)	filler (mm)	opaque mineral (mm)
1	0.1–0.5	0.1–0.5	0.1–0.3	0.1–0.5	0.1–0.5
2	0.1–0.5	0.1–0.5	0.2–0.3	0.1–0.5	0.1–0.5	0.1–0.3	0.1–0.5
3	0.1–0.5	0.1–0.5		0.1–0.5	0.1–0.5		0.1–0.5
4	0.1–0.5	0.1–0.5		0.1–0.25	0.1–0.25	0.05–0.15	0.05–0.15
5	0.1–0.5	0.1–0.5	0.1–0.3	0.1–0.25	0.1–0.25	0.05–0.2	0.05–0.4

3.2. Pore Structure Characterization of Different Sandstones

NMR technology is based on the nuclear spin properties of hydrogen protons in pore fluids. By measuring the transverse relaxation time (T ₂), the pore structure of rocks can be characterized. , The total area under the T ₂ distribution spectrum is proportional to the total number of hydrogen protons, thus directly reflecting the total porosity of the rock. Meanwhile, the distribution of T ₂ values is related to the pore size and can be converted into a pore-size distribution curve. The T ₂ relaxation process is influenced by multiple mechanisms, and its general expression is

$$\frac{1}{T_2}=\frac{1}{T_{2\mathrm{B}}}+\frac{1}{T_{2\mathrm{S}}}+\frac{1}{T_{2\mathrm{D}}}$$ 1

where T ₂ is the transverse relaxation time, T _2B is the bulk relaxation time, T _2S is the surface relaxation time, and T _2D is the diffusion relaxation time.

Under low-field NMR conditions, the contributions of T _2B and T _2D are typically negligible, and eq can be simplified as

$$\frac{1}{T_2}=F_{\mathrm{s}}\frac{p_2}{r}$$ 2

where ρ₂ is the transverse surface relaxivity, F _s is the pore shape factor, and r is the pore radius.

As shown in eq , the T ₂ value is inversely proportional to the pore radius r. Therefore, the T ₂ distribution can be directly used for the quantitative characterization of pore-size distribution in rocks.

As shown in Figure , the T ₂ spectrum of fully saturated sandstone exhibits a typical “three-peak” distribution, corresponding to micropores, mesopores, and macropores in the sandstone. To quantitatively analyze the pore characteristics of the sandstone, the areas of each spectrum peak and the porosity were statistically analyzed, as shown in Table . It can be observed that the porosity of the sandstone ranges from 7.26 to 13.2%. The combined area of the first and second peaks in the T2 spectrum exceeds 99.1%, indicating that micro- and mesopores constitute the majority of the sandstone pores. Specifically, for Rock No.1, the proportions of micropores and mesopores are 26.5 and 73.3%, respectively, suggesting that mesopores dominate its pore structure.

4.

NMR T₂ distribution curves of different sandstones.

4. Spectral Peak Area and Percentage Statistics of Different Sandstones.

rock no.	total area of T2 spectrum	first peak percentage (%)	second peak percentage (%)	third peak percentage (%)	porosity (%)
1	109174.49	26.58	73.32	0.09	12.86
2	112228.32	42.74	57.07	0.18	13.20
3	66705.18	52.18	47.07	0.73	7.26
4	59031.81	58.54	41.34	0.10	7.57
5	62589.64	44.11	54.95	0.92	7.42

Based on the characteristics of pore structure, sandstones were categorized into two groups: high-porosity (Rock Nos. 1 and 2) and low-porosity (Rock No. 3–5) sandstones. Within the low-porosity group, rock samples 3 to 5 were employed for the analysis of the impact of varying mineral content on their properties.

3.3. Mineral Content and Pore Structure with Mechanical Characterization

The stress–strain curve for the sandstone in this experiment is depicted in Figure . Statistical results for the uniaxial compressive strength (UCS) and elastic modulus (E) are presented in Table . The average UCS values for Rock samples 1 to 5 are 43.31, 51.73, 96.21, 105.36, and 133.8 MPa, while the respective E values are 7.42, 8.35, 13.01, 14.26, and 18.46 GPa. It can be observed that sandstones of the same type exhibit similar mechanical parameters, while different types of sandstone show significant variations in mechanical performance. These differences indicate that the UCS and E of sandstone are jointly influenced by the mineral content and pore structure. To further explore the relationship between them, correlation plots of UCS and E with mineral content and pore structure (porosity, pore type) were generated, as shown in Figure .

5.

Stress–strain curves of different sandstones.

5. UCS and E Statistics of Different Sandstones.

rock no.	uniaxial compressive strength (MPa)	Avg UCS (MPa)	CV UCS (%)	elastic modulus E (GPa)	Avg E (GPa)	CV E (%)
	45.52			7.47
1	39.65	43.31	7.38	7.23	7.42	2.29
	44.78			7.56
	52.95			8.42
2	47.92	51.73	6.88	8.02	8.35	3.39
	54.32			8.63
	101.89			13.54
3	91.12	96.21	4.54	12.98	13.01	2.89
	95.62			12.53
	99.86			15.47
4	110.45	105.36	3.13	12.64	14.26	3.97
	105.79			14.67
	136.35			18.64
5	133.81	133.80	1.34	18.58	18.46	0.23
	131.24			18.16

6.

Relationship between UCS, E, and microstructural characteristics of different sandstones: (a, b) mineral content (feldspar and quartz) and (c, d) pore structure.

As shown in Figure a,b, while samples 1 to 3 possess comparable mineral contents, their UCS and E values exhibit a progressive increase. This trend suggests that the mechanical properties of the rock are not governed by the mineralogical composition but are instead primarily controlled by porosity. From Figure c,d, the porosity of Rock Nos. (1–3) is recorded as 12.86%, 13.20%, and 7.26%, respectively. So, the UCS and E exhibit an increase with decreasing porosity, indicating a negative correlation. Typically, higher porosity implies an increased void space within the sandstone, leading to a weakening of the cohesive forces between mineral particles. Subsequently, elevated porosity alters the relative positions and arrangements of mineral particles, resulting in a weakened internal friction angle. Ultimately, the attenuation of cohesive forces and internal friction angle makes the sandstone more susceptible to failure under stress, leading to a reduction in UCS and E. Additionally, in high-porosity sandstones, Rock No. 1 exhibits a lower porosity than Rock No. 2. However, Rock No. 2 holds a dominant position in terms of UCS and E. This phenomenon is attributed to the fact that their proportions of micropores and mesopores are 26.5% and 42.7%, and 73.3% and 57%, respectively. The higher proportion of mesopores further weakens the cohesive forces and internal friction angle within the sandstone, ultimately leading to a further reduction in UCS and E. Therefore, when the mineral content of sandstone is similar, its mechanical performance is directly influenced by the pore structure (porosity and pore type). In other words, there is a negative correlation between UCS and E of sandstone and porosity, concurrently influenced by the proportion of mesopores.

As shown in Figure c,d, when the pore structure (porosity and pore types) of the sandstones is similar (Rock No. 3–5), their UCS and E are as follows: 96.21, 105.36, and 133.80 MPa; 13.01, 14.26, and 18.46 GPa. Consequently, it is hypothesized that the primary controlling factor influencing the mechanical properties of sandstones is the mineral content. As observed in Figure a,b, the mineral contents of Rocks No. 3 to 5 are as follows: feldspar: 30, 40, and 62%; quartz: 60, 48, and 22%; and other minerals: 10, 12, and 16%, respectively. The sum of feldspar and quartz exceeds 84%, constituting the framework of the sandstone. It can be observed that when the pore structures of sandstones are similar, the UCS and E exhibit a positive correlation with the contents of feldspar and other accessory minerals, showing an opposite trend to that of quartz. This phenomenon can be interpreted from a micromechanical perspective. Feldspar and other minerals contribute to the overall framework stability of the sandstone by improving intergranular bonding and enhancing load transfer between grains, thereby increasing the stiffness and deformation resistance. In contrast, although quartz is inherently a high-strength mineral, its greater brittleness and angular morphology tend to induce local stress concentrations and microcrack initiation under loading. These microcracks propagate along grain boundaries and weak interfaces, ultimately leading to a reduction in the overall UCS and E values of the sandstone.

Therefore, when the pore structure of sandstone is similar, its mechanical performance is directly influenced by the mineral content. In other words, the UCS and E of sandstone are positively correlated with the content of feldspar and cement minerals and negatively correlated with the content of quartz.

3.4. Failure Characteristics of Different Sandstones

As shown in Figure , there are significant differences in the macroscopic failure modes of sandstone in this experiment. As illustrated in Figure a, Rock No.1 exhibits a tensile failure mode characterized by multiple vertically oriented cracks and a small number of transverse cracks that collectively contribute to the failure morphology. As shown in Figure (b–e), Rock No. (2–5) exhibits a shear failure mode, characterized by shear slip rupture surfaces and multiple secondary cracks.

7.

Macroscopic failure modes of different sandstones.

The macroscopic failure pattern of sandstone is closely tied to its microscopic structure. , Consequently, the fracture mechanism was investigated by examining the SEM fracture surface morphology features, as shown in Figure . Therefore, an analysis was conducted in conjunction with Sections and 2.3. As shown in Figure (b–e), Rock Nos. (2–5) exhibit a consistent shear failure mode. Among these, Rock Nos. 2 and 3 share similar mineral content, but they differ in porosity. Similarly, Rock nos. (3–5) display analogous pore structures with varying mineral content. This suggests that neither porosity nor mineral content significantly influences the failure pattern of the sandstone. It is noteworthy that Rock No.1 exhibits a tensile failure mode. This is attributed to the uniform distribution of micropores and mesopores in Rock No. (2–5), whereas Rock No. 1 dominates with a mesopore ratio of 73.3%, placing it in a predominant position. The excessive number of mesopores weakens the interactions among sandstone mineral particles, making stress more prone to concentrate around these mesopores, thereby inducing the generation of microcracks. Simultaneously, when microcracks do not encounter dense particles like quartz, their propagation direction shows minimal deviation, often extending linearly and interfacing with other pores. As shown in Figure a, the SEM images of Rock No.1 predominantly depict the fragmentation and detachment of cementitious material, along with partial crystal fractures. Simultaneously, loose cementitious particles and the presence of pores are observed on the surface. Microcracks mainly originate at the contact boundaries between mineral particles and at the interfaces between mineral particles and the cementitious material, with a few occurring on mineral particles themselves. The sandstone, characterized by a uniform distribution of mesopores and macropores, inhibits the formation and propagation of microcracks between pores and hinders relative sliding between mineral particles, leading to the manifestation of a shear failure mode (Rock Nos. 2–5). As shown in Figure (b–e), the SEM images of Rock Nos. 2 to 5 exhibit a conspicuous increase in transgranular cracking (TG), along with a notable rise in the quantity of loose cementitious particles. This is attributed to the restriction of microcrack propagation at the contact boundaries between mineral particles and the cementitious material, gradually extending into the interior of mineral particles, thereby causing more fractures in the crystals. More detailed fracture information is provided in Figure S1 (Supporting Information), which shows SEM micrographs of postfailure sandstone samples (500×). Figure presents two types of schematic representations of the failure modes.

8.

SEM micrographs of postfailure sandstone samples (200×), TG denotes transgranular cracks.

9.

Failure modes of different sandstones: (a) tensile failure and (b) shear failure.

3.5. AE Energy and Cumulative AE Energy Characteristics of Different Sandstones

As the AE energy directly reflects the intensity of internal microcrack activity, , this section utilizes AE energy counts and cumulative AE energy counts for analysis, as shown in Figure . The time–stress curve of the sandstone is divided into four stages: the initial compaction stage (I), elastic deformation stage (II), yield stage (III), and postpeak stage (IV). Notably, distinct differences exist in the AE energy and cumulative AE energy curves for different sandstones. As shown in Figure a and b, Rock No.1 and Rock No. 2 both exhibit a substantial amount of AE energy signals during the loading process, accompanied by the phenomenon of the cumulative AE energy peak lagging behind the stress peak. This is because sandstones with higher porosity are more prone to deformation under stress, resulting in active AE signals. The lagging phenomenon of the cumulative AE energy peak is attributed to the friction between mineral particles and the closure of microcracks at the peak stress, inhibiting the macroscopic crack extension and maintaining the specimen’s relative integrity under higher stress. Subsequently, as the stress adjusts, internal cracks rapidly expand and interconnect, leading to brittle failure, accompanied by a sharp increase in cumulative AE energy. As shown in Figure (c–e), the AE energy and cumulative AE energy curves for rock samples 3 to 5 exhibit consistent features, revealing three distinct stages: Initial compaction phase (A), quiescent phase (B), and eruptive phase (C). Initial compaction phase (A): In the early stage of Phase I, the native fractures within the sandstone gradually close, leading to the emergence of AE energy signals, which are subsequently manifested as an increase in cumulative AE energy. Quiescent phase (B): With increasing stress, the sandstone is in a phase where native fractures are closing, and new cracks have not yet formed. Consequently, only a small number of AE energy signals are generated. Therefore, the cumulative AE energy remains at an approximately constant level. Eruptive phase (C): As the sandstone enters Phases III and IV, the development of internal cracks becomes active. This activity rapidly expands, leading to instability and failure, resulting in a substantial release of the AE energy and a steep increase in the cumulative AE energy. Since the AE energy and cumulative AE energy curves for Rock Nos. (3–5) share consistent characteristics; it can be concluded that the mineral content of the sandstone has no significant impact on the AE energy curves and AE energy characteristics.

10.

Time–stress-AE energy/cumulative AE energy curves of different sandstones.

When rock samples underwent failure, the cumulative AE energy values for Samples 1 to 5 were 57,874, 95,739, 204,130, 221,334, and 202,071 mV·ms, respectively. Combining Sections and 3.2, it is evident that when the mineral content of the sandstone is similar (samples 2 and 3), the low-porosity sample 3 exhibits a greater cumulative AE energy during failure. Building on Section , the fundamental reason for the discrepancy in cumulative AE energy lies in the different microscopic fracture mechanisms. For Sample 1, the predominant fracture mechanism is the rupture of cementitious material. In contrast, for samples 2 to 5, there is an increased occurrence of crystal deformation and breakage, which are often associated with significant AE energy release. Additionally, low-porosity sandstone possesses a higher degree of cementation and stronger self-confinement capacity, resulting in greater AE energy accumulation during unstable failure.

3.6. Fractal Characterization of AE Energy of Different Sandstones

Research indicates that the internal crack development and evolution process during rock instability exhibits typical nonlinear and self-similar characteristics, with the corresponding AE signals demonstrating distinct fractal features. − Specifically, the variation in fractal dimension (D) values directly reflects the systematic fracture characteristics of the rock’s internal structure. Therefore, building upon section , this section utilizes the G·P correlation dimension algorithm to calculate the D of the AE energy, further quantifying and analyzing the internal structural failure characteristics of the sandstone. The G·P correlation dimension algorithm is implemented as follows:

• (1)
  Taking the AE energy sequence of sandstone during uniaxial compression failure as the research subject, corresponding sets of sequences with a capacity of n are obtained:

  $$x=\{x_1,x_2,x_3,\mathrm{...},x_n\}$$ 3
• (2)
  In the sequence set with a capacity of n, appropriate embedding dimensions (m) and time delays (τ) are chosen for phase space reconstruction. Ultimately, an m-dimensional Euclidean space is established, yielding N = n – (m – 1)­τ phase points from it.

  $$x_n(m,\tau )=\{x_n,x_{n+\tau },\mathrm{...},x_{n+(m-1)\tau }\}$$ 4

  In this context: n = 1,2,3, ..., N; τ = kΔt, where τ represents a fixed time interval with k as a constant, and Δt denotes the time interval between consecutive samplings.
• (3)
  The corresponding correlation functions are expressed as follows:

  $$C[m,r(k)]=\frac{1}{N^2}\sum _{i=1}^N\sum _{j=1}^{N}H[r(k)-\parallel X_i-X_j\parallel ]$$ 5

  where H is the Heaviside function.

  $$H(u)=\{\begin{array}{l}1,u>0\\ 0,u<0\end{array}$$ 6

  In this context: r(k) represents the observation scale, where k takes values from 1 to z (z > 20).

• (4)
  By linearly fitting the double logarithmic coordinate points (C[m, r(k)], r(k)), the slope of the fitting line represents the D of the AE energy sequence if correlation is present.

  $$D(m)=\frac{\ln C[m,r(k)]}{\ln r(k)}$$ 7

  When D ceases to vary within a certain range with the increase of phase space dimension m, this specific phase space dimension m is considered the most suitable embedding dimension. In accordance with current research findings, this paper selects m = 5 as the embedding dimension for the AE energy sequence, as shown in Figure . The time–stress-D curve of the sandstone is depicted in Figure .

11.

Fractal dimension (D) fitting curves of AE energy: (a) Rock No. 1 and (b) Rock No. 2.

12.

Time–stress-D curves of different sandstones.

As shown in Figure , the evolution of D during the sandstone failure process can be classified into two distinct patterns: continuous decrease (Rock No. 1) and continuous fluctuation (Rock Nos. 2–5).The research indicates that the increase or decrease in parameter D typically signifies a reduction or enhancement in the internal structural order of rocks. − As shown in Figure a, for Rock No.1, D undergoes an initial increase from 0.89 to a peak of 2.78 during the early loading phase. Subsequently, a gradual decrease in Stage D is observed, with minor fluctuations occurring in Stage IV, ultimately reaching its minimum value of 0.0079. This phenomenon arises due to the disordered closure and extension of cracks within the sandstone, characterized by uneven sizes and a chaotic distribution during the initial loading phase. − Consequently, there is an enhancement in the chaos of the corresponding AE energy signals, manifested by an increase in the D value.

With increasing stress, microcracks within the sandstone further propagate, interconnect, and orderly aggregate to form localized fracture bands, leading to a continuous decrease in D. In Stage IV, postpeak stress, these localized fracture bands gradually connect and interconnect within the sandstone, ultimately evolving into macroscopic fracture bands that induce instability and failure. Simultaneously, the process of macroscopic fracture band formation involves displacement slip and the compressive failure of internal sandstone crystals. The corresponding AE energy signals exhibit a chaotic state, leading to multiple fluctuations and a subsequent decrease in D to its minimum value. As shown in Figure (b–e), the fractal characteristics of AE energy for rock samples 2 to 5 consistently demonstrate multiple fluctuations in D followed by a decrease to the minimum value. This phenomenon arises from the frequent dislocation and failure of microcracks and crystals within the sandstone during the loading process. Ultimately, these microcracks interconnect, nucleate, and gradually form macroscopic fracture bands in a disorderly and random distribution. The fluctuations in D indicate the dynamic pattern of “adjustment, balance, and imbalance” experienced by microcracks within the sandstone under stress. In summary, the changing patterns of parameter D provide a visual reflection of the nonlinear and dynamic evolution of internal damage in sandstone, capturing both trends and phase-specific characteristics.

The observed variations in the D parameter in this experiment exhibit significant differences, primarily stemming from distinct fracture mechanisms. As indicated in Section , the fracture surface of Rock No. 1 is predominantly characterized by the breakdown of cementitious materials accompanied by partial crystal fractures. In contrast, for rock samples 2 to 5, there is a notable increase in crystal fractures and fragmentation on the fracture surface. The destruction and expansion of cementitious materials in sandstone follow a relatively regular pattern under stress, resulting in the orderly release of AE energy and a sustained decrease in D. Conversely, the increased dislocation and fragmentation of crystals suggest ongoing stress adjustments, leading to a chaotic and disorderly release of AE energy, thus causing fluctuations in D. Based on the aforementioned analysis, the fractal characteristics of AE energy are directly influenced by the fracture mechanisms of the sandstone. The morphological features of the fracture surface can be used to infer the changing patterns of D, indicating a close correlation between the destruction of cementitious materials and crystals and the parameter D. The relationship between the changes in D and the features of the fracture morphology is presented in Table .

6. Characteristics of Cariation in D in Relation to Fracture Morphology.

trends in fractal dimension	fracture morphology characteristics of SEM
continuous decrease	cemented material destruction is dominant, along with mineral crystal fracture
continuous fluctuation	fracture of mineral crystals predominates, together with the destruction of cemented material

3.7. Analysis of the Fracture Mechanism Based on the RA and AF Values

In order to investigate the relationship between the mineral content and pore structure of sandstone and the evolution patterns of microcracks, this section employs a quantitative analysis based on the rise angle (RA) and average frequency (AF) parameters determined from the AE data to scrutinize the characteristics of crack evolution. − The calculation methods for RA and AF are outlined as follows.

$$\mathrm{RA}=\frac{A_{\mathrm{RT}}}{A_{\mathrm{A}}},\mathrm{ms}/\mathrm{V}$$ 8

$$\mathrm{AF}=\frac{A_{\mathrm{C}}}{A_{\mathrm{D}}},\mathrm{kHz}$$ 9

where A _RT is the rise time, A _A is the amplitude, A _C is the ringing count, and A _D is the duration.

Based on the current research findings on the classification of cracks using RA and AF parameters, tensile cracks exhibit low RA values and high AF values, while shear cracks exhibit high RA values and low AF values. , Applying the aforementioned definitions of RA and AF, the RA and AF values for different sandstones under uniaxial compression are calculated, and the quantities of each crack type are statistically analyzed, as shown in Figure . It is evident that the distribution ranges of RA and AF for the sandstones are relatively consistent, with RA values concentrated in the range of 0 to 100 ms/V and AF values concentrated in the range of 0 to 350 kHz. Through statistical analysis, the proportions of tensile and shear cracks for Rocks No. 1 to 5 are as follows: tensile: 73.08%, 30.66%, 26.3%, 26.16%, 31.68%; shear: 26.92%, 69.34%, 73.7%, 73.84%, 68.32%, respectively. Notably, there are significant differences in the proportions of tensile and shear cracks among different sandstones, with Rock No. 1 exhibiting a higher proportion of tensile cracks, while rock samples 2 to 5 are predominantly characterized by shear cracks. However, as indicated in Section , the statistical results of the RA-AF crack classification in sandstone are consistent with macroscopic features of failure.

13.

Characteristics of the RA-AF distribution of different sandstones.

To further analyze the evolution patterns of sandstone fractures during loading, cumulative AE energy curves for tensile/shear fractures and their corresponding counterparts were plotted, as shown in Figure . As stress is applied, both tensile and shear fractures appear simultaneously in different sandstones. Due to the end effect and compaction influence during initial loading, there is a slight increase in crack count. Subsequently, the shear crack count grows slowly, while the tensile crack count shows a noticeable calm period. When stress reaches the stage of instability failure, both types of cracks experience a sharp increase in quantity. It is noteworthy that sample No.1 exhibits a greater accumulation of tensile cracks compared to shear cracks, whereas samples 2–5 demonstrate the opposite statistical characteristic. Additionally, cumulative AE energy curves corresponding to cracks for samples 1–5 show similar trends in variation, yet a significantly higher AE energy is associated with shear fractures. Specifically, the proportions of AE energy corresponding to tensile and shear fractures for rock samples 1 to 5 are as follows: 40.12%, 59.88%; 22.88%, 77.12%; 22.96%, 77.04%; 22.99%, 77.01%; and 21.44%, 78.55%.

14.

Tension/shear cracks and corresponding AE energy curves for different sandstones.

Based on the segmentation outlined in Section , statistical charts depicting the correlation between fractures at various stages and their corresponding AE energies were plotted, as shown in Figure . As shown in Figure a, the proportion of tensile fractures and their corresponding AE energy for Rock No.1 gradually increase during Stages I and II. Subsequently, they reach their maximum values in Stage III, at 82.34 and 56.56%, respectively. Finally, in Stage IV, they decreased to 71.86 and 37.86%. Conversely, the proportion of shear fractures and their corresponding AE energy exhibit a decreasing trend, followed by an increase. As shown in Figures b–e, for Rock Nos. 2–5, there is no clear pattern observed in the proportion of tensile and shear fractures. However, shear fractures dominate in all four stages, with proportions ranging from 58.52 to 77.42%. The variation pattern of AE energy proportions corresponding to tensile and shear fractures aligns with that of Rock No.1. It is noteworthy that the proportion of AE energy corresponding to shear fractures is the smallest, at 56.63%, indicating their predominant position. This is attributed to shear stress causing relative sliding of mineral grains inside the rock, leading to friction and deformation, thus resulting in a higher AE energy. In contrast, tensile fractures form along the direction of extension of the rock’s bonding material, resulting in relatively lower AE energy. In Stage III, there is a phenomenon of a relative increase or decrease in AE energy corresponding to fractures. This is due to intense activity involving the rupture of bonding materials and the friction and fracture of mineral crystals during this stage, leading to relatively small changes in the corresponding AE energy.

15.

Percentage of tension/shear cracks and energy at different stages.

In summary, differences in the evolution characteristics of tension cracks and shear cracks in sandstones are observed and presumed to be related to mineral content and pore structure. As shown in Figure c–e, although the mineral contents of rock samples 3 to 5 differ, the characteristics of crack curves remain consistent, indicating that mineral content does not affect the microcracking evolution pattern of sandstone. During the destructive process, Rock No.1 exhibits significantly more tension cracks than Rock Nos. 2–5, attributable to the high percentage of mesopores in Rock No.1, reaching up to 73.3%. This high mesopore content weakens the cementation property between mineral particles, making microcracks induced by pressure in the mesopores more likely to expand into tension cracks. Additionally, the cumulative AE energy corresponding to shear cracks predominates during sandstone damage. This phenomenon is related to the sandstone’s damage mechanism and is consistent with SEM images (as shown in Figure ).

3.8. Characterization of the Dominant Frequency Evolution of Different Sandstones

Research indicates that the frequency-domain parameters of AE can more effectively reveal internal fracture information within rocks. − Therefore, the main frequency is obtained by applying the Fast Fourier Transform (FFT) to the raw AE waveform data, as shown in Figure . In order to further analyze the pattern of main frequency variation in sandstone during the loading process, a time–stress–main frequency distribution plot is generated, as shown in Figure .

16.

FFT transformation of the AE raw waveform signal.

17.

Differences in dominant frequency distribution among different sandstones.

As shown in Figure , the dominant frequencies of different sandstones are distributed across three intervals: low-frequency (0–20 kHz), mid-frequency (20–60 kHz), and high-frequency (60–160 kHz). It is noteworthy that Rock No. 2 exhibits a mid-frequency range of 20–80 kHz. Additionally, based on the distribution characteristics of high-frequency signals, two types are identified: High-frequency absent type at the beginning of loading (Rock Nos. 1 and 2) and high-frequency discrete type at the beginning of loading (rock samples 3 to 5). As shown in Figure a,b, the low- and mid-frequency signals of Rock Nos. 1 and 2 persist throughout the entire loading process, with high-frequency signals persisting after Stage II and all three frequency ranges experiencing a dense increase in Stages III and IV. As shown in Figure (c–e), the low- and mid-frequency signals of rock samples 3 to 5 span the entire loading process, but a reduction in mid-frequency signals occurs during Stage II. High-frequency signals sporadically appear in Stages I and II, presenting a discrete pattern, and all three frequency ranges show a dense increase in Stages III and IV. Overall, the low- and mid-frequency signals of the sandstone extend throughout the entire loading process. However, in low-porosity sandstones, there is a mid-frequency reduction in the midloading phase, while in high-porosity sandstones, high-frequency signals are absent in the early loading stage.

The literature suggests that the dominant frequencies in AE are generated by internal defects within the specimens, and the distinct frequency bands essentially indicate various failure modes when the specimen undergoes loading. − Since Sections (1–3) have already analyzed the internal fracture conditions and crack evolution characteristics of sandstone, this section investigates the complexity of internal fracture patterns based on the cumulative characteristics of low-, mid-, and high-frequency signals, as shown in Figure . Additionally, a discussion is conducted in conjunction with Sections and 2.3.

18.

Cumulative dominant frequency evolution characteristics of different sandstones.

As shown in Figure a,b, in Stage I, only low- and mid-frequency signals are observed in Rock Nos.1 and 2, with high-frequency signals emerging in Stage II. This is attributed to the increased porosity, enhancing the plasticity of the sandstone and allowing for more extensive deformation, resulting in a relatively simple internal fracture pattern in the early loading stages. With the escalation of stress, signals in all three frequency ranges appear simultaneously and gradually increase. This is due to the enhanced friction among mineral particles and the expansion of fissures within the sandstone, leading to an increased complexity in the internal fracture pattern. As shown in Figure (c–e), Rock Nos. (3–5) exhibit signals in all three frequency ranges during Stage I. This complexity arises from the low porosity of the sandstone, making it susceptible to friction and fracture during the compaction stage, resulting in a more intricate internal fracture pattern in the early loading stages. As stress increases, there is a noticeable plateau in the cumulative mid- and high-frequency signals. This occurs as the sandstone enters the compaction stage, characterized by the closure of pre-existing fissures and the absence of new cracks, leading to a weakening of the complexity in the internal fracture pattern. Rock samples 3 to 5 exhibit similar pore structures but varying mineral content, yet their three dominant frequency cumulative signal characteristics are consistent. This indicates that the mineral content does not impact the complexity of the internal fracture pattern in sandstone. Additionally, different sandstones (Figure a–e) show a dense increase and peak in the cumulative low, mid, and high-frequency signals during unstable failure, demonstrating a phenomenon termed as “synergetic growth of three frequencies.” This phenomenon is intrinsic to sandstone failure and is unrelated to the mineral content and pore structure characteristics. The occurrence of this phenomenon is attributed to the internal crack extension and penetration leading to the formation of a macroscopic fracture surface during sandstone unstable failure. At this point, the fracture pattern becomes more complex, resulting in a dense increase of signals in all three-frequency ranges.

4. Conclusions

In order to investigate the influence of mineral content and pore structure on the mechanical properties and AE characteristics of sandstone, uniaxial compression AE tests were conducted on five types of medium-grain sandstone. Combining NMR and SEM techniques, we systematically analyzed the relationships among mineral content, pore structure (porosity and proportion of pore types), mechanical properties, failure mechanisms, and AE features. The main conclusions are as follows:

• (1)The mechanical properties of sandstone, namely UCS and E, are governed by a dual dependency on mineralogy and pore architecture. A positive correlation is established with feldspar and accessory mineral content, whereas an inverse relationship is observed with quartz content. Concurrently, increasing porosity and the proportion of mesopores detrimentally affect both UCS and E, delineating clear petrophysical controls on mechanical performance.
• (2)The temporal evolution of AE energy and cumulative energy provides a diagnostic signature of the damage process. High-porosity sandstones exhibit persistent AE activity with postpeak energy release, indicative of progressive failure. In contrast, low-porosity variants display a triphasic pattern, compaction, quiescence, and eruption, reflecting distinct energy accumulation and release mechanisms linked to their internal structure.
• (3)Crack-type analysis via RA-AF values corroborates macroscopic failure modes and reveals a pore structure dependency. Tensile cracking predominates in sandstones with a high mesopore ratio, whereas shear cracking is prevalent in more uniformly porous specimens. The consistently higher cumulative AE energy associated with shear cracks underscores the critical role of frictional sliding and grain-boundary interactions during failure.
• (4)The distribution and evolution of AE dominant frequencies are intrinsically linked to porosity, thereby reflecting the complexity of the fracture network. The absence of early high-frequency signals in high-porosity sandstones contrasts with their discrete presence in low-porosity ones. The ubiquitous “synergetic growth of three frequencies” during macroscopic failure emerges as a fundamental AE signature of rupture, independent of mineralogical variations.

In this study, the mineral composition of the rock samples was primarily identified by using thin-section petrography. This method is a time-honored, widely applied, and generally recognized technique in the field of geology for qualitative-to-semiquantitative mineral identification. It is particularly suitable for preliminary mineralogical analysis and rock classification of field-collected samples. However, due to constraints in sample quantity and origin, the broader applicability of the relationships established among mineral composition, pore structure, and mechanical properties requires further validation. Future research should extend sampling and employ multiscale methods to strengthen the generalizability of these findings.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c10657.

• SEM micrographs of postfailure sandstone samples (500×), showing fracture morphology and transgranular cracks (Figure S1) (PDF)

S.T.: Writing-original draft. W.L.: Project administration and methodology. H.L.: Investigation, visualization, and methodology. L.Z.: Formal analysis and data curation. M.Y.: Project administration and methodology.

The authors declare no competing financial interest.