J9集团

https://doi.org/10.1016/j.jrmge.2025.04.018

*论文版权归原作者和出版方所有，本文仅为进建互换。

钙质砂的应力–应变个性受颗粒破碎（B）与初始相对密度（Dri）显著影响，但现有本构模型极少同时思考二者的耦合作用。为添补这一空缺，本文针对分歧Dri和应力蹊径的钙质砂发展系列三轴试验，系统钻研颗粒破碎与临界状态行为。

重要发现如下：（1）当应力比（η）恒按时，B随均匀有效应力（p'）呈双曲线关系；给定p'下，B随η线性增大；（2）临界状态线（CSL）随Dri增大而下移，而临界状态摩擦角（φcs）随B增大而减幼；谏鲜隽司，提出统一的颗粒破碎演化模型，用以量化分歧加载前提下钙质砂的破碎水平。将该模型与正常固结线（NCL）及CSL方程耦合，成功再现随B增大、NCL与CSL斜率增大的景象，并定量评估B对φcs的影响。最后，在临界状态土力学与亚塑性理论框架内，成立了同时引入B与Dri的亚塑性模型；该模型在分歧初始相对密度、应力蹊径及排水前提下的仿照了局与试验数据高度吻合，验证了其靠得住性。

Fig. 1. Physical properties of calcareous sand: (a) SEM image; and (b) Grain size distribution (GSD) curve of calcareous sand.

Fig. 2. Test schematic and apparatus: (a) Test schematic; and (b) GDS triaxial automated system.

Fig. 3. Effect of initial densities on the triaxial test results of calcareous sand: (a-b) CTC test, p_c=200 kPa; (c-d) TC test, p_c=200 kPa; (e-f) RTC test, p_c=200 kPa; (g-h) CU test, p_c=200 kPa; (i-j) CTC test, p_c=800 kPa; (k-l) TC test, p_c=800 kPa; (m-n) RTC test, p_c=800 kPa; and (o-p) CU test, p_c=800 kPa

Fig. 4. Variation in GSD curves of calcareous sand and relationship between B with p′ and η: (a-b) Effect of D_ri; (c-d) Effect of p_c; and (e-f) Effect of loading path.

Fig. 5. Relationship between B with p' and η: (a) B- log₁₀ p' relation; and (b) Determination of ω₀ and k_ω (Solid colourful lines represent simulation results by Eq. (8))

Fig. 6. Stress ratio of calcareous sand sheared to maximum axial strain: (a) CTC test; (b) TC test; (c) RTC test; and (d) CU test.

Fig. 7. Comparison of B-p' relations with different test results: (a) Dogs Bay sand; (b) Angular granite (PL: Proportional loading); and (c) Decomposed granite.

Fig. 8. Predicted and measured NCLs of calcareous sand with various initial densities. (a) Predicted versus experimental test results; (b) Influence of k_Dr (Eq. (36)); and (c) Influence of k_B (Eq. (36)).

Fig. 9. Predicted and measured CSLs of calcareous sand with various initial densities: (a) D_ri=0.1; (b) D_ri =0.3; (c) D_ri =0.6; and (d) D_ri =0.9.

Fig. 10. Schematic of the effect of particle breakage on the location of CSL in e-log₁₀p' plane

Fig. 11. Influence of parameter χ and β on predicted results: (a) Effect of χ (Eq. (44)); and (b) Effect of β (Eq. (44)).

Fig. 12. Relationship between critical friction angle φ_cs with particle breakage B of calcareous sand: (a) Experimental data; and (b) Effect of χ_B on predicted M_cs (Eq. (48)).

Fig. 13. Influence of breakage evolution parameters on model prediction results in drained triaxial test: (a-b) Effect of ω₀; (c-d) Effect of k_ω; and (e-f) Effect of p_B.

Fig. 14. Influence of initial density effect parameters on model prediction results in drained triaxial test: (a-b) Effect of D_ri; (c-d) Effect of k_Dr; and (e-f) Effect of χ.

Fig. 15. Influence of breakage effect parameters on model prediction results in drained triaxial test: (a-b) Effect of k_B; (c-d) Effect of β; and (e-f) Effect of χB.

Fig. 16. Comparison between model predictions with CTC tests results of calcareous sand at different D_ri: (a-b) D_ri =0.1; (c-d) D_ri =0.3; (e-f) D_ri =0.6; and (g-h) D_ri =0.9.

Fig. 18. Comparison between model predictions with TC tests results of calcareous sand at different D_ri: (a-b) D_ri =0.1; (c-d) D_ri =0.3; (e-f) D_ri =0.6; and (g-h) D_ri =0.9.

Fig. 20. Comparison of the predicted and measured values of B

Fig. 21. Change in GSD of calcareous sand with D_ri=0.1:(a-b) CTC test; (c-d) TC test; (e-f) RTC test; and (g-h) CU test.

Fig. 22 Comparison between model predictions with drained triaxial tests results of Silica sand at different D_ri: (a-b) D_ri =0.30; (c-d) D_ri =0.60; and (e-f) D_ri=0.90.

现有本构模型未能充分思考颗粒破碎（B）与初始相对密度（D_ri）对钙质砂的耦合影响。为此，本文发展了系列三轴压缩试验，涵盖分歧D_ri、应力蹊径与排水前提；谑匝榱司，提出了新的破碎演化模型，并建改了正常固结线（NCL）与临界状态线（CSL）方程，以同时纳入B与D_ri的结合作用。随后，将这些公式嵌入亚塑性框架，成立了改进的亚塑性本构模型。重要结论如下：

（1）三轴试验批注，B与D_ri对强杜纂变形拥有显著且相互依赖的影响。低围压下B较幼，D_ri起主导作用；随围压增大，B增长，D_ri的影响减弱。

（2）颗粒破碎重要受应力比η与均匀有效应力p′节造。η恒按时，B随p′增大而升高；p′恒按时，B与η成正比。提出的双曲线破碎演化模型仅需3个易标定参数，即可描述分歧应力蹊径、D_ri与围压下的破碎行为。

（3）新NCL与CSL方程可正确反映随B增大而陡化、随D_ri增大而下移的法规；临界状态摩擦角φ_cs随B线性降低。

（4）将破碎演化模型与建改NCL、CSL方程融入亚塑性框架，成立了可同时思考颗粒破碎与初始密度的扩大亚塑性模型，可精确预测级配演化、强杜纂变形。

只管模型预测机能优良，但验证仅限于等向固结与单调加载。现实岛礁与离岸工程常面对各向异性应力与风浪循环荷载，后续钻研将拓展模型至这些复杂工况，提升其工程合用性。

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