沪蓉西高速公路乌池坝岩溶隧道涌水成灾机理研究
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摘要
随着西部大开发战略深入实施,我国公路、铁路建设重点已逐渐由平原地带转移到山岭重丘地区,由此将产生大量的山区隧道,“多、长、大、深”是山区隧道的典型特点。制约特长隧道发展的因素主要有掘进技术、支护技术、通风技术、不良地质等。在现有技术经济条件下,最为主要的制约因素是不良地质作用,即隧道施工开挖过程中可能诱发各类地质灾害。常见隧道地质灾害包括软岩、断层破碎带、岩性不整合接触带、地下水、岩溶管道、岩溶塌陷、采空区和岩爆等。其中隧道涌水灾害是隧道工程建设中一个难题,国内外已建隧道中都曾经发生过许多严重涌水事故,大规模涌水常常造成巨大经济损失和人员伤亡。为此开展山区岩溶隧道涌水成灾机理方面的研究,对特长隧道涌水灾害的预测及防治具有重要的理论意义与工程实践意义。
本文以湖北沪蓉西乌池坝隧道为研究对象,综合采用地质学、水文地质学、岩土力学、地下水动力学等相关学科的理论基础知识结合数理统计、非线性理论、数值模拟等数学分析方法,试图从岩溶发育主控因素及失稳模式角度建立乌池坝隧道的涌水地质模型；在此基础上,从隧道涌水地下水动力学演化过程角度结合突变模型,探讨岩溶隧道涌水成灾机理及其力学演化过程；采用经验计算模型与数值计算模型相结合的量化分析手段,对乌池坝隧道的涌水量进行预测,并对多种预测方法进行对比分析；最后采用正交试验与回归分析相结合的方法,探讨上覆型、下伏型及侧伏型岩溶隧道与溶洞问的安全距离及其影响因素,建立三种岩溶隧道安全距离与影响因素间的数学预测模型。通过上述分析和研究,主要取得了以下结论与成果：
(1)岩溶发育受地层岩性、地下水动力分带、地质构造、地形地貌等因素控制,其中地层岩性是基础,地质构造是主导,水动力条件则是决定性因素。
(2)岩溶突水影响因素可概化为地质因素和工程因素两种。地质因素方面,岩溶含水介质通常具有不均一性和多样性,且水量分布极不均匀,层流与紊流共存,小裂隙构成主要贮水空间、大溶蚀裂隙构成主要导水通道。工程因素方面,岩体开挖卸荷、爆破扰动以及注浆失效等等都是主控影响因素,在很大程度上导致突水滞后性和不确定性。
(3)岩溶突水实质上是岩溶含水介质系统、水动力系统以及围岩力学平衡状态因地下工程开挖而发生急剧变化,存贮在地下水体能量瞬间释放,并以流体形式高速地向工程临空面内运移一种动力破坏现象。从水-岩相互作用机理来看,岩溶突水包含两个过程阶段,即岩溶突水蓄势机理和岩溶突水失稳机理,其中前者是一个漫长历史过程,后者是前者能量积蓄瞬间突变形式。
(4)从含导水构造能量储存、岩溶水动力扰动和能量释放以及含导水构造系统失稳角度提出岩溶突水的发生条件,并将岩溶突水过程划分为蓄势与失稳两个显著阶段；采用多场耦合软件计算开挖条件下岩溶突水形成过程的流态演变特征,实现了岩溶水由含水层中的渗流发展为潜在突水通道中的快速流,最后突入隧道内形成自由流的灾变演化过程。
(5)基于不同成因地质缺陷体的归类和阻水性能分析,提出地质缺陷诱发突水的两种典型灾变模式,分析了地质缺陷式突水通道的形成过程及其失稳的力学判据。就不同尺度地质缺陷体渗透特性的差异,建立了强渗流作用下充填介质的渗透失稳模型和充填体的滑移失稳突水模型,并将之应用于乌池坝隧道岩溶管道诱发突水的实例分析中,结合数值分析结果,揭示了充填介质渗透失稳形成堵塞体后整体滑移突水的灾变演化过程：对于非导水断层,考虑两区段充填介质的力学属性,引入水致弱函数反映强渗流对断层充填介质的活化作用,建立了断层充填体滑移失稳的燕尾突变模型,并基于灾变演化路径控制参数的分析提出相应的防治措施。基于大量数值计算结果,分析了断层活化诱发破裂通道的灾变机制,给出了断层突水的4种灾变路径,并对断层参数对突水的敏感性进行了分析。最后,基于不同揭露型突水模式的灾变分析,提出复合式突水类型,分析地质缺陷诱发隔水围岩失稳的非揭露型突水的灾变机制,并结合工程实例,进一步揭示了断层活化导通暗河水涌入与隧道存在水力联系的充填型溶腔,并导致隧道拱部完整围岩压裂突水的灾变演化机制。
(6)通过乌池坝隧道水文地质条件分析,采用"Visual MODFLOW2.7.1"三维渗流模拟和常规经验公式对乌池坝隧道涌水量进行预测,并对其结果进行对比分析,确保了预测结果的可靠性。乌池坝隧道整个隧道最小涌水量在12000-22000m3/d之间,正常值(施工期平水年)在24000～47000m3/d之间,大值(施工期丰水年)在30000～96000m3/d之间。
(7)通过FLAC3D数值模拟结合正交试验方案,对上覆型、下伏型及侧伏型岩溶隧道与溶洞间的安全距离进行分析,得到围岩级别、岩体侧压力系数、溶洞跨度、溶洞高跨比和隧道埋深五个影响因素对安全距离的影响程度和影响规律。对于上覆型和下伏型岩溶隧道,溶洞跨度对安全距离的影响较大,溶洞高跨比对安全距离的影响较小；对于侧伏型岩溶隧道,溶洞高跨比对安全距离的影响较大,溶洞跨度对安全距离的影响较小,即垂直于隧道与溶洞连线方向的溶洞尺寸对于安全距离的影响较大,而平行于隧道与溶洞连线方向的溶洞尺寸对于安全距离的影响较小。
(8)单因素回归分析结果显示,对于上覆型和下伏型岩溶隧道,隧道与溶洞间的安全距离与围岩级别及岩体侧压力系数呈指数关系,与溶洞跨度及溶洞高跨比呈线性关系,与隧道埋深呈对数关系；对于侧伏型岩溶隧道,隧道与溶洞间的安全距离与围岩级别呈指数关系,与岩体侧压力系数呈二次多项式关系,与溶洞跨度及溶洞高跨比呈线性关系,与隧道埋深呈对数关系。在此基础,通过多元回归分析建立了上覆型、下伏型及侧伏型岩溶隧道安全距离与上述五种影响因子间的数学预测模型。
With the in-depth implementation of the western development strategy, China's construction of highways, railways focus has gradually shifted to the plains in mountainous and hilly areas, which will generate a lot of mountain tunnel,"long, deep" is typical of the mountain tunnel characteristics. The main factors restricting the development of the long tunnel boring technology, supporting technology, ventilation technology, poor geological. Most major constraints in the existing technical and economic conditions, adverse geological, tunnel excavation process may induce various types of geological disasters. Common tunnel geological disasters including soft rock fracture zone, lithology unconformable contact with groundwater, karst conduits, karst collapse, goaf and rockburst. Tunnel gushing disaster is a difficult problem in the construction of the tunnel project, at home and abroad have been built many serious gushing accident have occurred in the tunnel, large-scale water gushing often cause huge economic losses and casualties. Have embarked mountainous karst tunnel gushing disaster the study of the mechanism of long tunnel gushing disaster prediction and prevention has important theoretical significance and engineering practice significance.
With the Wu-chi-ba Tunnel of Hurong Freeway as the research object, using a combination of theoretical basics of the related disciplines of geology, hydrogeology, rock mechanics, groundwater dynamics, combined with mathematical statistics, nonlinear theory, numerical simulation and mathematical analysis method, trying to establish the tunnel's gushing Wuchiba Geological model from the karst development master factors and the instability mode angle; gushing groundwater dynamics perspective of evolution from the tunnel on this basis, combined with catastrophe model to explore the karst tunnel gushing disaster mechanism Its mechanical evolution; experience computing model and numerical calculation model combining quantitative analysis means the tunnel Wuchiba inflow predict comparative analysis on a variety of forecasting methods; Finally, using orthogonal experimental and regression analysis a combination of methods to explore the safe distance between the overlying and underlying type and side-volt type karst tunnel and cave and its influencing factors, to establish a safe distance and influencing factors of three karst tunnel mathematical prediction model. Through the above analysis and research, made the following conclusions and results:
(1) karst development by factors such as lithology, groundwater dynamic zonation, geological structure, topography control, including the formation lithology, geological structure is led hydrodynamic conditions is the decisive factor.
(2) the irruption water impact factors can be summarized into two kinds of geological factors and engineering factors. Geological factors, karst aqueous medium usually with heterogeneity and diversity, and water distribution is very uneven, laminar and turbulent coexistence, small fissures constitute the main water storage space; large corrosion fissures constitute a major water guide channel. Engineering factors, rock excavation unloading, blasting disturbance and grouting failure are the master of influencing factors, caused largely the water inrush lag and uncertainty.
(3) The water from karst essentially system of karst aqueous medium, the equilibrium hydrodynamic system as well as the surrounding rock mechanics changed dramatically Underground Excavation, instantaneous release of energy stored in the groundwater bodies and fluid form of high speed engineering migration a driving force to undermine the free surface phenomenon. View from the water-rock interaction mechanism, the the irruption water contains two process stages, poised mechanism of water from karst and karst water inrush mechanism of instability, of which the former is a long historical process, the latter is the former energy savings instantly mutation form.
(4) energy storage containing hydraulic conductivity structure, karst hydrodynamic disturbances and energy release with Derivative the water structure system instability angles proposed the occurrence of water from karst conditions, and irruption water process is divided into two poised and destabilization significant stage; flow pattern evolution characteristics of multi-field coupling software calculates the excavation under the conditions of water from karst formation process, the development of karst water from the aquifer seepage rapid flow of potential water inrush channel, and finally broke into the tunnel formation The free flow catastrophic evolution process.
(5) analysis based on the different causes of geological defects classified and water barrier properties proposed geological defects induced water inrush two typical catastrophe mode analysis of geological defect type the sudden water channel formation process and its instability mechanical criterion. Differences in the permeability characteristics of different scale geological defects, the of strong seepage action filling media penetration instability model and filling slip instability of water inrush model, and applied to Wuchiba tunnel karst conduits induced water inrush instance analysis, combined with the results of numerical analysis, to reveal filling the media penetration instability formation blockage body after the overall slip sudden water cataclysm evolution; consider water for non-conducting faults, the mechanical properties of the two-section filling medium, the introduction of water-borne The weak function reflects the strong seepage on the activation of the fault filling medium, the establishment of a fault backfill slip instability swallowtail catastrophe model and control parameters based on the catastrophic evolution path analysis to propose appropriate prevention and control measures. Based on a large number of numerical results, analysis, fault reactivation induced rupture channel catastrophe mechanism, the inrush of water catastrophe path analysis and fault parameters of the sensitivity of the water inrush. Finally, expose water inrush mode-based catastrophe analysis proposed composite water inrush type analysis of geological defects induced instability impermeable wall rock the catastrophe of the non-exposed water inrush mechanism and engineering instance, further reveals the fault activation The conduction dark river water influx tunnel caverns filled hydraulic connection exists, and cause catastrophic evolution mechanism of the arch of the tunnel the complete surrounding rock fracturing water inrush.
(6) analysis through Wuchiba tunnel hydrogeological conditions, to using the "Visual MODFLOW2.7.1" Three Dimensional Seepage analog and conventional empirical formula forecast inflow of Wuchiba tunnel, and its results were analyzed to ensure that the predicted results reliability. The entire tunnel Wuchiba tunnel smallest inflow between12000～22000m3/d,, normal (construction period average year) between24000～47000m3/d, large value (construction period wet years) in the30000～96000m3/d.
(7) orthogonal test program FLAC3D numerical simulation analysis of the safe distance between the overlying and underlying and side-volt karst tunnels and caverns, Rock Classification rock side pressure coefficient, cave span the caves high-span ratio and tunnel depth of five influencing factors affect the extent and impact of the law on the safety distance. Safe distance for overlying and underlying karst tunnels, caverns span large cave high cross is smaller than the safe distance; side Volt karst tunnel, cave high cross than the safe distance, small cave span safe distance, that is perpendicular to the direction of the cave size of tunnels and caverns connection safety distance and parallel to the direction of the cave size of tunnels and caverns connection safe distance than small.
(8) Univariate regression analysis showed high cross than the overlying and underlying karst tunnels, tunnel and cave between the level of safety distance with the surrounding rock and rock mass lateral pressure coefficient exponential relationship, span and cave and cave a linear relationship with the logarithmic relationship; tunnel depth karst tunnel side Volt safe distance between the tunnel and cave Rock Classification exponential relationship was quadratic polynomial relationships with the rock side pressure coefficient, cave span and cave high cross than a linear relationship between logarithmic relationship with tunnel depth. On this basis, the overlying and underlying type and side-volt karst tunnel safe distance above five impact factor mathematical prediction model by multiple regression analysis.
本文以湖北沪蓉西乌池坝隧道为研究对象,综合采用地质学、水文地质学、岩土力学、地下水动力学等相关学科的理论基础知识结合数理统计、非线性理论、数值模拟等数学分析方法,试图从岩溶发育主控因素及失稳模式角度建立乌池坝隧道的涌水地质模型；在此基础上,从隧道涌水地下水动力学演化过程角度结合突变模型,探讨岩溶隧道涌水成灾机理及其力学演化过程；采用经验计算模型与数值计算模型相结合的量化分析手段,对乌池坝隧道的涌水量进行预测,并对多种预测方法进行对比分析；最后采用正交试验与回归分析相结合的方法,探讨上覆型、下伏型及侧伏型岩溶隧道与溶洞问的安全距离及其影响因素,建立三种岩溶隧道安全距离与影响因素间的数学预测模型。通过上述分析和研究,主要取得了以下结论与成果：
(1)岩溶发育受地层岩性、地下水动力分带、地质构造、地形地貌等因素控制,其中地层岩性是基础,地质构造是主导,水动力条件则是决定性因素。
(2)岩溶突水影响因素可概化为地质因素和工程因素两种。地质因素方面,岩溶含水介质通常具有不均一性和多样性,且水量分布极不均匀,层流与紊流共存,小裂隙构成主要贮水空间、大溶蚀裂隙构成主要导水通道。工程因素方面,岩体开挖卸荷、爆破扰动以及注浆失效等等都是主控影响因素,在很大程度上导致突水滞后性和不确定性。
(3)岩溶突水实质上是岩溶含水介质系统、水动力系统以及围岩力学平衡状态因地下工程开挖而发生急剧变化,存贮在地下水体能量瞬间释放,并以流体形式高速地向工程临空面内运移一种动力破坏现象。从水-岩相互作用机理来看,岩溶突水包含两个过程阶段,即岩溶突水蓄势机理和岩溶突水失稳机理,其中前者是一个漫长历史过程,后者是前者能量积蓄瞬间突变形式。
(4)从含导水构造能量储存、岩溶水动力扰动和能量释放以及含导水构造系统失稳角度提出岩溶突水的发生条件,并将岩溶突水过程划分为蓄势与失稳两个显著阶段；采用多场耦合软件计算开挖条件下岩溶突水形成过程的流态演变特征,实现了岩溶水由含水层中的渗流发展为潜在突水通道中的快速流,最后突入隧道内形成自由流的灾变演化过程。
(5)基于不同成因地质缺陷体的归类和阻水性能分析,提出地质缺陷诱发突水的两种典型灾变模式,分析了地质缺陷式突水通道的形成过程及其失稳的力学判据。就不同尺度地质缺陷体渗透特性的差异,建立了强渗流作用下充填介质的渗透失稳模型和充填体的滑移失稳突水模型,并将之应用于乌池坝隧道岩溶管道诱发突水的实例分析中,结合数值分析结果,揭示了充填介质渗透失稳形成堵塞体后整体滑移突水的灾变演化过程：对于非导水断层,考虑两区段充填介质的力学属性,引入水致弱函数反映强渗流对断层充填介质的活化作用,建立了断层充填体滑移失稳的燕尾突变模型,并基于灾变演化路径控制参数的分析提出相应的防治措施。基于大量数值计算结果,分析了断层活化诱发破裂通道的灾变机制,给出了断层突水的4种灾变路径,并对断层参数对突水的敏感性进行了分析。最后,基于不同揭露型突水模式的灾变分析,提出复合式突水类型,分析地质缺陷诱发隔水围岩失稳的非揭露型突水的灾变机制,并结合工程实例,进一步揭示了断层活化导通暗河水涌入与隧道存在水力联系的充填型溶腔,并导致隧道拱部完整围岩压裂突水的灾变演化机制。
(6)通过乌池坝隧道水文地质条件分析,采用"Visual MODFLOW2.7.1"三维渗流模拟和常规经验公式对乌池坝隧道涌水量进行预测,并对其结果进行对比分析,确保了预测结果的可靠性。乌池坝隧道整个隧道最小涌水量在12000-22000m3/d之间,正常值(施工期平水年)在24000～47000m3/d之间,大值(施工期丰水年)在30000～96000m3/d之间。
(7)通过FLAC3D数值模拟结合正交试验方案,对上覆型、下伏型及侧伏型岩溶隧道与溶洞间的安全距离进行分析,得到围岩级别、岩体侧压力系数、溶洞跨度、溶洞高跨比和隧道埋深五个影响因素对安全距离的影响程度和影响规律。对于上覆型和下伏型岩溶隧道,溶洞跨度对安全距离的影响较大,溶洞高跨比对安全距离的影响较小；对于侧伏型岩溶隧道,溶洞高跨比对安全距离的影响较大,溶洞跨度对安全距离的影响较小,即垂直于隧道与溶洞连线方向的溶洞尺寸对于安全距离的影响较大,而平行于隧道与溶洞连线方向的溶洞尺寸对于安全距离的影响较小。
(8)单因素回归分析结果显示,对于上覆型和下伏型岩溶隧道,隧道与溶洞间的安全距离与围岩级别及岩体侧压力系数呈指数关系,与溶洞跨度及溶洞高跨比呈线性关系,与隧道埋深呈对数关系；对于侧伏型岩溶隧道,隧道与溶洞间的安全距离与围岩级别呈指数关系,与岩体侧压力系数呈二次多项式关系,与溶洞跨度及溶洞高跨比呈线性关系,与隧道埋深呈对数关系。在此基础,通过多元回归分析建立了上覆型、下伏型及侧伏型岩溶隧道安全距离与上述五种影响因子间的数学预测模型。
With the in-depth implementation of the western development strategy, China's construction of highways, railways focus has gradually shifted to the plains in mountainous and hilly areas, which will generate a lot of mountain tunnel,"long, deep" is typical of the mountain tunnel characteristics. The main factors restricting the development of the long tunnel boring technology, supporting technology, ventilation technology, poor geological. Most major constraints in the existing technical and economic conditions, adverse geological, tunnel excavation process may induce various types of geological disasters. Common tunnel geological disasters including soft rock fracture zone, lithology unconformable contact with groundwater, karst conduits, karst collapse, goaf and rockburst. Tunnel gushing disaster is a difficult problem in the construction of the tunnel project, at home and abroad have been built many serious gushing accident have occurred in the tunnel, large-scale water gushing often cause huge economic losses and casualties. Have embarked mountainous karst tunnel gushing disaster the study of the mechanism of long tunnel gushing disaster prediction and prevention has important theoretical significance and engineering practice significance.
With the Wu-chi-ba Tunnel of Hurong Freeway as the research object, using a combination of theoretical basics of the related disciplines of geology, hydrogeology, rock mechanics, groundwater dynamics, combined with mathematical statistics, nonlinear theory, numerical simulation and mathematical analysis method, trying to establish the tunnel's gushing Wuchiba Geological model from the karst development master factors and the instability mode angle; gushing groundwater dynamics perspective of evolution from the tunnel on this basis, combined with catastrophe model to explore the karst tunnel gushing disaster mechanism Its mechanical evolution; experience computing model and numerical calculation model combining quantitative analysis means the tunnel Wuchiba inflow predict comparative analysis on a variety of forecasting methods; Finally, using orthogonal experimental and regression analysis a combination of methods to explore the safe distance between the overlying and underlying type and side-volt type karst tunnel and cave and its influencing factors, to establish a safe distance and influencing factors of three karst tunnel mathematical prediction model. Through the above analysis and research, made the following conclusions and results:
(1) karst development by factors such as lithology, groundwater dynamic zonation, geological structure, topography control, including the formation lithology, geological structure is led hydrodynamic conditions is the decisive factor.
(2) the irruption water impact factors can be summarized into two kinds of geological factors and engineering factors. Geological factors, karst aqueous medium usually with heterogeneity and diversity, and water distribution is very uneven, laminar and turbulent coexistence, small fissures constitute the main water storage space; large corrosion fissures constitute a major water guide channel. Engineering factors, rock excavation unloading, blasting disturbance and grouting failure are the master of influencing factors, caused largely the water inrush lag and uncertainty.
(3) The water from karst essentially system of karst aqueous medium, the equilibrium hydrodynamic system as well as the surrounding rock mechanics changed dramatically Underground Excavation, instantaneous release of energy stored in the groundwater bodies and fluid form of high speed engineering migration a driving force to undermine the free surface phenomenon. View from the water-rock interaction mechanism, the the irruption water contains two process stages, poised mechanism of water from karst and karst water inrush mechanism of instability, of which the former is a long historical process, the latter is the former energy savings instantly mutation form.
(4) energy storage containing hydraulic conductivity structure, karst hydrodynamic disturbances and energy release with Derivative the water structure system instability angles proposed the occurrence of water from karst conditions, and irruption water process is divided into two poised and destabilization significant stage; flow pattern evolution characteristics of multi-field coupling software calculates the excavation under the conditions of water from karst formation process, the development of karst water from the aquifer seepage rapid flow of potential water inrush channel, and finally broke into the tunnel formation The free flow catastrophic evolution process.
(5) analysis based on the different causes of geological defects classified and water barrier properties proposed geological defects induced water inrush two typical catastrophe mode analysis of geological defect type the sudden water channel formation process and its instability mechanical criterion. Differences in the permeability characteristics of different scale geological defects, the of strong seepage action filling media penetration instability model and filling slip instability of water inrush model, and applied to Wuchiba tunnel karst conduits induced water inrush instance analysis, combined with the results of numerical analysis, to reveal filling the media penetration instability formation blockage body after the overall slip sudden water cataclysm evolution; consider water for non-conducting faults, the mechanical properties of the two-section filling medium, the introduction of water-borne The weak function reflects the strong seepage on the activation of the fault filling medium, the establishment of a fault backfill slip instability swallowtail catastrophe model and control parameters based on the catastrophic evolution path analysis to propose appropriate prevention and control measures. Based on a large number of numerical results, analysis, fault reactivation induced rupture channel catastrophe mechanism, the inrush of water catastrophe path analysis and fault parameters of the sensitivity of the water inrush. Finally, expose water inrush mode-based catastrophe analysis proposed composite water inrush type analysis of geological defects induced instability impermeable wall rock the catastrophe of the non-exposed water inrush mechanism and engineering instance, further reveals the fault activation The conduction dark river water influx tunnel caverns filled hydraulic connection exists, and cause catastrophic evolution mechanism of the arch of the tunnel the complete surrounding rock fracturing water inrush.
(6) analysis through Wuchiba tunnel hydrogeological conditions, to using the "Visual MODFLOW2.7.1" Three Dimensional Seepage analog and conventional empirical formula forecast inflow of Wuchiba tunnel, and its results were analyzed to ensure that the predicted results reliability. The entire tunnel Wuchiba tunnel smallest inflow between12000～22000m3/d,, normal (construction period average year) between24000～47000m3/d, large value (construction period wet years) in the30000～96000m3/d.
(7) orthogonal test program FLAC3D numerical simulation analysis of the safe distance between the overlying and underlying and side-volt karst tunnels and caverns, Rock Classification rock side pressure coefficient, cave span the caves high-span ratio and tunnel depth of five influencing factors affect the extent and impact of the law on the safety distance. Safe distance for overlying and underlying karst tunnels, caverns span large cave high cross is smaller than the safe distance; side Volt karst tunnel, cave high cross than the safe distance, small cave span safe distance, that is perpendicular to the direction of the cave size of tunnels and caverns connection safety distance and parallel to the direction of the cave size of tunnels and caverns connection safe distance than small.
(8) Univariate regression analysis showed high cross than the overlying and underlying karst tunnels, tunnel and cave between the level of safety distance with the surrounding rock and rock mass lateral pressure coefficient exponential relationship, span and cave and cave a linear relationship with the logarithmic relationship; tunnel depth karst tunnel side Volt safe distance between the tunnel and cave Rock Classification exponential relationship was quadratic polynomial relationships with the rock side pressure coefficient, cave span and cave high cross than a linear relationship between logarithmic relationship with tunnel depth. On this basis, the overlying and underlying type and side-volt karst tunnel safe distance above five impact factor mathematical prediction model by multiple regression analysis.
引文
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