Study on creep characteristics of fractured rock masses in caved zones with different roof strengths
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摘要: 采空区垮落带分布着大量破碎岩体，其中垮落后破碎岩体的强度是导致采空区长期蠕变存在差异的关键因素，亟需明确不同强度破碎岩体的蠕变特性。基于相似理论，选取软岩、中硬岩和硬岩3种不同强度的破碎岩体相似模型，采用室内分级加载蠕变试验与理论分析相结合的方法，系统性对比不同强度破碎岩体蠕变特性。研究结果表明：不同强度破碎岩体的初始蠕变率与稳定蠕变率均随应力增大而减小，且初始阶段蠕变率变化较快；与软岩、硬岩破碎岩体相比，中硬破碎岩体在蠕变过程中发生更为明显的颗粒破碎并引发颗粒重排列，导致其初始蠕变率在2 kN时达到峰值 0.176 h−1，呈现出明显的峰值特征；此外，中硬破碎岩体在进入稳定蠕变阶段前蠕变率存在一定波动，而软岩和硬岩破碎岩体则表现为平稳衰减。研究成果揭示了不同强度破碎岩体的差异化蠕变特性，为采空区垮落带长期变形预测与地质灾害防控提供了一定的理论指导。Abstract:
Objective The caved zone in goaf areas is filled with fractured rock masses, and the strength of these fractured rock masses after collapse serves as a key factor causing differential long-term creep characteristics of the goaf. This study aims to comprehensively explore the creep characteristics of fractured rock masses with varying strengths. Method Grounded in the similarity theory, we selected analogous models of fractured rock masses representing three strength categories: soft rock, moderately hard rock, and hard rock. By integrating indoor step-loading creep tests with theoretical analysis, a systematic comparison of creep characteristics of fractured rock masses with varying strengths was carried out. Results The creep test results of three types of fractured rock masses reveal distinct deformation characteristics. Soft rock masses exhibit “sudden axial strain increments” under loads of 3 kN and 4 kN, while moderately hard rock masses display this phenomenon under a broader range of 3–5 kN. Evolution patterns of instantaneous, creep, and total strains show marked differences as the creep stress increases: soft rock masses demonstrate progressive decreases before stabilizing (instantaneous strain dropping from 0.084% at 1 kN to stable values beyond 4 kN); moderately hard rock masses exhibit an initial increase followed by subsequent decrease with peak strains occurring at different stresses (instantaneous at 2 kN, creep at 3 kN, total at 2 kN); and hard rock masses present more complex characteristics with instantaneous strain initially declining (0.033% to 0.020% in the 1–3 kN range) before rebounding slightly, while creep strain shows a triphasic pattern (increase–decrease–increase) peaking at 0.009% (3 kN) and total strain exhibits an overall trend of initial decrease followed by subsequent increase. Notably, all rock types share decreasing initial and steady-state creep rates with increasing stress. Compared with soft and hard rock masses, moderately hard rock masses experience more significant particle breakage and rearrangement during the creep process. This leads to an initial peak creep rate of 0.176 h−1 at 2 kN, exhibiting distinct peak characteristics. In contrast, hard rock masses exhibit rapid decay in creep rate and quick stabilization, reflecting their dense internal structure and strong interparticle contacts. These characteristics endow hard rock masses with rapid and stable mechanical response properties during the load-bearing process. The response differences of rock masses with varying strengths under the same load show positive correlation between rock strength and initial creep rate but an inverse relationship with steady-state rate. This indicates that while high-strength rocks respond more vigorously initially, they stabilize faster than low-strength rocks which sustain a longer duration of deformation. Conclusion Under incremenal loading, all three types of fractured rock masses exhibit decreasing trends in both initial and steady-state creep rates with increasing load, with particularly pronounced creep rate variations in the initial stage. Significance This study reveals creep characteristics of fractured rock masses of varying strength, providing a theoretical foundation for predicting long-term deformation of caved zones in goaf areas and developing geohazard prevention and control strategies. -
Key words:
- different strength /
- fractured rock mass /
- similar materials /
- creep characteristics
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图 1 试件制样及试验过程示意图
Figure 1. Schematic diagram of specimen preparation and testing process
(a) The process of making test specimens; (b) Schematic diagrams of an uniaxial compression test and a direct shear test; (c) The entire process of particle cutting and creep test model making
图 2 蠕变前后颗粒形态对比图
a—蠕变前颗粒形态；b—试验结束后筛分不同粒径；c—蠕变后颗粒形态
Figure 2. Comparison of particle morphology before and after creep
(a) Particle morphology before creep; (b) Sieving of different particle sizes after the test; (c) Particle morphology after creep
图 3 软岩破碎岩体全程蠕变曲线
a—3 kN蠕变曲线；b—4 kN蠕变曲线；c—软岩破碎岩体蠕变曲线
Figure 3. Full-process creep curve of fractured soft rock mass
(a) Creep curve under 3 kN load; (b) Creep curve under 4 kN load; (c) Creep curve of fractured soft rock mass
图 4 软岩破碎岩体瞬时、蠕变应变趋势图
Figure 4. Trend diagram for instantaneous and creep strain of fractured soft rock mass
(a) Strain vs.creep stress; (b) Strain proportion vs. creep stress
图 5 软岩破碎岩体分级加载蠕变曲线
Figure 5. Creep curve of fractured soft rock under incremental loading
图 6 软岩破碎岩体蠕变率随蠕变应力变化趋势
Figure 6. Variation of creep rate with creep stress in fractured soft rock mass
(a) Initial creep rate; (b) steady-state creep rate
图 7 中硬岩破碎岩体全程蠕变曲线
a—2 kN蠕变曲线；b—3 kN蠕变曲线；c—中硬岩破碎岩体蠕变曲线；d—4 kN蠕变曲线；e—5 kN蠕变曲线
Figure 7. Full-process creep curve of fractured moderately hard rock mass
(a) Creep curve under 2 kN load; (b) Creep curve under 3 kN load; (c) Creep curve of fractured moderately hard rock mass; (d) Creep curve under 4 kN load; (e) Creep curve under 5 kN load
图 8 中硬岩破碎岩体瞬时、蠕变应变趋势图
Figure 8. Trend diagram for instantaneous and creep strains of fractured moderately hard rock mass
(a) Strain vs. creep stress; (b) Strain proportion vs.creep stress
图 9 中硬岩破碎岩体分级加载蠕变曲线
Figure 9. Creep curve of fractured moderately hard rock mass under incremental loading
图 10 中硬岩破碎岩体蠕变率随蠕变应力变化趋势
Figure 10. Variation of creep rate with creep stress in fractured moderately hard rock mass
(a) Initial creep rate; (b) Steady-state creep rate
图 12 硬岩破碎岩体瞬时、蠕变应变趋势图
Figure 12. Trend diagram for instantaneous and creep strains of fractured hard rock mass
(a) Strain-creep stress; (b) Strain proportion vs. creep stress
图 13 硬岩破碎岩体分级加载蠕变曲线图
Figure 13. Creep curves of fractured hard rock mass under incremental loading
图 14 硬岩破碎岩体蠕变率随蠕变应力变化趋势
Figure 14. Variation of creep rate with creep stress in fractured hard rock mass
(a) Initial creep rate; (b) Steady-state creep rate
图 15 不同强度破碎岩体蠕变前后粒径分布以及级配变化
Figure 15. Particle size distribution and gradation changes of fractured rock mass with different strengths before and after creep
(a) Initial creep rate; (b) Moderately hard rock; (c) Hard rock; (d) Gradation changes before and after creep
图 16 3种不同强度破碎岩体相似材料强度−蠕变率
Figure 16. Strength vs.creep rate of similar materials in three types of fractured rock masses with different strengths
(a) Strength vs. initial creep rate; (b) Strength vs.steady-state creep rate
表 1 岩石坚硬程度分类
Table 1. Classification of rock hardnes
坚硬程度 硬岩 中硬岩 软岩 饱和单轴抗压强度/MPa Rc>60 60>Rc>15 15>Rc>5 Rc—岩石单轴饱和抗压强度实测值 
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表 2 不同强度岩性物理力学参数
Table 2. Physical and mechanical parameters of lithologies with different strengths
原岩强度 γ/（kN/m3） σc/MPa E/MPa μ c/MPa φ/（°） 软岩 22.7 16.8 2280 0.25 36.5 3.2 中硬岩 22 31.1 5769 0.196 38.2 6.28 硬岩 25.1 63.9 6870 0.27 39.3 8.84 γ—重度；σc—单轴抗压强度，E—弹性模量，μ—泊松比，c—黏聚力，φ—内摩擦角
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表 3 不同强度岩性蠕变力学参数
Table 3. Creep mechanical parameters of lithologies with different strength
原岩强度 E1/MPa η1/（GPa·h） E2/MPa η2/（GPa·h） 软岩 7.36 10709.84 15.92 434.34 中硬岩 9.39 12851.21 22.15 1228.93 硬岩 14.88 21165.31 35.70 2114.76 E1—控制延迟弹性模量；E2—弹性剪切模量、η1—决定延迟弹性速率、η2—黏滞流动速率
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表 4 相似常数选取
Table 4. Selection of similarity constants
相似常数 相似比 相似常数 相似比 几何相似常数 30 应力相似常数 27 泊松比相似常数 1 应变相似常数 1 黏聚力相似常数 27 弹性模量常数 27 内摩擦角相似常数 1 重度相似常数 0.9
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表 5 不同强度相似材料配比
Table 5. Proportions of similar materials with different strengths
相似材料强度 酒精松香溶液含量/% IB/IBS I/IB 液压油含量/% 软岩 12.77 0.82 0.56 1.83 中硬岩 18.70 0.67 0.52 5.67 硬岩 24.88 0.56 0.58 3.87 IB/IBS—精铁粉与重晶石粉质量之和与骨料总质量的比值；I/IB—精铁粉质量与精铁粉和重晶石粉质量之和的比值
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表 6 不同强度蠕变试验方案
Table 6. Creep test scheme for different strengths
蠕变试验相似
材料强度方案0.65 MPa
试样（软岩）1.29 MPa
试样（中硬岩）2.14 MPa
试样（硬岩）蠕变应力/kN 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 蠕变时长/h 24 24 48
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表 7 不同强度蠕变试验方案
Table 7. Creep test scheme for rocks of different strengths
相似材料强度 拟合结果 0.65 MPa试样（软岩） $ \begin{array}{l}\dot{{\varepsilon }_{0}}=0.07747\times {{\mathrm{e}}}^{-1.37306\sigma }+0.00856\\ \dot{{\varepsilon }_{{\mathrm{s}}}}=0.03155\times {{\mathrm{e}}}^{-1.35275\sigma }+0.00196\end{array} $ R2=0.976
R2=0.9441.29 MPa试样（中硬岩） $ \begin{array}{l}\dot{{\varepsilon }_{0}}=0.60271\times {{\mathrm{e}}}^{-0.63791\sigma }+0.00481\\ \dot{{\varepsilon }_{{\mathrm{s}}}}=0.114\times {{\mathrm{e}}}^{-1.13069\sigma }+0.00173\end{array} $ R2=0.894
R2=0.8742.14 MPa试样（硬岩） $ \begin{array}{l}\dot{{\varepsilon }_{0}}=0.48059\times {{\mathrm{e}}}^{-0.2026\sigma }-0.09625\\ \dot{{\varepsilon }_{{\mathrm{s}}}}=0.00132\times {{\mathrm{e}}}^{-0.91859\sigma }+0.00028826\end{array} $ R2=0.842
R2=0.741$ {\dot{\varepsilon }}_{{}_{\text{0}}} $—初始蠕变率；$ {\dot{\varepsilon }}_{{{\mathrm{s}}}} $—稳定蠕变率；σ—应力； R2—相关系数
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