To efficiently link the continuum mechanics for rocks with the structural statistics of rock masses,a theoretical and methodological system called the statistical mechanics of rock masses(SMRM)was developed in the pas...To efficiently link the continuum mechanics for rocks with the structural statistics of rock masses,a theoretical and methodological system called the statistical mechanics of rock masses(SMRM)was developed in the past three decades.In SMRM,equivalent continuum models of stressestrain relationship,strength and failure probability for jointed rock masses were established,which were based on the geometric probability models characterising the rock mass structure.This follows the statistical physics,the continuum mechanics,the fracture mechanics and the weakest link hypothesis.A general constitutive model and complete stressestrain models under compressive and shear conditions were also developed as the derivatives of the SMRM theory.An SMRM calculation system was then developed to provide fast and precise solutions for parameter estimations of rock masses,such as full-direction rock quality designation(RQD),elastic modulus,Coulomb compressive strength,rock mass quality rating,and Poisson’s ratio and shear strength.The constitutive equations involved in SMRM were integrated into a FLAC3D based numerical module to apply for engineering rock masses.It is also capable of analysing the complete deformation of rock masses and active reinforcement of engineering rock masses.Examples of engineering applications of SMRM were presented,including a rock mass at QBT hydropower station in northwestern China,a dam slope of Zongo II hydropower station in D.R.Congo,an open-pit mine in Dexing,China,an underground powerhouse of Jinping I hydropower station in southwestern China,and a typical circular tunnel in Lanzhou-Chongqing railway,China.These applications verified the reliability of the SMRM and demonstrated its applicability to broad engineering issues associated with jointed rock masses.展开更多
In this study, a constitutive model based on microscopic physical mechanism of silicone rubber foams was established. A theoretical statistical model of rubber elasticity considering the effect of dangling chains was ...In this study, a constitutive model based on microscopic physical mechanism of silicone rubber foams was established. A theoretical statistical model of rubber elasticity considering the effect of dangling chains was modified to build this model. When a strain amplification factor （X） was introduced, the theoretical model could fit the tensile stress-strain data of mono- and bi-modal foam matrix well （Adj. R-Square = 0.9989, 0.9983）. Parameters related to the polymer network, namely, average molecular weight （Me） and volume fraction （Ф） of chain segments between adjacent cross-linking points （network strands）, were calculated by probabilistic method from the number-average molecular weight （Mn）, vinyl content （wvi） of the primary polysiloxanes and percent conversion （q） of vinyl groups. The primary and infinite strain amplification factors （X0, X∞） and decay exponent （z）, introduced by X and related to the nanoparticles, were obtained by fitting. Inspired by the fact that the actual strain of matrix was lower than that of the foams＇, we introduced another item, strain hysteresis item （H, related with the foam porosity and cell structure）, into the statistical model as well. With the same above values of Mc, Ф, X0 and X∞, the model could also fit the compressive stress-strain data of mono- and bi-modal foams well （Adj. R-Square = 0.9948, 0.9985）. Interestingly, the strain hysteresis items of the mono- and bi-modal foams almost completely coincided under all experimental strains, which may be attributed to the almost equal porosity and similar cell structure of the two foams. This constitutive model may connect the macroscopic stress-strain behaviour to the parameters of microscopic molecular structures, promisingly providing a basis for the performance improvement and optimization of silicone rubber foams.展开更多
Based on the characteristics of sea ice drifting and ridging at meso-small scale, the Drucker-Prager （D-P） yield criteria was introduced into the Viscoelastic-Plastic （VEP） constitutive model for the study of sea ...Based on the characteristics of sea ice drifting and ridging at meso-small scale, the Drucker-Prager （D-P） yield criteria was introduced into the Viscoelastic-Plastic （VEP） constitutive model for the study of sea ice dynamics. In this model, the Kelvin-Vogit viscoelastic model was adopted in the elastic stage, and the associated normal flow rule was used in the plastic stage. Using the VEP model, the sea ice ridging process was simulated in an idealized rectangular basin, and the simulation results show that the simulated ice ridge thickness is consistent with the analytical solution. Moreover, the VEP model with the D-P yield criteria was also applied for the sea ice simulation of Bohai Sea, and the ice thickness, concentration, velocity, and ice stress were obtained in 48 h. The simulated thickness distributions agree well with the satellite images. The singular problem in the Mohr^7oulomb （M-C） yield criteria was overcome by the D-P yield criteria, and the computational efficiency was also improved. In the numerical simulations described above, the smoothed particle hydrodynamics was applied.展开更多
基金The authors are grateful to the financial support from the National Natural Science Foundation of China(Grant No.41831290)the Key R&D Project from Zhejiang Province,China(Grant No.2020C03092).
文摘To efficiently link the continuum mechanics for rocks with the structural statistics of rock masses,a theoretical and methodological system called the statistical mechanics of rock masses(SMRM)was developed in the past three decades.In SMRM,equivalent continuum models of stressestrain relationship,strength and failure probability for jointed rock masses were established,which were based on the geometric probability models characterising the rock mass structure.This follows the statistical physics,the continuum mechanics,the fracture mechanics and the weakest link hypothesis.A general constitutive model and complete stressestrain models under compressive and shear conditions were also developed as the derivatives of the SMRM theory.An SMRM calculation system was then developed to provide fast and precise solutions for parameter estimations of rock masses,such as full-direction rock quality designation(RQD),elastic modulus,Coulomb compressive strength,rock mass quality rating,and Poisson’s ratio and shear strength.The constitutive equations involved in SMRM were integrated into a FLAC3D based numerical module to apply for engineering rock masses.It is also capable of analysing the complete deformation of rock masses and active reinforcement of engineering rock masses.Examples of engineering applications of SMRM were presented,including a rock mass at QBT hydropower station in northwestern China,a dam slope of Zongo II hydropower station in D.R.Congo,an open-pit mine in Dexing,China,an underground powerhouse of Jinping I hydropower station in southwestern China,and a typical circular tunnel in Lanzhou-Chongqing railway,China.These applications verified the reliability of the SMRM and demonstrated its applicability to broad engineering issues associated with jointed rock masses.
基金financially supported by the National Natural Science Foundation of China(Nos.51473151 and 51703210)
文摘In this study, a constitutive model based on microscopic physical mechanism of silicone rubber foams was established. A theoretical statistical model of rubber elasticity considering the effect of dangling chains was modified to build this model. When a strain amplification factor （X） was introduced, the theoretical model could fit the tensile stress-strain data of mono- and bi-modal foam matrix well （Adj. R-Square = 0.9989, 0.9983）. Parameters related to the polymer network, namely, average molecular weight （Me） and volume fraction （Ф） of chain segments between adjacent cross-linking points （network strands）, were calculated by probabilistic method from the number-average molecular weight （Mn）, vinyl content （wvi） of the primary polysiloxanes and percent conversion （q） of vinyl groups. The primary and infinite strain amplification factors （X0, X∞） and decay exponent （z）, introduced by X and related to the nanoparticles, were obtained by fitting. Inspired by the fact that the actual strain of matrix was lower than that of the foams＇, we introduced another item, strain hysteresis item （H, related with the foam porosity and cell structure）, into the statistical model as well. With the same above values of Mc, Ф, X0 and X∞, the model could also fit the compressive stress-strain data of mono- and bi-modal foams well （Adj. R-Square = 0.9948, 0.9985）. Interestingly, the strain hysteresis items of the mono- and bi-modal foams almost completely coincided under all experimental strains, which may be attributed to the almost equal porosity and similar cell structure of the two foams. This constitutive model may connect the macroscopic stress-strain behaviour to the parameters of microscopic molecular structures, promisingly providing a basis for the performance improvement and optimization of silicone rubber foams.
基金Project supported by the National Natural Science Foundation of China (Grant No: 40206004)
文摘Based on the characteristics of sea ice drifting and ridging at meso-small scale, the Drucker-Prager （D-P） yield criteria was introduced into the Viscoelastic-Plastic （VEP） constitutive model for the study of sea ice dynamics. In this model, the Kelvin-Vogit viscoelastic model was adopted in the elastic stage, and the associated normal flow rule was used in the plastic stage. Using the VEP model, the sea ice ridging process was simulated in an idealized rectangular basin, and the simulation results show that the simulated ice ridge thickness is consistent with the analytical solution. Moreover, the VEP model with the D-P yield criteria was also applied for the sea ice simulation of Bohai Sea, and the ice thickness, concentration, velocity, and ice stress were obtained in 48 h. The simulated thickness distributions agree well with the satellite images. The singular problem in the Mohr^7oulomb （M-C） yield criteria was overcome by the D-P yield criteria, and the computational efficiency was also improved. In the numerical simulations described above, the smoothed particle hydrodynamics was applied.
