A probability based model of block failure capacity of pile foundation in clay soil under axial load is developed. The model was based on the first order second moment method. Instead of using point variability, the s...A probability based model of block failure capacity of pile foundation in clay soil under axial load is developed. The model was based on the first order second moment method. Instead of using point variability, the soil inherent variability is modelled as random field model. Based on this model, a reliability based factor of safety for designing pile group foundation, taking into account bock failure mechanism, is proposed. Furthermore, using simplified lognormal model, the relationship between the factor of safety used in design practice and target reliability may be derived explicitly.展开更多
We investigate a percolation process where an additional parameter q is used to interpolate between the classical Erd¨os–R′enyi(ER) network model and the smallest cluster(SC) model. This model becomes the ER ne...We investigate a percolation process where an additional parameter q is used to interpolate between the classical Erd¨os–R′enyi(ER) network model and the smallest cluster(SC) model. This model becomes the ER network at q = 1, which is characterized by a robust second order phase transition. When q = 0, this model recovers to the SC model which exhibits a first order phase transition. To study how the percolation phase transition changes from second order to first order with the decrease of the value of q from 1 to 0, the numerical simulations study the final vanishing moment of the each existing cluster except the N-cluster in the percolation process. For the continuous phase transition,it is shown that the tail of the graph of the final vanishing moment has the characteristic of the convexity. While for the discontinuous phase transition, the graph of the final vanishing moment possesses the characteristic of the concavity.Just before the critical point, it is found that the ratio between the maximum of the sequential vanishing clusters sizes and the network size N can be used to decide the phase transition type. We show that when the ratio is larger than or equal to zero in the thermodynamic limit, the percolation phase transition is first or second order respectively. For our model, the numerical simulations indicate that there exists a tricritical point qcwhich is estimated to be between0.2 < qc< 0.25 separating the two phase transition types.展开更多
文摘A probability based model of block failure capacity of pile foundation in clay soil under axial load is developed. The model was based on the first order second moment method. Instead of using point variability, the soil inherent variability is modelled as random field model. Based on this model, a reliability based factor of safety for designing pile group foundation, taking into account bock failure mechanism, is proposed. Furthermore, using simplified lognormal model, the relationship between the factor of safety used in design practice and target reliability may be derived explicitly.
基金Supported by the National Natural Science Foundation of China under Grant Nos.61172115 and 60872029the High-Tech Research and Development Program of China under Grant No.2008AA01Z206+1 种基金the Aeronautics Foundation of China under Grant No.20100180003the Fundamental Research Funds for the Central Universities under Grant No.ZYGX2009J037,and Project No.9140A07030513DZ02098
文摘We investigate a percolation process where an additional parameter q is used to interpolate between the classical Erd¨os–R′enyi(ER) network model and the smallest cluster(SC) model. This model becomes the ER network at q = 1, which is characterized by a robust second order phase transition. When q = 0, this model recovers to the SC model which exhibits a first order phase transition. To study how the percolation phase transition changes from second order to first order with the decrease of the value of q from 1 to 0, the numerical simulations study the final vanishing moment of the each existing cluster except the N-cluster in the percolation process. For the continuous phase transition,it is shown that the tail of the graph of the final vanishing moment has the characteristic of the convexity. While for the discontinuous phase transition, the graph of the final vanishing moment possesses the characteristic of the concavity.Just before the critical point, it is found that the ratio between the maximum of the sequential vanishing clusters sizes and the network size N can be used to decide the phase transition type. We show that when the ratio is larger than or equal to zero in the thermodynamic limit, the percolation phase transition is first or second order respectively. For our model, the numerical simulations indicate that there exists a tricritical point qcwhich is estimated to be between0.2 < qc< 0.25 separating the two phase transition types.
