Jordan Journal of Civil Engineering

Statistical Damage Constitutive Model of Shotcrete under Axial Compression


Xiao Guan; Jixi Chen;


The constitutive model of shotcrete under axial compression was established based on the mathematics and damage theory. The stress–strain relationship under axial compression was tested and statistically analyzed by using 34 NC specimens and 31 SC specimens. The two types of concrete had the same water-binder ratios. The probability distribution function that the peak strain of shotcrete and normal concrete followed was investigated by using the K–S test function of MATLAB software and the chi-square test. The parameter values of established constitutive shotcrete models were discussed. The experimental results on the axial compression of 34 prism specimens of normal concrete (NC) and 31 prism specimens of shotcrete (SC) were analyzed statistically. The relative parameters of the constitutive model and the probability distribution function of damage variable were subsequently determined by using the Monte Carlo stochastic simulation and K–S test methods. In addition, the characteristics curve of the stress–strain of NC and SC with the same water–binder ratio was analyzed and the influence rule on peak stress and peak strain of concrete specimens was discussed. The statistical constitutive SC model under axial compression considering the influence of damage threshold and plastic strain was established by adding a damage threshold parameter to the two traditional parameters of the Weibull’s distribution function. The range of damage threshold and the influence mechanism of plastic strain on the constitutive model were also investigated. In this study, the influence of randomness on SC was fully considered. Based on the comparison of experimental results and simulation results, a stochastic statistical damage constitutive model was established and its rationality and applicability were verified. It can provide a reliable basis for theoretical research and engineering application of SC.


Shotcrete, Randomness, Probability distribution, Constitutive model, Damage threshold.