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A New Perspective on the Semi-quantitative Meso-structural Failure Mechanism of Deep Weak Interlayer Zone Under Different Stress Paths

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Abstract

To essentially explore and quantitatively clarify the mesoscopic failure mechanism of deep weak interlayer zone (WIZ) induced by complex stress levels and stress paths (i.e., particle breakage and orientation, pore morphology, etc.), a semi-quantitative mesoscopic structural damage analysis methodology has been proposed, by involving SEM-MATLAB image processing technique with representative meso-structural parameters after sufficient analysis of basic geotechnical properties of WIZ. Results show that the natural WIZ exhibiting a flocculated structure could be characterized as a well-graded geotechnical material forming main clay minerals, in which most pores are intergranular, with the pore size distribution concentrated in 0.007–200 μm. Higher initial confining pressure and axial loading tend to intensify the particle breakage degree and particle size distribution characteristics of WIZ more than that of axial and circumferential unloading, in which the stress path II of axial pressure loading and confining pressure unloading under the initial confining pressure of 25 MPa is the most severe with average particle area reduced by 56% and particle Korcak fractal dimension increased by 36%. The broken particles undergoing a series of irreversible dislocation, tumbling and rotation under the action of shear and tensile stress, tend to orient in the direction of 0°–15°, in which particles in stress path IV aggregate in two directions of 0–15° and 60–90° due to the bidirectional unloading. The unloading stress path IV shows the most distinct directional orientation and orderliness, with particle anisotropy increased by 267% and directional probability entropy reduced by 13%. Particle breakage and orientation in WIZ are accompanied by obvious filling, expansion and propagation of the meso-pores and meso-cracks, in which stress path IV under lower confining pressure most affects the morphological complexity of pore and crack boundaries with the pore morphology fraction dimension increased by 13.5%. The quantitative theoretical correlation of macro-meso parameters has been established by the stepwise regression analysis of two most relevant and representative correlation indexes (i.e., Korcak fractal dimension and pore morphology fractal dimension) with the ultimate bearing strength of WIZ, which has been proved to have high fitting accuracy by comparing the regression results with the test measured values. The meso-structural damage mechanism of WIZ under stress paths II and IV could, respectively, match the failure law of structural stress-induced collapse in the spandrel and the plastic squeezing-out failure of WIZ on the high sidewall of underground excavations. Research could provide feasible ideas for the relationship between macroscopic failure and mesoscopic damage of WIZ, as well as the effective basis for the further discussion of macro-meso constitutive model establishment.

Highlights

  • A semi-quantitative method by SEM-MATLAB image processing technique was proposed to explore the mesoscopic failure mechanism of weak interlayer zone.

  • The particle breakage, particle orientation, pore morphology and crack evolution induced by complex stress paths were quantitatively explored.

  • The quantitative theoretical correlation of macro-meso parameters was established by stepwise regression analysis.

  • The correlation between meso-structural variation and engineering failure mechanism of weak interlayer zone was discussed.

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Data availability

In this research, new data were created or analyzed. Data will be shared upon request and consideration by the authors.

Abbreviations

\(A_{{\text{a}}}\) :

Average particle area of WIZ

\(A_{i}\) :

Area of a single particle of WIZ

\(A_{i}^{{{\text{pore}}}}\) :

Area of pores of WIZ

\(A_{\min }\) :

Minimum particle area of WIZ

\(A_{1}\) :

Total cross-sectional pore area of WIZ

\(A_{2}\) :

Total cross-sectional area of WIZ

\(C_{{\text{u}}}\) :

Uniformity coefficient

\(C_{{\text{c}}}\) :

Curvature coefficient

CT:

Computed tomography

\(d_{60}, d_{30}, d_{10}\) :

Sieve diameter

\(d\) :

Particle diameter of WIZ

\(d_{{\text{P}}}\) :

Pore diameter of WIZ

\(D_{{\text{k}}}^{{{\text{par}}}}\) :

Particle Korcak fractal dimension

\(D^{{{\text{pore}}}}\) :

Pore morphology fraction dimension of WIZ

\(e\) :

Void ratio

\(F_{i} \left( \alpha \right)\) :

Probability density function of WIZ

\(g\) :

Gravity constant

\(G_{x} ,\,G_{y}\) :

Filters including the horizontal and vertical derivative approximations

\(G_{{\text{s}}}\) :

Specific gravity

\(H(s,t)\) :

Total image information entropy

\(H_{m}\) :

Orientation probability entropy of WIZ

\(I_{n}\) :

Anisotropic rate of WIZ

\(I_{{\text{P}}}\) :

Plasticity index

J :

Input image

\(L, B\) :

Length of the major axis and the length of the minor axis of the fitting standard deviation ellipse of WIZ

\(m\) :

Total quality of WIZ

\(m_{s}\) :

Quality of water in WIZ

\(m_{d}\) :

Quality of WIZ in the dry state

\(N_{{\text{T}}}\) :

Total number of particles of WIZ participating in the statistics

\(N\left( {A \ge A_{i} } \right)\) :

Total number of particles with area greater than or equal to\(A_{i}\)

\(n_{i}\) :

Number of particles whose major axis is in the ith direction slice

\(n_{a}\) :

Apparent Porosity of WIZ

P 1, P 2 :

Probability distributions of image object and image background

\(p_{ij}\) :

2-D histogram of the image

\(P_{i}\) :

Perimeter of pores of WIZ

\(\rho\) :

Natural density

\(q_{{\text{u}}}\) :

Ultimate bearing strength of WIZ

\(S_{{\text{r}}}\) :

Saturation

(s, t):

Threshold vector for pixel intensity and the local average of pixels

\(V\) :

Volume of WIZ

\(V_{{\text{p}}}\) :

Volume of pores in natural WIZ

\(V_{{\text{s}}}\) :

Volume of particle skeletons in natural WIZ

\(V_{{\text{w}}}\) :

Volume of water in natural WIZ

\(W_{{\text{P}}}\) :

Plastic limit

\(W_{{\text{L}}}\) :

Liquid limit

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Acknowledgements

The authors greatly acknowledge financial support from the National Natural Science Foundation of China (Grant Nos. 52279114, 51909241, 52279117 and 52008376), the China Postdoctoral Science Foundation (Grant No. 2023T160200) and Henan Province Science and Technology Innovation Talent Program (Grant No. 2023HYTP002). The authors wish to thank Prof. **a-ting Feng for his kind scientific guidance.

Funding

This study was funded by National Natural Science Foundation of China, 52279114, Shu-Qian Duan, 51909241, Shu-Qian Duan, 52279117, Ding-** Xu, 52008376, Jie-Cheng **ong, Henan Province Science and Technology Innovation Talent Program, 2023HYTP002, Shu-Qian Duan, China Postdoctoral Science Foundation, 2023T160200, Shu-Qian Duan.

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Authors and Affiliations

  1. School of Civil Engineering, Zhengzhou University, Zhengzhou, 450001, Henan, China

    Shu-Qian Duan & Jie-Cheng **ong

  2. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, Hubei, China

    Ding-** Xu, Quan Jiang & Shi-Li Qiu

  3. Yellow River Engineering Consulting Co. Ltd., Zhengzhou, 450003, Henan, China

    Po Gao

  4. Shaanxi Public Resources Trading Center, **’an, 710000, Shaanxi, China

    Bei Cao

  5. School of Highway, Chang’an University, **’an, 710064, Shaanxi, China

    Guo-feng Liu

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  1. Shu-Qian Duan
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Contributions

S-QD: investigation, formal analysis, writing-original draft; PG: laboratorial experiment, methodology, writing—review; D-PX: conceptualization, writing—review; BC and G-FL: onsite investigation; QJ and S-LQ: experimental help; J-CX: overall guidance, date curation.

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Correspondence to Ding-** Xu.

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Duan, SQ., Gao, P., Xu, DP. et al. A New Perspective on the Semi-quantitative Meso-structural Failure Mechanism of Deep Weak Interlayer Zone Under Different Stress Paths. Rock Mech Rock Eng 57, 3171–3195 (2024). https://doi.org/10.1007/s00603-024-03760-6

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