Dynamic characteristics analysis of moistening loess tunnel of Yintao water supply main channel
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摘要: 为了得到增湿后黄土围岩隧洞在地震作用下的动力特性， 基于初始弹性模量和抗剪强度指标与含水量的关系， 采用时程分析法， 对增湿情况下的黄土围岩-隧洞结构进行地震动力分析. 数值计算结果表明： 随着含水量的增加， 隧洞衬砌各部位主应力绝对值减小， 自振圆频率减小， 自振周期相应增大； 与输入的地震加速度峰值相比， 当黄土隧洞围岩含水量小于临界含水量时， 隧洞顶部加速度峰值大于输入地震加速度峰值， 大于临界含水量时则出现相反的结果； 同一含水量下， 隧洞衬砌对称部位最大、 最小主应力交替出现， 使隧洞衬砌材料发生疲劳损伤， 是隧洞衬砌破坏的主要原因. 本文研究结果可以为在不同含水量情况下黄土围岩-隧洞结构的抗震分析提供参考.Abstract: In order to obtain the dynamic characteristics of tunnel in loess surrounding rock under seismic action after moistening， the seismic dynamics of the loess surrounding rock with moistening and tunnel structure had been analyzed with the time-history method， basing on the relationship between initial elastic modulus， the shear strength parameters and the water content. The numerical computation results showed that， with the water content of the loess surrounding rock increasing， the absolute value of principal stress and the autooscillation circular frequency all decreased relatively， while the period of free vibration increased correspondingly. When the water content was less than its critical value， the peak acceleration of the tunnel roof was larger than the original seismic peak acceleration. Otherwise， it was opposite. Under the same water content， the maximum and minimum principal stress appeared alterna-tely， making the tunnel lining material fatigue damage， which was the main reason for the tunnel lining damage. The results can provide a reference for the seismic analysis on the different water content conditions of loess surrounding rock and tunnel structure.
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Keywords:
- moistening /
- the loess tunnel /
- time-history analysis /
- water content /
- peak acceleration /
- principal stress
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图 2 El-Centro地震波加速度示意图
Figure 2. Schematic diagram of El-Centro seismic wave acceleration
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图 3 黄土隧洞顶部地震峰值加速度随含水量的变化
Figure 3. Variation of seismic peak acceleration with water content of the loess tunnel roof
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图 4 左拱肩(a)和右拱肩(b)主应力图
Figure 4. The principal stress of left- (a) and right-spandrel (b)
表 1 黄土隧洞围岩计算参数
Table 1 The calculation parameters of tunnel in loess surrounding rock
w γ/(kN·m-3) E/MPa c/kPa φ/° μ ξ 7.42% 1.64 130 57.8 24.1 0.3 0.12 9.36% 1.61 118 39.5 25.2 0.3 0.12 11.95% 1.59 100 31.0 26.0 0.3 0.12 13.25% 1.56 97 20.2 26.5 0.3 0.12 15.10% 1.54 93 17.2 27.1 0.3 0.12 注： w为含水量(下同)， γ为容量， E为初始弹性模量， c为黏聚力， φ为内摩擦角， μ为泊松比， ξ为阻尼比． 
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表 2 黄土隧洞围岩含水量与圆频率关系表
Table 2 The relationship between water content and circular frequency of tunnel in loess surrounding rock
w ω1 ω2 ω3 ω4 ω5 ω6 ω7 ω8 7.42% 0.68998 1.5569 2.0702 2.4639 2.7083 3.3117 3.4490 3.4992 9.36% 0.66358 1.4974 1.9908 2.3695 2.6048 3.1851 3.3172 3.3648 11.95% 0.61490 1.3876 1.8446 2.1955 2.4139 2.9514 3.0741 3.1172 13.25% 0.61142 1.3798 1.8341 2.1831 2.4003 2.9348 3.0568 3.0994 15.10% 0.60259 1.3599 1.8076 2.1516 2.3657 2.8925 3.0128 3.0545 注： ω1—ω8分别为第1—8阶圆频率.
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表 3 黄土隧洞围岩含水量与阻尼系数关系表
Table 3 The relationship between water content and damping coefficients of tunnel in loess surrounding rock
w η λ 7.42% 0.137 0.060 9.36% 0.132 0.062 11.95% 0.122 0.067 13.25% 0.121 0.068 15.10% 0.120 0.069 注： η为质量阻尼系数， λ为刚度阻尼系数.
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表 4 黄土隧洞顶部含水量与地震峰值加速度关系表
Table 4 The relationship between water content and seismic peak acceleration of the loess tunnel roof
w t/s A/(m·s-2) 7.42% 2.22 2.029 9.36% 2.22 1.978 11.95% 2.22 1.943 13.25% 2.22 1.940 15.10% 2.22 1.933 注： A为地震峰值加速度．
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表 5 黄土隧洞衬砌主应力及最大位移
Table 5 The principal stress and maximum displacement of the loess tunnel lining
w 衬砌位置 σmax/MPa σmin/MPa s/cm 7.42% 左拱肩 3.02 -2.64 2.72 右拱肩 2.64 -3.02 2.70 左拱脚 2.60 -2.97 2.69 右拱脚 2.96 -2.61 2.67 9.36% 左拱肩 2.97 -2.63 2.95 右拱肩 2.62 -3.00 2.92 左拱脚 2.58 -2.94 2.91 右拱脚 2.92 -2.58 2.89 11.95% 左拱肩 2.75 -2.55 3.52 右拱肩 2.52 -2.82 3.50 左拱脚 2.46 -2.57 3.48 右拱脚 2.56 -2.47 3.46 13.25% 左拱肩 2.09 -1.88 3.90 右拱肩 1.80 -2.16 3.87 左拱脚 1.73 -2.10 3.85 右拱脚 2.02 -1.83 3.83 15.10% 左拱肩 1.92 -1.67 4.12 右拱肩 1.58 -1.99 4.10 左拱脚 1.51 -1.84 4.08 右拱脚 1.84 -1.62 4.06 注：σmax为最大主应力，σmin为最小主应力，s为最大位移．
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