Analysis on Precipitation-Induced Subsidence of Covered Karst Soil Caves Regarding Spatial Shape
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摘要:
为揭示覆盖型岩溶土洞降水致陷机理、洞体形状尺寸影响及极限平衡状态下内在规律，以常见直筒塌陷椭球土洞为研究对象，构建其降水致陷力学模型，依据玻义耳-马略特定律推导了土洞空腔负压计算公式，以此获得土洞塌落稳定系数表达式，并对比验证计算公式的可行性；进一步获得了极限平衡状态下土体物理力学参数、降水参数、土洞空间形状尺寸及覆土厚度之间内在关系式；基于算例开展了地下水降水参数与土洞形状尺寸参数影响、极限平衡状态下内在规律分析. 研究结果表明：初始水位高于洞顶时，土洞塌落稳定系数与地下水降深展现“Z”字形规律变化，下降稳定水位降越拱顶瞬间极易引发土洞塌陷；初始水位处于洞体时，两者呈现前陡后缓的负相关变化规律，且洞内初始水位越高，降幅越大；初始水位低于洞底时，降深影响很小. 椭球长短半轴之比对稳定系数影响符合增函数变化规律，截面离心率越大越稳定，而圆形球体则最不利；矢高和稳定系数呈线性关系，矢高增加成拱效应显著，土洞越稳定. 极限平衡状态下，初始水位一定时，降深与覆盖层厚度正相关，呈现前缓后陡变化趋势，而覆盖层厚度一定时，降深与初始水位负相关；土洞水平截面离心率越大或矢高越大，达到极限平衡状态所需地下水降深则越大，表现为前缓后陡变化规律.
Abstract:In order to reveal the precipitation mechanism of covered Karst caves, the influence of the shape and size of the cave body and the internal law under the limit equilibrium, a common ellipsoid soil cave in straight collapse is investigated and its mechanical model of precipitation-induced subsidence is constructed. The calculation formula of the cavity negative pressure for the soil cave is deduced according to Boyle-Maliot law, so as to obtain the expression of the stability coefficient for the soil cavecollapse, and the feasibility of the calculation formula is verified by comparison. Further, the internal relations among the physical and mechanical parameters of soil mass, precipitation parameters, the spatial shape and size of soil hole and the overburden soil thickness under the limit equilibrium are obtained. Utilizing a calculation example, the influence of groundwater precipitation parameters and the shape and size parameters of the soil cave, and the internal law analysis under the limit equilibrium state are carried out. It is pointed out that when the initial water level is higher than the cave top, the stability coefficient of soil cave collapse and groundwater drawdown show a “Z”-shaped change, and it is very easy to cause soil cave collapse the moment the falling stable water level falls over the vault. When the initial water level is in the cave body, they show a negative correlation with changes steep in the front and slow in the back, and the higher the initial water level in the cave, the greater the decline; when the initial water level is lower than the cave bottom, the effect of drawdown is very small. The influence of the ratio of the long and short half axes of the ellipsoid on the stability coefficient conforms to the pattern of the increasing function. The greater the eccentricity of the cross section, the more stable it is, while the circular sphere is the most unfavorable. There is a linear relationship between the arch height and the stability coefficient. The arching effect is significant when the arch height increases, and the soil hole is more stable. Under the limit equilibrium, when the initial water level is fixed, the drawdown is positively correlated with the thickness of the overburden layer, showing a trend of slow change before and steep change after; however, when the thickness of the overburden layer is fixed, the drawdown is negatively correlated with the initial water level. The greater the horizontal section eccentricity of the soil cave or the higher the arch height, the deeper the groundwater required to reach the limit equilibrium, which is characterized by the changes gentle front and steep back.
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图 1 土洞降水致陷力学模型
Figure 1. Mechanical model of soil cave collapse induced by precipitation
图 3 降水参数
$ {h}_{0}、\Delta h $ 对稳定系数的影响Figure 3. Influence of groundwater parameters
${h_0}$ and$\Delta h$ on stability coefficient
图 4
$ a、b $ 对稳定系数的影响Figure 4. Influence of size parameters a and b on stability coefficient
图 6 极限状态下降水参数与覆盖层厚度内在规律
Figure 6. Inherent law of precipitation parameters and overburden thickness in limit state
图 7 极限状态下降水参数与土洞形状尺寸内在规律
Figure 7. Inherent law of precipitation parameters and shape and size of soil cavity in limit state
表 1 土体物理力学参数
Table 1. Physical and mechanical parameters of soil
土层 γ/（kN·m−3） C/kPa ϕ/（°） 填土 18.0～20.0 32.0～40.0 12.0～18.0 粉砂 15.0～18.0 5.0～9.0 4.0～10.0 砂 17.0～23.0 6.0～12.0 12.0～15.0 黏土 18.0～20.0 35.0～46.0 18.0～25.0 
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表 2 土洞降水致陷计算结果
Table 2. Calculation results of precipitation-induced subsidence of covered karst soil cave
编号 a，b，c/m h0/m ∆h/m K 抽水前 抽水后 T7 3.75，1.75，1.75 1.63 2.2 2.15 0.95 T8 9.50，6.00，6.00 6.08 2.2 1.05 0.53 T10 2.50，2.50，2.50 2.58 2.2 1.85 0.86
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