Splitting grouting is widely applied in the reinforcement of soft soil layers. Accurate calculation of the reinforcement range and rational design of grouting hole arrangement are essential to ensure grouting effectiveness and improve reinforcement efficiency. To quantify the reinforcement region of splitting grouting and optimize the spacing between grouting holes, an analytical model and computational procedure for the reinforcement range of splitting grouting are established. The characteristics of the reinforcement zone in dual-hole splitting grouting are clarified based on the condition of grouting pressure superposition between adjacent grouting holes. The reinforcement region and optimal spacing for multi-hole splitting grouting are determined. Based on the radial propagation of the slurry from the grouting hole and the attenuation of grouting pressure ( \({p_r}\) ) along the propagation path, this study incorporates the crack initiation pressure ( \({p_0}\) ) of the injected soil to develop a reinforcement boundary model under the critical condition \({p_r}={p_0}\) . The corresponding calculation procedure for the reinforcement radius ( \({r_s}\) ) is clearly defined, providing a theoretical foundation for the quantitative evaluation of the reinforcement region in splitting grouting. Using the spacing between grouting holes as a criterion, the condition for pressure superposition between adjacent holes is established. The variation in the reinforcement region with different hole spacings is analyzed. When the spacing \(d>2{r_s}\) , there is no interaction between adjacent grouting holes, and the reinforcement region consists of two independent circular zones with radius \({r_s}\) . When the spacing \(d \leqslant 2{r_s}\) , pressure superposition occurs, resulting in a rectangular reinforcement zone, whose dimensions are governed by the hole spacing. For single-row, staggered, rectangular, and circular grouting holes layouts, the minimum reinforcement units are identified as linear, triangular, rectangular, and circular configurations, respectively. Based on the reinforcement zone of dual-hole grouting, the effective reinforcement region of each layout is analyzed. The overall reinforcement region for multi-hole grouting can then be obtained by superimposing the reinforcement regions of individual units. Using the criterion that the injected soil between grouting holes is just adequately reinforced, the optimal spacing for each grouting pattern is calculated. The findings of this study provide valuable references for the design and optimization of grouting reinforcement engineering.
