# A Novel Continuous-Discontinuous Multi-Field Numerical Model for Rock Blasting
###### Abstract  
During blasting, rock failure is caused by blasting wave and explosive gas pressure, as a multi-field coupled process. Most numerical models focus on the effect of blasting wave where the gas pressure is commonly accounted for by empirical relations, ignoring the penetration and permeation of gas flow in cracks. This can underestimate the failure region. In this work, a novel multi-field model is developed in the framework of a continuous-discontinuous element method (CDEM), which is a coupled finite-discrete method with explicit integration strategy. The deformation and cracking of rock mass and the distribution of gas pressure are captured. The proposed method is verified by comparing the results to other results provided in published literature. Especially, by simulating the cases with blocked and unblocked blasting hole, we found that: (i) The fracture degree of the case with blocked blasting hole was 30% higher than that of the unblocked blasting hole. (ii) The radial main cracks in the fracture area are mainly caused by the explosive gas, and the tiny and dense cracks near the hole are induced by the explosion stress wave. (iii) The explosion crushing zone is mainly formed by the action of explosion stress wave, while the crack zone is formed by the combined action of the explosion stress wave and explosive gas. The proposed method provides a useful tool to properly simulate a rock blasting process. rock blasting: continuous-discontinuous element method (CDEM); multi-field coupled processes; dynamic loading; gas permeation; numerical simulations +
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commonly results in local fragmentation and large displacements. The hybrid continuous-discontinuous method with explicit integration can be advantageous considering the computing time and numerical stability. For example, the authors of [PERSON] and [PERSON] [22] simulated a rock blasting process based on a DEM-SPH coupling method, for which the SPH model is used to capture the gas flow and DEM is adopted to simulate rock fractures. The authors of [PERSON] et al. [23] built an FEM-SPH coupling method to simulate rock blasting and found that the discontinuity and in situ stress of rock have significant influence on the blasting results. The authors of [PERSON] et al. [24] used a hybrid continuous-discontinuous method to simulate the rock blasting induced by high-pressure gas and explosives, indicating that the former case provided fewer radial fractures. The above research shows that the hybrid continuous-discontinuous method has unique advantages in the field of explosion simulation. In this work, in the framework continuous-discontinuous element method (CDEM) [25; 26; 27; 28; 29; 30], we build a coupled hydro-mechanical multi-field model for simulating the rock blasting considering the coupled effects of blasting wave and gas pressure. The main features of our model include:  
* The domain is discretized into deformable blocks and interfaces which can capture the continuous-discontinuous process of rock blasting. * The explosive gas flow is simulated with Darcy's law and plate flow, where the opening of cracks directly increase the gas permeation coefficient. * A multi-field coupled iterative procedure is designed based on explicit integration framework for assuring efficiency and reliability. By comparing our numerically-obtained results and experimental results provided by other literatures, our model is validated, which properly predicts the damage region of rock blasting considering blocked and unblocked blasting holes. The paper is organized as follows: In Section 2, the framework of the continuous-discontinuous element method and multi-field coupling model are introduced, including control equations and numerical procedures. Subsequently, the equivalent loadings are described, including the dynamic loads induced by blasting wave and the quasi-static loads caused by the explosive gas pressure. In Section 3, a classical blasting test is used to verify the model.