Creep property and damage constitutive model of dioritic porphyrite under cyclic loading-unloading
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摘要: 分級加載壓縮蠕變試驗未能充分考慮穩定蠕變中的黏塑性應變，故采用三軸循環加卸載壓縮蠕變試驗來實現巖石的黏彈、塑性應變分離，從而使巖石黏彈、塑性應變在巖石蠕變的各個階段得以充分考慮。以某水電站閃長玢巖為例，探討該類巖石蠕變特性。在破壞前，巖石的瞬時彈性應變以及瞬時塑性應變隨著偏應力逐級增大呈線性增長；隨著偏應力的增加，黏彈性應變和黏塑性應變呈非線性增長。引入一個分數階Abel黏壺與Kelvin模型串聯形成新型黏彈性模型；用分數階Abel黏壺代替傳統的黏塑性模型中的線性牛頓體并基于損傷建立黏塑性損傷模型。然后將新型黏彈性模型和黏塑性損傷模型與瞬時彈性模型和瞬時塑性模型串聯組成一個新的巖石蠕變損傷模型。最后將該模型與巖石蠕變曲線進行擬合，從而證明該模型的適用性。Abstract: The hierarchical loading compression creep test fails to fully consider the viscoplastic strain in a stable creep. Thus, the triaxial cyclic loading compression creep test is adopted to realize the separation of viscoelastic and viscoplastic strain to fully consider the two strains in each stage of the creep. With the development of hydropower project construction in China being moved towards the mountain valley, the geological conditions and engineering environment faced by geotechnical engineering become more complex. Moreover, in the process of geotechnical engineering design, engineering construction, and safe operation, the effect of the rheological, mechanical properties of rock becomes more difficult to ignore. This engineering problem is becoming more significant for the staff involved. Therefore, rheological, mechanical properties of rock have become a very important research content. This study took the diorite porphyry of one hydropower station as an example to discuss the creep characteristics of this type of rock. Before the failure, the instantaneous elastic strain and instantaneous plastic strain increase linearly as the deviator stress gradually increases. With increased deviator stress, the viscoelastic strain and viscoplastic strain exhibit a nonlinear increase. The fractional Abel viscous pot and Kelvin model were introduced to form a new viscoelastic model. The fractional Abel viscous pot was used to replace the linear Newtonian fluid in the traditional viscoplastic model, and a viscoplastic damage model was established based on the damage variables. The new viscoelastic plastic model and viscoplastic damage model were then connected in series with the transient elastic model and transient plastic model to form a new rock creep damage model. Finally, the model is fitted with the rock creep curve to prove the applicability of the model.
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圖 1 閃長玢巖三軸壓縮蠕變試驗結果。（a）應變、應力?時間曲線；（b）應力?應變曲線
Figure 1. Triaxial compression creep test results of diorite porphyrite: (a) strain and stress vs time curves; (b) stress?strain curve
圖 2 不同偏應力加載閃長玢巖的瞬時應變。（a）瞬時彈性應變；（b）瞬時塑性應變
Figure 2. Instantaneous strain of diorite porphyry under different deviatoric stress loading: (a) instantaneous elastic strain; (b) transient plastic strain
圖 3 不同偏應力加載時閃長玢巖的蠕變應變。（a）黏彈性應變；（b）黏塑性應變
Figure 3. Creep strain of diorite porphyry under different deviatoric stress loading: (a) viscoelastic strain; (b) viscoplastic strain
圖 6 90 MPa 為例示意圖。（a）擬合結果對比；（b）黏彈、塑性應變分離結果
Figure 6. 90 MPa schematic diagram: (a) comparison of fitting results; (b) results of viscoelastic and plastic strain separation
圖 9 試驗與模型擬合結果。（a）穩態流變擬合；（b）加速流變擬合
Figure 9. Test and model fitting results: (a) steady state rheological fitting; (b) accelerated rheological fitting
表 1 閃長玢巖三軸循環加卸載蠕變試驗黏彈塑性應變分析
Table 1. Viscoelastic strain analysis of diorite porphyrite triaxial cyclic loading and unloading creep test
σa/MPa σb/MPa εm/ 10?3 εme/ 10?3 εmp/ 10?3 εc/ 10?3 εce/ 10?3 εcp/ 10?3 εp/ 10?3 60 0 9.967 4.342 5.625 1.588 0.213 1.375 7.000 70 0 11.799 4.937 6.862 1.732 0.337 1.395 8.257 80 0 14.169 5.807 8.361 1.854 0.432 1.423 9.784 90 0 17.526 6.937 10.589 2.053 0.552 1.501 12.091 100 0 20.382 4.761 
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表 2 Kelvin模型與改進Kelvin模型擬合參數
Table 2. Fitting parameters of the Kelvin model and improved Kelvin model
(σ1?σ3) / MPa Viscoelastic model ηceo/ GPa?h Gce/ GPa ηce/ GPa?h n R2 60 Kelvin model — 99.57 488.12 — 0.974 New viscoelastic model 666.67 240.96 848.46 0.430 0.998 70 Kelvin model — 74.75 187.54 — 0.864 New viscoelastic model 238.10 256.41 398.15 0.263 0.996 80 Kelvin model — 65.16 112.93 — 0.808 New viscoelastic model 175.44 222.22 254.26 0.212 0.996 90 Kelvin model — 57.75 104.06 — 0.784 New viscoelastic model 140.85 225.56 302.36 0.194 0.995
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表 3 蠕變模型參數
Table 3. Creep model parameters
（σ1?σ3）/
MPaA B C E n m b tp R2 60 0.03 0.083 0.284 0.655 0.43 0.156 — — 0.991 70 0.098 0.091 0.644 0.799 0.263 0.106 — — 0.997 80 0.152 0.12 0.874 0.628 0.212 0.159 — — 0.996 90 0.213 0.133 0.746 0.722 0.194 0.206 — — 0.994 100 0.096 0.482 60.35 3.657 0.665 0.677 0.59 0.345 0.999
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