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摘要: 通过三轴剪切试验, 对比在不同加筋率和围压下, 聚丙烯纤维加筋泡沫轻质土的剪切力学特性; 研究了泡沫轻质土各强度参数与加筋率、围压之间的关系, 获取了加筋泡沫轻质土裂纹扩展规律, 建立了应力-应变全曲线方程, 提出了加筋泡沫轻质土各强度参数关于加筋率和围压的本构方程; 将不同加筋率的试验数据归一化处理后进行分析, 得到了加筋泡沫轻质土的应力-应变全曲线方程, 获取了曲线方程中各参数关于加筋率、围压2个变量之间的函数关系。分析结果表明: 加筋泡沫轻质土三轴剪切强度和黏聚力均随加筋率增加呈现先增加后减小的趋势, 在加筋率达到0.75%时达到峰值; 加筋泡沫轻质土的内摩擦角受加筋率影响较小, 说明纤维作用主要是通过改变材料黏聚力来影响加筋泡沫轻质土的强度; 而强度降低率随着加筋率增加呈现明显的下降趋势, 最大从40%左右降低至10%左右时达到稳定; 加筋率一定时, 加筋泡沫轻质土的极限强度和残余强度均随着围压的升高呈增加趋势; 经过分析体积裂纹曲线发现加筋泡沫轻质土破坏时主要经历受压、产生裂缝、纤维承受拉力限制裂缝、裂缝扩展张力过大纤维拔出4个阶段, 而加筋泡沫轻质土达到屈服阶段时往往包括裂纹的稳定扩展阶段和裂纹的不稳定扩展阶段2个裂纹发育过程, 由于缺乏筋材, 泡沫轻质土属于脆性破坏, 因此, 没有裂纹不稳定增长阶段。Abstract: Through the triaxial shear test, the shear mechanical properties of polypropylene fiber reinforced foam lightweight soil under different reinforcement ratios and confining pressures were compared. The relationships between the strength parameters of the reinforced lightweight foamed soil and the reinforcement rate and confining pressure were investigated. The crack propagation law of reinforced lightweight foamed soil was obtained, and the stress-strain full curve equation was established. The constitutive equations for the strength parameters of foam lightweight soil in terms of reinforcement ratio and confining pressure were proposed. The experimental results with different reinforcement ratios were analyzed through the data normalization. The stress-strain full curve equation of reinforced foam lightweight soil was obtained. The functional relationships between the parameters of the curve equation and the two variables(reinforcement rate and confining pressure) were obtained. Analysis result shows that the triaxial shear strength and cohesion of reinforced foamed lightweight soil emerge a trend that increases first and then decreases with the increase of the reinforcement rate, and reach the peak values when the reinforcement rate reaches 0.75%. While the reinforcement ratio has limited influence on the internal friction angle of reinforced foam lightweight soil, which indicates that the function of fiber affects the strength of reinforced foam lightweight soil by changing the cohesive force of the material. The strength reduction rate presents an obvious descend trend with the increase of the reinforcement rate, at most, it decreases from about 40% to about 10%, and then keeps stable. When the reinforcement rate is kept constant, the ultimate strength and residual strength of reinforced foamed lightweight soil present an increase trend with the confining pressure. Through analyzing the volume crack curve, it is found that the reinforced lightweight foamed soil is mainly subjected to four stages when it is damaged: compression, cracking, crack restriction because of the fiber tension, and pulling out of fiber due to the large crack extension. When the reinforced foam lightweight soil reaches the yield stage by two crack development processes: the stable and unstable growth of crack. Due to the lack of reinforcement, the failure type of foam lightweight soil belongs to brittle failure, hence, there is no instability growth stage of crack.
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图 5 不同围压下强度降低率随加筋率曲线
Figure 5. Curves of strength reduction rate with reinforcement ratio under different confining pressures
图 6 抗剪强度指标随加筋率变化曲线
Figure 6. Changing curves of shear strength indicators with reinforcement ratio
图 11 参数i关于Rf和σ3二元函数
Figure 11. Bivariate functions of parameter i with respect to Rf and σ3
图 12 参数k关于Rf和σ3二元函数
Figure 12. Bivariate functions of parameter k with respect to Rf and σ3
图 13 参数A关于Rf和σ3二元函数
Figure 13. Bivariate functions of parameter A with respect to Rf and σ3
图 14 参数B关于Rf和σ3二元函数
Figure 14. Bivariate functions of parameter B with respect to Rf and σ3
表 1 聚丙烯纤维物理参数
Table 1. Physical parameters of polypropylene fiber
纤维名称 聚丙烯纤维 长度/mm 12 抗酸碱性能 极高 分散性 极好 燃点/℃ 580 熔点/℃ 160~180 纤维类型 束状单丝 直径/μm 31 断裂伸长率/% 10~28 弹性模量/MPa ≥3 850 密度/(g·cm-3) 0.91 抗拉强度/MPa ≥500 
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表 2 加筋泡沫轻质土强度降低率
Table 2. Strength reduction rates of reinforced foam light soils
围压/kPa 不同加筋率(%)加筋泡沫轻质土强度降低率/% 0 0.25 0.50 0.75 1.00 1.25 1.50 50 40.16 14.58 12.24 11.14 8.20 9.44 12.66 70 34.65 16.78 11.91 8.35 7.35 10.03 11.40 100 39.48 20.15 15.87 9.85 9.83 10.60 11.21
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表 3 抗剪强度指标汇总
Table 3. Summary of shear strength indicators
加筋率/% 0 0.25 0.50 0.75 1.00 1.25 1.50 内摩擦角/(°) 40.757 42.765 43.127 44.308 40.786 43.573 42.315 黏聚力/kPa 199.032 208.614 251.570 388.687 378.863 269.727 158.338
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表 4 Gompertz函数拟合结果
Table 4. Fitting result of Gompertz function
加筋率/% 围压/kPa k i R2 0.00 50 3.780 0.516 0.945 0.25 50 4.471 0.179 0.942 0.50 50 5.271 0.343 0.957 0.75 50 8.500 0.294 0.964 1.00 50 11.870 0.228 0.954 1.25 50 10.420 0.229 0.947 1.50 50 7.138 0.205 0.947 0.00 70 3.665 0.531 0.947 0.25 70 4.301 0.367 0.923 0.50 70 2.302 0.533 0.945 0.75 70 6.114 0.248 0.968 1.00 70 7.202 0.398 0.946 1.25 70 5.188 0.205 0.925 1.50 70 4.937 0.313 0.969 0.00 100 3.288 0.523 0.941 0.25 100 4.131 0.456 0.947 0.50 100 3.798 0.313 0.915 0.75 100 6.237 0.372 0.923 1.00 100 4.838 0.365 0.938 1.25 100 3.798 0.313 0.937 1.50 100 5.185 0.385 0.957
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表 5 Exponential函数拟合结果
Table 5. Fitting result of exponential function
加筋率/% 围压/kPa A B R2 0.00 50 4.185 -18.46 0.943 6 0.25 50 3.650 -28.60 0.972 4 0.50 50 4.899 -33.74 0.976 6 0.75 50 7.858 -18.09 0.948 7 1.00 50 14.787 -14.46 0.972 3 1.25 50 22.212 -7.62 0.987 7 1.50 50 2.103 -30.47 0.946 1 0.00 70 1.959 -15.62 0.960 0 0.25 70 9.870 -17.70 0.966 7 0.50 70 7.864 -20.04 0.966 3 0.75 70 1.187 -20.96 0.946 5 1.00 70 4.513 -19.91 0.945 4 1.25 70 4.385 -10.58 0.911 4 1.50 70 15.180 -11.74 0.950 3 0.00 100 1.015 -14.60 0.935 5 0.25 100 4.185 -18.46 0.933 2 0.50 100 6.603 -35.89 0.910 4 0.75 100 15.130 -5.11 0.956 4 1.00 100 2.959 -3.33 0.873 2 1.25 100 10.850 -4.44 0.966 5 1.50 100 44.900 -5.87 0.939 7
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表 6 形状参数i统计结果
Table 6. Statistical result of shape parameter i
围压/kPa 不同加筋率(%)Gompertz形状参数i 0.00 0.25 0.50 0.75 1.00 1.25 1.50 50 0.516 0.179 0.343 0.294 0.228 0.229 0.205 70 0.531 0.367 0.533 0.248 0.398 0.205 0.313 100 0.523 0.456 0.313 0.372 0.365 0.313 0.385
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表 7 形状参数k统计结果
Table 7. Statistical result of shape parameter k
围压/kPa 不同加筋率(%)Gompertz形状参数k 0.00 0.25 0.50 0.75 1.00 1.25 1.50 50 3.780 4.471 5.271 8.500 11.870 10.420 7.138 70 3.665 4.301 2.302 6.114 7.202 5.188 4.937 100 3.288 4.131 3.798 6.237 4.838 3.798 5.185
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表 8 形状参数A统计结果
Table 8. Statistical result of shape parameter A
围压/kPa 不同加筋率(%)Gompertz形状参数A 0.00 0.25 0.50 0.75 1.00 1.25 1.50 50 4.185 3.650 4.899 7.858 14.787 22.212 2.103 70 1.959 9.870 7.864 1.187 4.513 4.385 15.180 100 1.015 4.185 6.603 15.130 2.959 10.850 44.900
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表 9 形状参数B统计结果
Table 9. Statistical result of shape parameter B
围压/kPa 不同加筋率(%)Gompertz形状参数B 0.00 0.25 0.50 0.75 1.00 1.25 1.50 50 -18.46 -28.60 -33.74 -18.09 -14.46 -7.62 -30.47 70 -15.62 -17.70 -20.04 -20.96 -19.91 -10.58 -11.74 100 -14.60 -18.46 -35.89 -5.11 -3.33 -4.44 -5.87
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