A discussion of the Prandlt calculation formula for anti-uplift stability of the bottom of a foundation pit wall in deep soft soil areas
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摘要:
深厚软土地区采用Prandlt公式计算基坑抗隆起稳定性常常不满足规范要求，给基坑支护设计带来较大困惑。本文在分析基坑开挖与Prandlt公式计算地基极限承载力的力学边界条件差异的基础上，指出采用Prandlt计算式、临界宽度法和计入基坑内侧土体抗剪强度等改进计算方法的不足，提出同时考虑基坑支护体内外两侧土体抗剪作用的改进计算公式。通过对4个计算公式各参数的敏感度分析，发现内摩擦角是影响基坑墙底抗隆起稳定性的首要因素，基坑挖深和支护体插入深度是主要影响因素，土体黏聚力是次要影响因素，土体重度的影响可以忽略。软土内摩擦角较小，在基坑挖深一定的条件下，只有通过加大支护体插入深度才能保证基坑墙底抗隆起稳定性，因此，考虑基坑支护体内外两侧土体抗剪强度的有利作用可合理优化基坑支护设计。本文通过工程实例研究，验证了计入基坑支护体内外两侧土体抗剪强度作用的合理性；同时，根据浙江软土地区多项工程墙底抗隆起稳定安全系数计算结果的统计分析，指出目前规范取值标准偏高，在软土地区不尽合理，建议在积累工程经验的基础上，适当降低规范计算方法的标准限值。
Abstract:The Prandlt formula is often used to calculate the anti-uplift stability of foundation pits in deep soft soil areas, which often fails to meet the specification requirements and brings great confusion to the design of foundation pit support. Based on the analysis of the difference in mechanical boundary conditions between the foundation pit excavation and the Prandlt formula for calculating the foundation bearing capacity, this paper points out the shortcomings of the improved calculation methods such as the Prandlt formula, critical width method, and takes into account the shear strength of the soil inside the foundation pit method, and puts forward an improved calculation formula considering the shear effect of the soil inside and outside the foundation pit support. Through sensitivity analysis of each parameter of the four calculation formulas, it is found that the internal friction angle is the most important factor affecting the stability of foundation pit wall bottom against uplift. The excavation depth and the insertion depth of the supporting body are the main influencing factors, the cohesion of soil body is the secondary influencing factor, and the influence of soil weight can be ignored. The friction angle of soft soil is small. Under certain excavation depth, the stability against uplift of foundation pit wall bottom can be guaranteed only by increasing the insertion depth. Therefore, considering the favorable effect of shear strength of soil on the inner and outer sides of foundation pit support, the foundation pit design can be reasonably optimized. This paper also verifies the rationality of taking into account the shear strength effect of soil on the inner and outer sides of the foundation pit support through engineering case studies. At the same time, according to the statistical analyses of wall bottom stability calculation of many projects, it is pointed out that the current standard is too high and unreasonable in soft soil areas. It is suggested that the standard limited value of the standard calculation method should be appropriately reduced on the basis of accumulated engineering experience.
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Key words:
- soft soil area /
- anti-uplift stability /
- Prandlt formula /
- improvement
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表 1 影响因素基准参数和变化范围
Table 1. Benchmark parameters and variation range of the influencing factors
因素 基坑挖深
h/m围护桩插入
深度t/m土层重度
γ/（kN·m−3）土层黏聚力
c/kPa土层内摩擦角
φ/（°）基准参数 9.65 12.85 17.85 4.34 10.68 变化范围 6～15 8～20 15～20 2～8 5～15 
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表 2 各影响因素敏感度排序
Table 2. Ranking of sensitivity of various influencing factors
因素敏感度排序 公式 因素 h t γ c φ 基准值 9.65 12.85 17.85 4.34 10.68 Kb 敏感度 0.0387 0.0303 0.0007 0.0136 0.083 排序 2 3 5 4 1 KJ 敏感度 0.0398 0.0306 0.0051 0.0309 0.0766 排序 2 4 5 3 1 KJJ 敏感度 0.039 0.0287 0.0013 0.0163 0.0844 排序 2 3 5 4 1 KL 敏感度 0.0218 0.0161 0.0005 0.0093 0.0554 排序 2 3 5 4 1
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表 3 基坑支护设计岩土参数表
Table 3. Parameters of the foundation pit design
土层名称 土层厚度/m
γ/(kN·m−3)抗剪强度指标 十字板剪切试验 固结快剪 三轴UU c/kPa φ/（°） c/kPa φ/（°） Cu/kPa Cu’/kPa ②1 18 15.9 8.3/11.9* 6.7/9.6* 7.3 0.4 21.28 7.08 ②2 20 16.2 8.5/12.1* 6.9/9.8* 8.4 0.4 35.84 12.53 注：表中带*数据为峰值强度。
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表 4 坑底和墙底抗隆起计算结果对比
Table 4. Comparison of the anti-uplift calculation results between pit bottom and wall bottom
序号 围护桩插入比 坑底抗隆起稳定系数K0 墙底抗隆起稳定系数 Kb KJ KJJ KL 1 1∶1.5 1.397/1.305** 1.194/1.621* 1.491/2.035* 1.321/1.796* 1.318/1.602* 2 1∶1.8 1.482/1.415** 1.258/1.70* 1.578/2.147* 1.388/1.879* 1.350/1.642* 3 1∶2.0 1.524/1.489** 1.295/1.745* 1.627/2.209* 1.425/1.925* 1.368/1.666* 4 1∶2.2 1.558/1.564** 1.326/1.784* 1.670/2.264* 1.460/1.966* 1.384/1.685* 5 1∶2.4 1.587/1.639** 1.366/1.819* 1.711/2.313* 1.488/2.003* 1.405/1.702* 6 1∶2.6 1.807/1.868** 1.391/1.850* 1.745/2.357* 1.514/2.035* 1.417/1.718* 7 1∶3.0 1.996/2.145** 1.435/1.904* 1.804/2.431* 1.559/2.091* 1.439/1.745* 8 1∶4.0 2.231/2.715** 1.515/2.002* 1.912/2.568* 1.642/2.194* 1.478/1.794* 注：表中带*数值是按固结快剪峰值强度指标取值；带**数值是采用上海市规范按固结快剪峰值强度指标取值。
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表 5 浙江地区基坑抗隆起稳定系数不同公式计算结果
Table 5. Calculation results of different formulas for stability coefficient of foundation pit against uplift in the Zhejiang area
序号 项目名称 开挖深度/m 插入深度/m 土体力学参数 安全系数 c/kPa φ/（°） Kb KJ KJJ KL 1 湖州憩园小区 4.95 11.40 9.50 6.60 1.41 1.78 1.55 1.45 2 乐清丽都华府 5.00 12.00 11.00 6.80 1.48 1.91 1.64 1.49 3 华联万豪酒店 11.60 8.90 5.00 19.00 2.57 2.70 2.80 2.28 4 乐清长途车站 5.80 13.90 10.00 7.00 1.46 1.86 1.61 1.47 5 乐清游泳馆 5.10 11.70 10.00 7.00 1.46 1.86 1.62 1.48 6 北仑人民医院 4.30 8.50 9.50 9.20 1.72 2.07 1.92 1.66 7 绍兴嘉悦广场 6.25 12.30 10.00 6.00 1.27 1.65 1.40 1.36 8 杭州杨家村安置房 7.00 10.00 16.00 8.70 1.62 2.15 1.82 1.61 9 绿都湖滨花园 6.05 12.20 11.00 7.90 1.53 1.95 1.70 1.53 10 温州广化路C地块 7.60 15.20 10.00 8.00 1.49 1.88 1.64 1.50 11 温州皇家酒店 8.35 14.20 10.00 7.00 1.31 1.67 1.44 1.39 12 温州广化路A地块 6.50 13.00 10.00 9.00 1.65 2.03 1.82 1.60 13 杭政储出（2007）3号地块 7.00 14.00 16.10 6.30 1.42 2.03 1.58 1.46 14 万坤西溪 4.85 7.50 8.00 10.00 1.67 1.93 1.85 1.63 15 镇海传化物流信息港 8.80 11.50 17.50 10.50 1.81 2.37 2.02 1.74 16 宁波万达广场 11.00 16.50 14.00 12.00 1.98 2.47 2.19 1.84 备注：表中所有项目土层重度γ均取16.5 kN/m3；带下划线的数值不满足规范要求。
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