Innovation Points

(1) Reveal the effects of fissure angle, filling, and confining stress on the mechanical/failure characteristics of defective sandstone;

(2) In the FEM-CZM simulation, potential fracture surfaces are constructed by globally embedding zero-thickness cohesive elements.

Research Scheme

1.Sample Preparation

Sample source:Homogeneous red sandstone taken from a quarry in Linyi, Shandong, China, with an average bulk density of 2.13 g/cm³, P-wave velocity of 4212 m/s, particle size distribution of 0.1-0.25 mm, and main mineral components of quartz (61.67%), plagioclase (19.38%), etc.

Sample processing:The original rock was processed into rectangular samples of 140×70×30 mm³, and artificial holes (radius 6 mm) and fissures (length 12 mm, width 1.5 mm) were fabricated using water jet cutting technology, with the hole center coinciding with the geometric center of the sample.

Filling treatment:Gypsum was used to simulate weak filling, and a slurry was prepared at a powder-to-water ratio of 3:1. After injection into the prefabricated defects, it was initially cured at room temperature for 24 h, then standard-cured in an environment of 25°C and 95% relative humidity for 28 d. After curing, the uniaxial compressive strength of the filling was 7.52 MPa.

Fig. 1. Information on defective sandstone samples: (a) original location; (b) mineral composition; (c) geometric configuration; (d) final prepared samples.

2. Test Setup and Methods

Test equipment:The JAW-600 servo-controlled testing system was used, with both horizontal and normal loading subsystems having a loading capacity of 0-600 kN and a rate range of 0.01-100 mm/min.

Fig. 2. JAW-600 servo-controlled testing system: (a) system overview; (b) loading system; (c) hydraulic loading cylinder; (d) hydraulic jack; and (e) LVDT

Experimental groups:Four groups of experiments were designed to investigate the effects of fissure angle, filling condition, and confining pressure.

"U" represents uniaxial compression, "B" represents biaxial compression, and "F" represents filled samples.

For the U group and FU group, the fissure angles (α) were 0°, 30°, 60°, and 90°; the B group and FB group included different fissure angles under constant confining pressure (σ₂=1 MPa), and different confining pressures (σ₂=1, 2, 3, 4 MPa) under vertical fissures (α=90°).

Fig. 3. Experimental design: (a) test scheme and (b) nomenclature and sample numbering

Loading method:

For uniaxial compression, the principal stress σ₁ was applied at a constant displacement rate of 0.1 mm/min until sample instability;

for biaxial compression, the confining pressure σ₂ was first applied at a rate of 100 N/s to the preset value, and after stabilization, the axial stress σ₁ was applied at a rate of 0.1 mm/min until complete failure of the sample.

Lubricant was applied to both ends of the samples to reduce end-face friction.

Fig. 4. Loading procedures: (a) uniaxial compression and (b) biaxial compression

3. Numerical Simulation

(1) Constitutive model

Solid elements:The Mohr-Coulomb criterion was adopted.

Cohesive elements:The bilinear traction-separation law was used to define the constitutive behavior, divided into an initial linear elastic stage and a damage evolution stage.

Damage initiation adopted the traction-based quadratic nominal stress criterion, and damage evolution was quantified by the damage variable D.

Fig. 10. Schematic diagram of the bilinear traction-separation law

(2) Numerical model establishment and parameter calibration

Model establishment: A three-dimensional model was constructed in ABAQUS, including the defective rock mass, filling, and rigid loading plates, with geometric dimensions consistent with the experiments and a mesh size of 1.5 mm.

Fig. 11. Establishment of the defective sandstone model: (a) biaxial compression numerical model; (b) filling material model; (c) embedding mechanism of cohesive elements

Parameter calibration: First, uniaxial,triaxial compressionand Brazilian splitting tests were conducted on red sandstone cylindrical samples to obtain basic parameters (as shown in Table 2, uniaxial compressive strength 23.20 MPa, etc.), and then the mesoscopic parameters were iteratively adjusted by the trial-and-error method.

Fig. 12. Calibration process of mechanical parameters of red sandstone specimens. (Readers are referred to the online version of this article for an explanation of the color references in this figure legend.)

Research Results

1. Stress-strain curves

The curves are divided into four stages: initial compaction stage (I), linear elastic deformation stage (II), nonlinear hardening stage (III), and post-peak stage (IV).

In the post-peak stage, the samples exhibit significant brittle failure characteristics, and the higher the confining pressure, the more obvious the brittleness; the pre-peak curves of filled samples are smoother, with fewer sudden stress drops, a slower post-peak stress decline rate, and stronger plastic deformation capacity; high confining pressure shortens the initial compaction stage and intensifies post-peak brittle failure.

Fig. 5. Stress-strain curves of defective sandstone samples under different fissure angles (α) and confining stresses (σ2)

2. Strength and deformation parameters

Peak compressive strength and elastic modulus:Positively correlated with both fissure angle and confining pressure. Gypsum filling has a more significant effect on improving uniaxial compressive strength.

Peak axial strain:Negatively correlated with confining pressure, with no obvious correlation with fissure angle; filling significantly reduces the peak axial strain.

Fig. 6. Strength and deformation parameters of defective sandstone specimens with different fissure angles

Fig. 7. Strength and deformation parameters of defective sandstone specimens under different confining stresses

3.Final failure modes

Ten types of macroscopic cracks were identified, including 3 types of tensile cracks (T-I, T-II, T-III), 2 types of shear cracks (S-I, S-II), far-field cracks (F), surface spalling (SS), and hole collapse (HC).

With increasing fissure angle, the failure mode changes from tensile crack dominance to shear crack dominance; in filled samples, hole collapse (HC) cracks are greatly reduced, and cracks are finer and more dispersed; under biaxial compression, surface spalling (SS) cracks are more common.

Fig. 8. Geometric configuration and characteristics of each crack type

Fig. 9. Final failure modes of defective sandstone samples

4. Numerical simulation conclusions

(1) Result validation

Defective sandstone samples with α=60° were selected, and simulations were compared with experimental results under 4 conditions. The linear elastic stages of the stress-strain curves were close, the peak strengths were comparable, the post-peak stress decline trends were consistent, and the crack initiation locations and propagation paths in the failure modes were similar, with a relative error of < 5%,verifying the reliability of the model.

Fig. 13. Comparison of numerical simulation and laboratory test results of defective sandstone samples with α = 60°

(2) von Mises stress evolution

Initial compression stage (point O): under biaxial compression, slight stress concentration appears near the hole and fissure due to confining pressure;

Linear elastic stage (point A): under uniaxial compression, the stress shows an X-shaped distribution, while under biaxial compression it shows a band-like distribution;

Nonlinear hardening stage (points B, C): stress concentration intensifies, and microcracks propagate toward the surface;

Post-peak stage (points D, E): microcracks coalesce to form fracture zones, stress drops sharply, and the stress distribution in filled samples is more uniform.

Fig. 14. Stress evolution of the defective sandstone model with α = 60°

5. Damage evolution of cohesive elements

Cohesive elements did not reach the damage initiation criterion, and no elements failed; with increasing axial strain, cohesive elements at stress concentration locations failed first, initially dominated bytensilefailure.

Damage initiation locations: in the unfilled model, at the hole edge and fissure tips; in the filled model, at the fissure tips and within the filling; damage initiation in the unfilled model occurred earlier.

Final failure: under biaxial compression, the number of failed cohesive elements and the proportion of tensile failure were significantly higher than under uniaxial compression.

Fig. 15. Failure characteristics of cohesive elements in the defective sandstone model with α = 60°

6. Influence mechanisms of different factors

(1) Influence of fissure angle

With increasing fissure angle, the tensile stress concentration zone shrinks, the compressive stress concentration zone expands, and the displacement gradient decreases; the crack initiation mechanism changes from tensile failure caused by tensile stress concentration to shear failure caused by compressive stress concentration, and the crack initiation location shifts from the hole edge → fissure tip → back to the hole surface at α=90°;

strength increases with increasing fissure angle

Fig. 16. Axial stress nephograms and axial displacement nephograms of defective sandstone models under different fissure angles

Fig. 17. Crack initiation characteristics of defective sandstone models with different fissure angles

Fig. 18. Number of failed cohesive elements and proportion of failure modes in defective sandstone models under ultimate failure at different fissure angles

(2) Influence of filling condition

Filling can significantly weaken the stress concentration in the defect zone, reduce the extent of the tensile stress concentration zone, lower the maximum stress value, and make the displacement distribution more uniform;

Fig. 19. Comparative analysis of the mechanical response and crack evolution characteristics between unfilled and filled sandstone models

Fig. 20. Comparison of the number of failed cohesive elements and the proportion of failure modes at ultimate failure between unfilled and filled defective sandstone models

(3) Influence of confining pressure

Increasing confining pressure expands the compressive stress concentration zone and shrinks the tensile stress concentration zone, suppressing tensile stress concentration at the hole and fissure;the displacement gradient decreases, and the displacement distribution becomes more uniform;

although increasing confining pressure does not change the crack initiation location, it can effectively inhibit crack propagation;

confining pressure increases the elastic modulus and peak strength and reduces the peak axial strain by enhancing the overall load-bearing capacity and increasing the intergranular friction and cohesion within the rock matrix.

Fig. 21. Comparative analysis of the mechanical response and fracture evolution characteristics of defective sandstone models under different confining stresses

Fig. 22. Comparison of the number of failed cohesive elements and the proportion of failure modes in unfilled sandstone models under different confining stresses