Design and experimental research on model soils used for shaking table tests of superstructure-soil-tunnel interaction system
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摘要: 为使上部结构-土-隧道相互作用体系各部分的加速度相似比相匹配,真实还原地震作用下整个体系的动力响应,采用理论分析和试验相结合的方法,设计了一种以锯末、河砂、粉质黏土以及水为成分的模型土。对试配的不同材料配比的模型土进行了大量30 kPa围压下的共振柱试验,并以此为基础设计进行了正交试验,创建Y(Sγr,Sα,Q)函数以判定模型土与原型土G/Gmax-
γ 动力特性曲线的相似性。正交试验结果表明：模型土的材料锯末、河砂与粉质黏土最优质量比为18%∶27%∶55%,含水率为50%；最优方案模型土基本满足了其与原型土加速度相似比Sa等于3、动剪切模量比G/Gmax随剪应变γ 变化的关系曲线相似的预期目标；并获得了各添加材料对模型土相关动力参数的影响规律。另外,进行了50,70 kPa围压下的最优配比模型土的共振柱试验,验证了其基本满足与原型土在不同围压下G/Gmax-γ 动力特性曲线的相似性,同时对比二者的阻尼比λ 随剪应变γ 的变化关系曲线,得出二者关于阻尼比的相似性尚可；并基于卓越周期相似分析再次验证模型土与原型土的相似性。研究结论可为今后有关振动台试验模型土的配制提供一定的参考。Abstract: In order to match the similitude ratio of acceleration of a superstructure-soil-tunnel interaction system and truly restore its dynamic response under earthquake action, a kind of model soil composed of sawdust, river sand, silty clay and water is designed by combining the theoretical analysis with experiments. A large number of resonant column tests on the model soils with different material ratios are carried out at confining pressure of 30 kPa, then the orthogonal test scheme is designed and conducted, and Y(Sγr, Sα, Q) function is created to judge the similitude about dynamic shear modulus ratio-shear strain curves between model and prototype soils. The orthogonal test results show that the optimal mass ratio of sawdust, river sand and silty clay is 18%∶27%∶55%, and the moisture content is 50%. The model soil with the optimal proportion basically satisfies the expected target that its similitude ratio of acceleration to the prototype soil is 3 and its correlation curve of dynamic shear modulus ratio-shear strain is similar to that of the prototype soil. The influence laws about dynamic parameters of model soils are obtained for various additive materials. In addition, the resonant column tests on the model soil with the optimal proportion are carried out at confining pressures of 50 and 70 kPa. It is verified that the similitude between the model and prototype soils at different confining pressures is basically satisfied, their correlation curves about damping ratio and shear strain are compared, and it is obtained that their similitude about damping ratio is reasonable. Based on the similarity analysis of the predominant period, the similitude between the model and prototype soils is verified again. The research conclusions may provide some reference for the preparation of model soils in shaking table tests in the future.-
Keywords:
- shaking table test /
- model soil /
- resonant column test /
- orthogonal test
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图 2 原型土及试配方案G/Gmax-
γ 曲线Figure 2. Curves of G/Gmax-
γ of prototype soil and test schemes![]()
图 3 原型土及正交方案G/Gmax-
γ 曲线Figure 3. Curves of G/Gmax-
γ of prototype soil and orthogonal schemes![]()
图 5 不同围压下模型土与对应深度原型土的G/Gmax-
γ 曲线Figure 5. Curves of G/Gmax-
γ of model soils and corresponding depths of prototype soils at different confining pressures![]()
图 6 不同围压下模型土与对应深度原型土的
λ -γ 曲线Figure 6. Curves of
λ -γ of model soils and corresponding depths of prototype soils at different confining pressures表 1 天津某场地地勘报告
Table 1 Geological survey report of a site in Tianjin
土层类别 土层厚度d/m 埋深h/m 密度ρ/(g·cm-3) 剪切波速vse/(m·s-1) 最大动剪切模量Gmax/MPa 杂填土 3.1 3.1 1.85 132 32.23 粉质黏土 1.6 4.7 1.90 147 41.06 粉土 2.8 7.5 2.00 152 46.21 粉质黏土 3.1 10.6 1.90 168 53.63 粉质黏土 2.0 12.6 1.90 194 71.51 粉质黏土 2.0 14.6 2.00 223 99.46 粉质黏土 3.4 18.0 2.00 231 106.72 粉质黏土 7.5 25.5 2.00 240 115.20 粉土 2.6 28.1 2.00 242 117.13 粉质黏土 4.0 32.1 2.06 270 150.17 粉质黏土 2.4 34.5 2.06 285 167.32 粉质黏土 4.7 39.2 2.06 296 180.49 粉质黏土 2.8 42.0 1.99 311 192.47 
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表 2 模型相似关系
Table 2 Similitude relations of model
物理量 相似关系 上部结构 隧道 土 长度l [L] SL=1/30 SL=1/30 SL=1/30 线位移δ [L] Sδ=SL=1/30 Sδ=SL=1/30 Sδ=SL=1/30 弹性模量E [FL-2] SE=0.3 SE=0.265 SE=SG 等效质量密度ρe [FL-4T2] Sρe=3 Sρe=2.65 ρm/ρp 频率ω [T-1] Sω=1/ST=9.523 Sω=1/ST=9.523 9.523 时间t [T] ST=SL√Sρe/SE=0.105 0.105 0.105 加速度幅值a [LT-2] Sa=SE/(SLSρe)=3 3 SG/SρSl=3
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表 3 正交试验方案及部分结果
Table 3 Orthogonal test schemes and partial results
方案 锯末A/% 河砂B/% 含水率C/% 密度ρ/(g·cm-3) 最大动剪切模量Gmax/MPa 加速度相似比Sa 1 18 21 35 1.42 9.516 3.51 2 18 27 50 1.49 8.283 2.91 3 18 33 60 1.56 6.799 2.28 4 23 21 50 1.33 9.165 3.60 5 23 27 60 1.46 7.402 2.64 6 23 33 35 1.20 8.751 3.81 7 28 21 60 1.25 6.318 2.64 8 28 27 35 1.06 6.350 3.12 9 28 33 50 1.09 6.319 3.00 注： 因素A为锯末含量,即锯末占锯末、河砂和粉质黏土总质量的百分比（m锯末/m总）,因素B为河砂含量,即河砂占锯末、河砂和粉质黏土总质量的百分比（m砂/m总）。
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表 4 正交方案Stokoe模型拟合参数及Q值、Y值
Table 4 Fitting parameters of Stokoe model and values of Q and Y for orthogonal tests
方案 参考剪应变 γr 曲率系数 α Q(γr, α) Y(Sγr, Sα, Q) P 0.00118 0.943 0 0 1 0.00174 0.925 0.033 2.71×10-6 2 0.00130 1.015 0.003 1.80×10-7 3 0.00195 0.954 0.055 3.18×10-6 4 0.00320 0.628 0.179 0.0585 5 0.00191 1.075 0.062 0.0004 6 0.00266 0.834 0.134 0.0028 7 0.00349 0.750 0.219 0.0351 8 0.00343 0.748 0.217 0.0337 9 0.00181 1.201 0.063 0.0013 注： P代表粉质黏土。
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表 5 各因素对曲线相似性影响极差分析
Table 5 Range analysis of influences of various factors on similitude of curves
项目 因素 锯末A 河砂B 水C K1 6×10-6 0.093 0.036 K2 0.061 0.034 0.059 K3 0.070 0.004 0.035 极差 0.070 0.089 0.024 主→次 B→A→C 注： Ki为正交方案任一列上水平号为i时所对试验结果之和。
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表 6 模型土的Gmax的方差分析
Table 6 Variance analysis of Gmax of model soils
项目 因素 锯末A 河砂B 水C 组间均方MSA 4.249 2.525 1.559 组内均方MSe 0.820 1.539 1.715 F值（F=MSA/Mse） 5.181 1.641 0.908 单因素显著性 显著 不显著 不显著
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表 7 模型土的Gmax/ρ的方差分析
Table 7 Variance analysis of Gmax/ρ of model soils
项目 因素 锯末A 河砂B 水C 组间均方MSA 0.722 0.350 2.717 组内均方MSe 1.001 1.125 0.432 F值（F=MSA/Mse） 0.721 0.311 6.289 单因素显著性 不显著 不显著 显著
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表 8 模型土与原型土的加速度相似比相关参数
Table 8 Correlation parameters about similitude ratio of acceleration of model and prototype soils
类别 围压σ/kPa 最大动剪切模量Gmax/MPa 加速度相似比Sa 原型土 402 115 2.9 模型土 30 8.3 原型土 670 150 2.76 模型土 50 10.3 原型土 940 192 2.54 模型土 70 12.0
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表 9 模型土与原型土G/Gmax-
γ 曲线相似性相关参数Table 9 Correlation parameters about similitude of G/Gmax-
γ of model and prototype soils类别 围压σ/kPa 参考剪应变γr 曲率系数α Q Y 原型土 402 0.00106 0.945 0.003 8.44×10-7 模型土 30 0.00130 1.015 原型土 670 0.00127 0.961 0.004 1.68×10-7 模型土 50 0.00134 1.074 原型土 940 0.00136 0.935 0.007 1.11×10-7 模型土 70 0.00139 1.104
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