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A tangential modulus model for coarse granular materials and the corresponding method for parameter identification
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摘要: 运用两座250 m级高土石坝的实测沉降资料与有限元计算结果，分析了高土石坝的应变量级与应力水平，在此基础上分析了双曲线应力应变模型及其参数确定方法的合理性。研究表明，250 m级高土石坝竖直向应变量级可以达到5%，故常规三轴试验可以适应变形预测对应变范围的要求，但坝内应力水平普遍较低，与确定参数所用的高应力水平段试验数据不协调，从而给土石坝应力变形计算带来不确定性。为更充分地运用低应力水平时的试验结果，建议了应力应变数据的多项式拟合方法，提出一个新的切线模量表达式。对比研究表明，双曲线模型及其参数确定方法高估了等向压缩应力状态下粗粒料的初始切线模量；低估了剪切应力状态下粗粒料的切线模量。文中所提出的表达式可以更好地与应力应变试验结果相吻合，且参数的不确定性大为降低，为提高土石坝应力变形计算的可靠性奠定了基础。Abstract: The strain magnitude and the stress level in high earth and rockfill dams were studied based on the field settlement data and the corresponding finite element simulation results of two typical dams with heights of about 250 m. The reasonability of the widely used hyperbolic model and its parameter identification method were analyzed. It is found that the shear strain in 250 m-high earth and rockfill dams can achieve a magnitude of 5%, and triaxial experiments can be satisfactorily used in deformation prediction. However, the stress level in dams is generally lower than those segments of experimental data used for parameter determination, which adds considerable uncertainty to stress and deformation analysis. To use the experimental data at low stress level fully, a polynomial method is suggested to fit the stress stain data and a new tangential modulus model is proposed. It is found that the initial loading modulus under an isotropic stress state is overestimated by the hyperbolic model, while the tangential modulus under a shear stress state is underestimated. The newly proposed model can fit the experimental data better and the degree of uncertainty in the calibrated parameters is considerably reduced, which lays a foundation for improving the reliability of stress and deformation analysis for high earth and rockfill dams.
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Key words:
- earth and rockfill dam /
- coarse granular material /
- stress and strain /
- hyperbolic model
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图 1 水布垭面板坝最大断面沉降监测结果(2010-04-22)(单位:m)
Figure 1. Settlement monitoring data at the maximum section in Shuibuya CFRD (2010-04-22)(unit: m)
图 2 有限元计算的水布垭面板坝最大断面竖向应变分布云图
Figure 2. Contours of vertical strain at the maximum section in Shuibuya CFRD obtained by FEM simulations
图 3 有限元计算的水布垭面板坝最大断面应力水平分布云图
Figure 3. Contours of stress level at the maximum section in Shuibuya CFRD obtained by FEM simulations
图 4 糯扎渡心墙坝最大断面部分沉降监测结果(单位:m)
Figure 4. Some selected settlement monitoring data at the maximum section in Nuozhadu ECRD(unit:m)
图 5 有限元计算的糯扎渡心墙坝最大断面竖直向应变分布云图
Figure 5. Contours of vertical strain at the maximum section in Nuozhadu ECRD obtained by FEM simulations
图 6 有限元计算的糯扎渡心墙坝最大断面应力水平分布云图
Figure 6. Contours of stress level at the maximum section in Nuozhadu ECRD obtained by FEM simulations
图 8 双曲线模型参数确定与土石坝实际应力状态的偏差
Figure 8. Contradiction in parameter calibration and real states in earth and rockfill dams
图 9 土石坝筑坝粗颗粒料的三轴压缩试验结果
Figure 9. Triaxial compression experiments on typical coarse granular materials in rockfill dams
图 10 两种模型得到的初始模量与围压的关系
Figure 10. Relationships between initial modulus and confining pressure in two models
图 11 两种筑坝粗颗粒料切线模量与应力水平的关系
Figure 11. Relationships between tangential modulus and stress level for two dam materials
图 12 两种筑坝粗颗粒料切线模量与应力比的关系
Figure 12. Relationships between tangential modulus and stress ratio for two dam materials
表 1 基于两种坝料三轴压缩试验结果得到的拟合参数
Table 1. Fitting parameters obtained based on triaxial compression experiments on two dam materials
坝料 围压σ3/MPa (σ1- σ3)f/MPa εf/% c1 c2 c3 c4 堆石料 0.4 1.995 8.41 4.612 6 -9.196 1 8.632 2 -3.048 6 0.8 3.727 10.66 3.902 7 -6.664 4 5.729 0 -1.967 2 1.2 5.103 11.93 3.674 4 -5.988 3 4.908 1 -1.594 1 2.0 7.804 12.09 3.057 0 -3.854 1 2.630 8 -0.833 6 3.0 11.198 12.12 2.448 3 -2.381 2 1.431 5 -0.498 6 砂砾石料 0.4 2.091 6.33 3.924 6 -6.221 2 4.631 5 -1.335 0 0.8 3.752 7.93 3.297 4 -4.132 4 2.272 9 -0.437 8 1.2 5.216 10.08 3.576 1 -4.718 1 2.522 4 -0.380 5 2.0 8.096 9.85 2.245 8 -0.492 0 -1.961 2 1.207 4 3.0 11.332 10.86 2.103 3 0.161 7 -2.770 7 1.505 6 
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表 2 运用不同应力水平段试验结果得到的拟合参数c1
Table 2. Obtained values of c1 based on different segments of triaxial compression experiments
坝料 围压/MPa 拟合参数c1 |②-①|/①/‰ ①: SL=0~1.0 ②: SL=0.1~1.0 堆石料 0.4 4.612 6 4.626 0 2.9 0.8 3.902 7 3.903 5 0.2 1.2 3.674 4 3.682 7 2.3 2.0 3.057 0 3.064 4 2.4 3.0 2.448 3 2.453 8 2.2 砂砾石料 0.4 3.924 6 3.960 8 9.2 0.8 3.297 4 3.316 0 5.6 1.2 3.576 1 3.598 5 6.3 2.0 2.245 8 2.259 7 6.2 3.0 2.103 3 2.125 3 10.5
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