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 Geomechanics and Engineering   Volume 15, Number 5, August10 2018 , pages 1029-1038 DOI: https://doi.org/10.12989/gae.2018.15.5.1029 S-I model of horizontal jet grouting reinforcement for soft soil Ning Zhang, Zhongyin Li, Qingsong Ma, Tianchi Ma, Xiaodong Niu, Xixi Liu and Tao Feng Abstract A superposition-iteration (S-I) model is proposed to simulate the jet grouting pre-reinforcing impact for a shallow-buried tunnel. The common model is deduced by theoretical (force equilibrium) analysis and then transformed into the numerical formulation. After applying it to an actual engineering problem, the most obvious deficiency was found to be continuous error accumulation, even when the parameters change slightly. In order to address this problem, a superposition-iteration model is developed based on the basic assumption and superposition theory. First, the additional deflection between two successive excavation steps is determined. This is caused by the disappearance of the supporting force in the excavated zone and the soil pressure in the disturbed zone. Consequently, the final deflection can be obtained by repeatedly superposing the additional deflection to the initial deflection in the previous steps. The analytical solution is then determined with the boundary conditions. The superposition-iteration model is thus established. This model was then applied and found to be suitable for real-life engineering applications. During the calculation, the error induced by the ill-conditioned problem of the matrix is easily addressed. The precision of this model is greater compared to previous models. The sensitivity factors and their impact are determined through this superposition-iteration model. Key Words superposition-iteration; tunnel reinforcement; horizontal jet grouting; analytical solution Address Ning Zhang: Institute of Hydroelectric and Geotechnical Engineering, North China Electric Power University, Beijing, 102206, China Zhongyin Li and Qingsong Ma: Beijing Sany Heavy Machinery Co., Ltd, Beijing 102226, China Tianchi Ma, Xiaodong Niu, Xixi Liu and Tao Feng: 1.) Shandong Provincial Key Laboratory of Ocean Engineering, Qingdao 266100, China 2.) Shandong Provincial Key Laboratory of Marine Environment and Geological Engineering, Ocean University of China, 266100 Qingdao, China

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