Determination of the optimal row distance for double row piles and the calculation method for earth pressure between piles
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摘要:
无连梁双排桩由于其复杂的受力特性和桩间土压力模型不统一导致较难应用于实际工程。为了深入了解双排桩的受力特性和快速计算出桩间土压力，运用GEO5数值模拟软件研究桩排距对桩身受力的影响；同时，基于刚体极限平衡理论提出了一种简便计算桩间土压力的新方法，即通过先求出前后排桩各自的剩余下滑力，再分别去除前（后）排桩，进而利用求解余下单排桩的剩余下滑力来辅助计算双排桩桩间土压力。结果表明：（1）当桩排距在2b～6b（b为桩截面短边长）时，前后排桩剩余下滑力几乎相等，但前后排桩最大内力差值却逐渐增大；（2）随着桩排距的增加，双排桩的推力之和呈现先增大后减小的趋势，但前排桩桩后推力几乎不变，这主要是由于后排桩桩后推力的变化所引起的，双排桩的最优排距应在2b～4b之间；（3）当桩排距在2b～6b时，双排桩中前排桩桩后推力等于同位置单排桩桩后推力和桩前抗力之和的一半；后排桩桩前抗力等于同位置单排桩桩后推力和桩前抗力之和的一半，最大误差也仅为0.07%；（4）通过与原方案及已有学者的研究成果对比分析，其结果与前人研究成果基本吻合，验证了本文计算方法的可靠性。研究结果对于快速确定双排桩的最优排距及桩间土压力的计算具有重要的参考价值。
Abstract:The double-row pile system without a connecting beam is challenging to implement in practical engineering because of its complex load characteristics and the lack of a standardized model for soil pressure between piles. To better understand the stress characteristics of double-row piles and to efficiently calculate the inter-pile soil pressure, this study used the numerical simulation software GEO5 to investigate the impact of pile row spacing on the stress of piles. In addition, a new method based on the theory of limit equilibrium of rigid bodies was proposed to calculate the soil pressure between piles easily. This method calculated the residual sliding forces of the front and back rows of piles separately, and then sequentially removed the front and back rows to calculate the remaining single-row pile residual sliding forces, which are used to calculate the soil pressure between the double-row piles. The results showed that when the spacing of pile rows is between 2b and 6b (b is the length of the short side of the pile section), the residual sliding force of the front and rear row piles is almost equal. However, the difference between the maximum internal force of the front and rear row piles increases gradually. As the pile row spacing increases, the sum of the pile thrust of the double-row piles initially increases and then decreases, while the thrust behind the front row of piles remains almost unchanged. This variation is primarily influenced by changes in the thrust behind the back row of piles. The optimal spacing for the double-row piles should be between 2b and 4b. When the spacing of pile rows is between 2b and 6b, the front pile rear thrust in double-row piles is equal to half of the sum of the single-row pile rear thrust and pile front resistance at the same position. Similarly, the rear pile front resistance is equal to half of the sum of the single row pile rear thrust and pile front resistance at the same position, with a maximal error of only 0.07%. Comparison with the original scheme and the existing studies shows that the results are consistent with previous findings, validating the reliability of the calculation method presented in this study. In conclusion, this study provides a valuable insight for rapidly determining the optimal spacing of double-row piles and calculating the soil pressure between piles.
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表 1 岩土体物理力学参数
Table 1. Physical and mechanical parameters of rock and soil mass
名称 重度/（kN·m−3） 黏聚力/kPa 内摩擦角/（°） 滑体 20.2 33.8 20.8 滑带 21.2 31.0 19.0 滑床 24.0 2500 .030.0 注：滑带和滑体为第四系人工耕植土层、残坡积层黏土与崩积碎块石土；滑床为寒武系邱家河组绿泥石千枚岩。 
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表 2 双排桩桩身受力表
Table 2. Stress on double row piles
桩排距
/m前排桩/（kN·m−1） 后排桩/（kN·m−1） 桩后推力 桩前抗力 剩余下滑力 桩后推力 桩前抗力 剩余下滑力 2b 1273.99 1116.85 157.14 1636.01 1480.31 155.70 3b 1273.77 1116.90 156.87 1711.25 1555.69 155.56 4b 1273.71 1116.92 156.79 1791.33 1635.57 155.76 5b 1273.72 1116.91 156.81 1872.74 1716.72 156.02 6b 1273.81 1116.89 156.92 1955.46 1799.06 156.40 7b 1282.48 1117.08 165.40 2019.98 1874.01 145.97 8b 1282.90 1116.98 165.92 1939.28 1793.76 145.52
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表 3 方案三桩身受力表
Table 3. Pile body stress in Scheme 3
桩排距/m 仅布置后排桩/（kN·m−1） 桩后滑坡推力 桩前土体抗力 剩余下滑力 2b 1636.63 1322.01 314.62 3b 1711.80 1397.55 314.25 4b 1791.88 1477.20 314.68 5b 1873.29 1558.03 315.26 6b 1956.01 1639.99 316.02 7b 2018.30 1706.76 311.54 8b 1937.98 1626.96 311.02
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表 4 不同排距下α、β值
Table 4. α, β values under different row spacing
桩排距/m α β 2b 0.502 0.495 3b 0.501 0.495 4b 0.501 0.495 5b 0.501 0.495 6b 0.502 0.495 7b 0.529 0.469 8b 0.530 0.468
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