隧道下伏溶洞顶板安全厚度确定方法
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摘要
为解决溶洞与隧道间安全距离如何确定的问题,在研究现有动荷载下顶板安全厚度确定方法的基础上,推导出固支梁振动微分方程,建立隧道与溶洞间岩层失稳的双尖点突变模型,分析其失稳力学机制及破坏条件,得到安全厚度的非线性方程,并运用Matlab进行迭代法编程求解;分析爆破振动强度、频率、围岩特性、隧道跨度等对安全厚度的影响。结果表明:隧道与溶洞间岩层安全厚度是由岩层的内外因素共同决定;在同一振动荷载幅值下,安全厚度与振动频率呈非线性关系;在同一振动频率下,安全厚度与爆破振动荷载幅值呈线性关系;安全厚度随弹性模量的增加而逐渐减小,随溶洞跨度的增加呈近似正比例增加。
To solve the difficult problem of how to determine the safe distance between karst caves and tunnels,the vibration differential equation of fixed-supported beam was established on the basis of the study of the existing methods for determining the safe thickness of roofs under dynamic load,and the double cusp catastrophe model of rock stratum instability between tunnels and karst caves was deduced.Then,its instability mechanism and failure conditions were analyzed,the nonlinear equation of the safe thickness was obtained before Matlab programming-based iteration method was utilized to solve the equation. What's more,analysis was also made on the impact of blasting vibration intensity,frequency,features of surrounding rocks and tunnel span on the safe thickness. It was found that the safe distance between tunnels and karst caves was determined by the internal and external factors of the rock strata; in addition,under the same amplitude of vibration load,the safe thickness has a nonlinear relationship with vibration frequency,while it has a linear relationship with blasting vibration amplitude when at the same vibration frequency; meanwhile, the safe thickness gradually decreases with the increase of elastic modulus,and was approximately proportional to increase along with the increase of the karst cave span.
To solve the difficult problem of how to determine the safe distance between karst caves and tunnels,the vibration differential equation of fixed-supported beam was established on the basis of the study of the existing methods for determining the safe thickness of roofs under dynamic load,and the double cusp catastrophe model of rock stratum instability between tunnels and karst caves was deduced.Then,its instability mechanism and failure conditions were analyzed,the nonlinear equation of the safe thickness was obtained before Matlab programming-based iteration method was utilized to solve the equation. What's more,analysis was also made on the impact of blasting vibration intensity,frequency,features of surrounding rocks and tunnel span on the safe thickness. It was found that the safe distance between tunnels and karst caves was determined by the internal and external factors of the rock strata; in addition,under the same amplitude of vibration load,the safe thickness has a nonlinear relationship with vibration frequency,while it has a linear relationship with blasting vibration amplitude when at the same vibration frequency; meanwhile, the safe thickness gradually decreases with the increase of elastic modulus,and was approximately proportional to increase along with the increase of the karst cave span.
引文
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[2]刘成禹,刘招伟.基于地表沉降的岩溶发育区分析[J].现代隧道技术,2014,51(3):67-72.LIU Chengyu,LIU Zhaowei.Analysis of karst development zones based on surface settlement[J].Modern Tunnelling Technology,2014,51(3):67-72.
[3]戴自航,范夏玲,卢才金.岩溶区高速公路路堤及溶洞顶板稳定性数值分析[J].岩土力学,2014,35(增1):382-390.DAI Zihang,FAN Xialing,LU Caijin.Numerical analysis of stability of highway embankments and karst cave roofs in karst region[J].Rock and Soil Mechanics,2014,35(S1):382-390.
[4]魏锋,陈忠达,陈峙峰,等.路堤下伏溶洞受力模式和变形破坏的数值模拟[J].中国公路学报,2018,31(6):195-206.WEI Feng,CHEN Zhongda,CHEN Zhifeng,et al.Numerical simulation of the mechanical characteristic and failure mode of karst subgrade[J].China Journal of Highway and Transport,2018,31(6):195-206.
[5]张华伟,谢妮,刘孔科,等.高层建筑桩基荷载下溶洞顶板的安全厚度[J].科学技术与工程,2017,17(32):165-173.ZHANG Huawei,XIE Ni,LIU Kongke,et al.Safe thickness of roof of karst cave under pile foundation load in high-rise buildings[J].Science,Technology and Engineering,2017,17(32):165-173.
[6]高峰,周科平,胡建华,等.充填体下矿体开采安全顶板厚度数学预测模型[J].岩土力学,2008,29(1):177-181.GAO Feng,ZHOU Keping,HU Jianhua,et al.Mathematical forecasting model of safety thickness of roof for mining ore body under the complicated backfilling[J].Rock and Soil Mechanics,2008,29(1):177-181.
[7]王晓军,冯萧,赵奎,等.多因素组合影响阶段矿柱上采顶板临界厚度研究[J].岩土力学,2013,34(12):3 505-3 512.WANG Xiaojun,FENG Xiao,ZHAO Kui,et al.Study of critical thickness of roof of level pillar stopping under multifactor influence[J].Rock and Soil Mechanics,2013,34(12):3 505-3 512.
[8]贺建清,喻畅英,肖兰,等.基于上限定理确定岩溶区桩端极限承载力及其下伏溶洞顶板安全厚度[J].自然灾害学报,2017,26(2):47-52.HE Jianqing,YU Changying,XIAO Lan,et al.Determination of ultimate bearing capacity of pile tip and safe thickness of roof of underlying karst cave based on upper bound theorem[J].Journal of Natural Disaster,2017,26(2):47-52.
[9]江学良,曹平,杨慧,等.水平应力与裂隙密度对顶板安全厚度的影响[J].中南大学学报:自然科学版,2009,40(1):212-216.JIANG Xueliang,CAO Ping,YANG Hui,et al.Effect of horizontal stress and rock crack density on roof safety thickness of underground area[J].Journal of Central South University:Science and Technology,2009,40(1):212-216.
[10]汪华斌,刘志峰,赵文锋,等.桥梁桩基荷载下溶洞顶板稳定性研究[J]岩石力学与工程学报,2013,32(增2):3 650-3 657.WANG Huabin,LIU Zhifeng,ZHAO Wenfeng,et al.Research on stability of cave roof under pile loading in bridge construction engineering[J]Chinese Journal of Rock Mechanics and Engineering,2013,32(S2):3 650-3 657.
[11]赵明华,雷勇,张锐.岩溶区桩基冲切破坏模式及安全厚度研究[J].岩土力学,2012,33(2):524-530.ZHAO Minghua,LEI Yong,ZHANG Rui.Study of punching failure mode and safe thickness of pile foundation in karst region[J].Rock and Soil Mechanics,2012,33(2):524-530.
[12]赖永标.隐伏溶洞与隧道间安全距离及其智能预测模型研究[D].北京:北京交通大学,2012.LAI Yongbiao.Study on safe distance between concealed karst cave and tunnel and its intelligent prediction model[D].Beijing:Beijing Jiaotong University,2012.
[13]闫长斌,徐国元.动荷载诱发上下交叠硐室间顶柱失稳的突变理论分析[J].工程力学,2007,24(4):46-51.YAN Changbin,XU Guoyuan.Analysis on instability of the top pillar between overlap underground chambers induced by dynamic loadings with catastrophe theory[J].Engineering Mechanics,2007,24(4):46-51.
[14]江学良.岩石地下洞室与边坡相互影响研究[D].长沙:中南大学,2008.JIANG Xueliang.Study on interaction of rock underground cavern and slope[D].Changsha:Central South University,2008.
[15]清华大学工程力学系固体力学教研组振动组.机械振动(上册)[M].北京:机械工业出版社,1980:346-350.
[16]张我华,邱战洪,陈合龙.堤坝和基础非线性动力失稳灾变的分岔突变分析[J].浙江大学学报:工学版,2007,41(1):88-96.ZHANG Wohua,QIU Zhanhong,CHEN Helong.Bifurcation and catastrophe analysis of non-linear dynamic instability disaster for dam and foundation system[J].Journal of Zhejiang University:Engineering Science,2007,41(1):88-96.
[17]左宇军,李夕兵,马春德,等.动静组合载荷作用下岩石失稳破坏的突变理论模型与试验研究[J].岩石力学与工程学报,2005,24(5):741-746.ZUO Yujun,LI Xibing,MA Chunde,et al.Catastrophe theory model and experimental study of rock instability failure under combined dynamic and static loading[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(5):741-746.
[18]左宇军,李术才,秦泗凤,等.动力扰动诱发承压水底板关键层失稳的突变理论研究[J].岩土力学,2010,31(8):2 361-2 366.ZUO Yujun,LI Shucai,QIN Sifeng,et al.A catastrophe model for floor water-resisting key stratum instability induced by dynamic disturbance[J].Rock and Soil Mechanics,2010,31(8):2 361-2 362.