CN115186324A - Method for evaluating influence of shallow tunnel overexcavation on collapse of arch - Google Patents
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Abstract
本发明公开了一种评估浅埋隧道超挖对拱部塌方影响的方法。它主要包括如下步骤：根据浅埋隧道超挖情况，确定超挖形状以及超挖面积；计算浅埋隧道塌方体重力做功；计算浅埋隧道塌方体内能耗散；根据最小能耗原理以及边界条件，求解塌方范围以及塌方量大小；改变不同的超挖角度、超挖高度、超挖面积，评估其对浅埋隧道塌方范围以及塌方大小的影响。本发明可以应用于浅埋地下工程中关于拱部超挖对塌方的影响分析，并且能够考虑超挖角度、超挖高度以及超挖面积等因素的影响，为评估超挖影响以及塌方的加固与防治提供理论方法指导。
The invention discloses a method for evaluating the influence of shallow buried tunnel over-excavation on arch collapse. It mainly includes the following steps: according to the over-excavation situation of the shallow-buried tunnel, determine the shape of the over-excavation and the over-excavation area; calculate the gravity work of the collapse of the shallow-buried tunnel; calculate the energy dissipation in the collapse of the shallow-buried tunnel; according to the principle of minimum energy consumption and boundary conditions , solve the landslide range and the size of the landslide; change different over-excavation angles, over-excavation heights, and over-excavation areas to evaluate the impact on the landslide range and size of shallow tunnels. The invention can be applied to the analysis of the influence of the over-excavation of the arch on the collapse in the shallow buried underground engineering, and can consider the influence of the over-excavation angle, the over-excavation height, the over-excavation area, etc. Provide theoretical and methodological guidance for prevention and treatment.
Description
技术领域technical field
本发明属于隧道施工技术领域，具体涉及一种评估浅埋隧道超挖对拱部塌方影响的方法。The invention belongs to the technical field of tunnel construction, and in particular relates to a method for evaluating the influence of shallow buried tunnel over-excavation on arch collapse.
背景技术Background technique
随着越来越多的隧道将会修建，如目前川藏线中，隧道占了很大一部分比例。由于受围岩本身地质条件，还有钻爆施工参数等影响，超挖在隧道施工现场是常见的现象。目前相关研究文献基本是研究超挖对围岩变形受力等方面的，既有专利也多为一些检测与控制装置，如专利：一种用于铁路隧道线性超挖控制的间隔装药工具（CN201922381532.5）等。隧道塌方是常见的事故，超挖也是导致隧道塌方的主要诱因，特别是对于浅埋隧道，超挖过大时，会产生冒顶塌方。然而，尚未有文献从理论上分析超挖对浅埋隧道塌方的影响，也缺少相应的评估方法。As more and more tunnels will be built, such as the current Sichuan-Tibet line, tunnels account for a large proportion. Due to the influence of the geological conditions of the surrounding rock itself and the construction parameters of drilling and blasting, over-excavation is a common phenomenon in tunnel construction sites. At present, the relevant research literature basically studies the deformation and force of the surrounding rock caused by the over-excavation. There are both patents and some detection and control devices, such as the patent: a spaced charging tool for linear over-excavation control of railway tunnels ( CN201922381532.5) and so on. Tunnel collapse is a common accident, and over-excavation is also the main cause of tunnel collapse, especially for shallow tunnels, when over-excavation is too large, roof collapse will occur. However, there is no literature to theoretically analyze the impact of overexcavation on the collapse of shallow tunnels, and there is also a lack of corresponding evaluation methods.
发明内容SUMMARY OF THE INVENTION
本发明的目的在于针对现有技术中存在的上述技术问题，提供一种评估浅埋隧道超挖对拱部塌方影响的方法。The purpose of the present invention is to provide a method for evaluating the influence of shallow buried tunnel over-excavation on arch collapse in view of the above-mentioned technical problems existing in the prior art.
本发明的目的是通过如下的技术方案来实现的。The purpose of the present invention is achieved through the following technical solutions.
该评估浅埋隧道超挖对拱部塌方影响的方法，包括如下步骤。The method for evaluating the influence of shallow tunnel over-excavation on arch collapse includes the following steps.
（1）根据浅埋隧道超挖情况，确定超挖形状以及超挖面积；超挖形状简化为三角形，其超挖面积由下式确定。(1) According to the over-excavation situation of the shallow-buried tunnel, determine the over-excavation shape and over-excavation area; the over-excavation shape is simplified to a triangle, and its over-excavation area is determined by the following formula.
式中，Sc为超挖区面积；R为隧道拱部半径；θ为超挖角度；h为超挖高度；π为圆周率。In the formula, S c is the area of the over-excavation area; R is the radius of the tunnel arch; θ is the over-excavation angle; h is the over-excavation height; π is the pi.
（2）计算浅埋隧道塌方体重力做功，其由下式确定。(2) Calculate the gravity work of the collapse of the shallow tunnel, which is determined by the following formula.
式中，Pγ为浅埋隧道塌方体重力做功；L1为浅埋隧道地表塌方区宽度的一半，L2为浅埋隧道洞内塌方区宽度的一半；γ为围岩重度；g(x)为隧道拱部轮廓函数；f(x)为塌方形状函数；v为机动容许速度场；x为直角坐标系中x轴坐标值。In the formula, P γ is the gravity work done by the collapse of the shallow tunnel; L 1 is half the width of the surface collapse area of the shallow tunnel; L 2 is half the width of the collapse area in the shallow tunnel; γ is the weight of the surrounding rock; g(x ) is the profile function of the tunnel arch; f(x) is the collapse shape function; v is the maneuvering allowable velocity field; x is the x-axis coordinate value in the Cartesian coordinate system.
其中，隧道拱部轮廓函数g(x)，具体由下式进行确定。Among them, the tunnel arch contour function g(x) is specifically determined by the following formula.
式中，H为浅埋隧道埋深。In the formula, H is the depth of the shallow tunnel.
（3）计算浅埋隧道塌方体内能耗散，其由下式确定。(3) Calculate the energy dissipation in the collapse of the shallow tunnel, which is determined by the following formula.
式中，PD为浅埋隧道塌方体内能耗散；
（4）根据最小能耗原理以及边界条件，求解塌方范围以及塌方量大小，其包括如下步骤。(4) According to the principle of minimum energy consumption and boundary conditions, solve the range of collapse and the magnitude of collapse, which includes the following steps.
（Ⅰ）由浅埋隧道塌方体重力做功与内能耗散，构建如下函数。(I) The following functions are constructed from the gravity work and internal energy dissipation of the collapse of the shallow tunnel.
式中：
（Ⅱ）由泛函数的变分原理，可得其对应的欧拉方程为。(II) According to the variational principle of functional functions, the corresponding Euler equation can be obtained as .
结合边界条件，求解可得：
式中，c1为系数。In the formula, c 1 is the coefficient.
（Ⅲ）由几何条件可知。(III) It can be known from the geometric conditions.
由此可以得到以下式。Thereby, the following formula can be obtained.
（Ⅳ）由能量守恒定律，即浅埋隧道塌方体重力做功与内能耗散相等，可得。 (IV) According to the law of conservation of energy, that is, the gravity work of a shallow buried tunnel collapse is equal to the internal energy dissipation, and can be obtained.
（Ⅴ）联合步骤（Ⅲ）与（Ⅳ）的公式，可构成一个方程组，从而可以解得浅埋隧道地表塌方区宽度2L1和洞内塌方区宽度2L2的值，塌方大小即塌方面积可由下式求得。(V) Combine the formulas of steps (III) and (IV) to form a system of equations, so that the values of the width 2L 1 of the surface collapse area of the shallow buried tunnel and the width 2L 2 of the collapse area in the tunnel can be solved, and the size of the collapse is the area of the collapse. It can be obtained by the following formula.
（Ⅵ）根据上述，结合实际超挖情况，即可求得超挖引起的浅埋隧道塌方范围，包括塌方面积、塌方高度以及塌方宽度等；改变超挖高度、超挖角度等相关参数，即可求得超挖高度、超挖角度以及超挖面积对浅埋隧道拱部塌方的影响，从而为评估超挖影响以及浅埋隧道塌方的加固与防治提供理论方法指导。(VI) According to the above, combined with the actual over-excavation situation, the collapse range of the shallow tunnel caused by over-excavation can be obtained, including the area of the collapse, the height of the collapse, and the width of the collapse; The influence of over-excavation height, over-excavation angle and over-excavation area on the collapse of the arch of the shallow tunnel can be obtained, so as to provide theoretical method guidance for evaluating the impact of over-excavation and the reinforcement and prevention of the collapse of the shallow tunnel.
本发明与现有技术和研究方法相比，具有如下的优点：Compared with the prior art and research methods, the present invention has the following advantages:
现有文献技术研究主要是针对超挖后对围岩以及支护的影响；现有专利技术只是对超挖进行检查或者控制装置等方面。缺少超挖对浅埋隧道塌方的影响，以及超挖后浅埋隧道塌方范围有多大，塌方高度与宽度是多少，这些直接影响到后续对塌方的治理与加固。The technical research in the existing literature is mainly aimed at the influence of the over-excavation on the surrounding rock and support; the existing patented technology is only for the inspection or the control device of the over-excavation. The impact of the lack of over-excavation on the collapse of shallow tunnels, the extent of the collapse of shallow tunnels after over-excavation, and the height and width of the collapse directly affect the subsequent management and reinforcement of the collapse.
本发明为评估浅埋隧道超挖对拱部塌方影响，提供了一种理论计算方法；并通过改变超挖高度、超挖角度等相关参数，即可求得超挖高度、超挖角度对浅埋隧道塌方的影响，从而为超挖影响下的塌方治理提供参考。本发明的方法不仅可以应用于交通隧道，还可应用于采矿巷道、水工隧洞、地铁区间隧道等地下工程中关于超挖对塌方的影响分析，从而为评估超挖影响以及塌方的加固与防治提供理论方法指导。The invention provides a theoretical calculation method for evaluating the influence of over-excavation of shallow tunnels on the collapse of the arch; and by changing the relevant parameters such as the over-excavation height and the over-excavation angle, the effect of the over-excavation height and the over-excavation angle on the shallow tunnel can be obtained. The impact of buried tunnel collapse, thus providing a reference for landslide control under the influence of over-excavation. The method of the invention can be applied not only to traffic tunnels, but also to the analysis of the influence of over-excavation on landslides in underground projects such as mining tunnels, hydraulic tunnels, subway tunnels, etc., so as to evaluate the influence of over-excavation and the reinforcement and prevention of landslides Provide theoretical and methodological guidance.
附图说明Description of drawings
图1为本发明实施例超挖下隧道塌方示意图。FIG. 1 is a schematic diagram of a tunnel collapse under overexcavation according to an embodiment of the present invention.
图1中，H为隧道埋深；L 1为浅埋隧道地表塌方区宽度的一半，L 2 为浅埋隧道洞内塌方区宽度的一半；；R为隧道拱部半径；θ为超挖角度；h为超挖高度；f(x)为塌方形状函数；g(x)为隧道拱部轮廓函数；v为机动容许速度场；x为直角坐标系中x轴坐标值。In Figure 1 , H is the buried depth of the tunnel; L1 is half the width of the surface collapse area of the shallow buried tunnel, L2 is half the width of the collapse area in the shallow buried tunnel; R is the radius of the tunnel arch; θ is the over-excavation angle ; h is the over-excavation height; f(x) is the collapse shape function; g ( x ) is the tunnel arch contour function; v is the maneuvering allowable velocity field; x is the x -axis coordinate value in the Cartesian coordinate system.
图2为不同超挖高度对塌方高度、塌方宽度、塌方面积的影响。Figure 2 shows the effect of different over-excavation heights on the collapse height, collapse width, and collapse area.
图3为不同超挖角度对塌方高度、塌方宽度、塌方面积的影响。Figure 3 shows the effects of different over-excavation angles on the collapse height, collapse width, and collapse area.
具体实施方式Detailed ways
下面结合附图和实施例对本发明作进一步的描述。The present invention will be further described below with reference to the accompanying drawings and embodiments.
本实施例工程的具体数据如下：研究超挖高度h的影响时，其他参数取值分别为：A=0.15，B=0.6，σ c=0.5MPa，σ t=σ c/100，R=11m，γ=20kN/m3，θ=6°，超挖高度h分别选取0m，0.2m，0.4m，0.6m，0.8m，1.0m六种情况进行计算。The specific data of the project in this example are as follows: when studying the influence of the over-excavation height h , the values of other parameters are: A = 0.15, B = 0.6, σ c =0.5MPa, σ t = σ c /100, R = 11m , γ=20kN/m 3 , θ =6°, the over excavation height h is selected from six cases of 0m, 0.2m, 0.4m, 0.6m, 0.8m and 1.0m respectively for calculation.
研究超挖角度θ的影响时，其他参数取值分别为：A=0.15，B=0.6，σ c=0.5MPa，σ t=σ c/100，R=11m，γ=20kN/m3，h=0.6m，超挖角度θ分别选取0°，2°，4°，6°，8°，10°六种情况进行计算。When studying the influence of the overcut angle θ , the values of other parameters are: A =0.15, B =0.6, σc = 0.5MPa , σt = σc /100, R = 11m , γ=20kN/ m 3 , h =0.6m, the over excavation angle θ is calculated from six cases of 0°, 2°, 4°, 6°, 8°, and 10°.
参见图1，本实施例评估浅埋隧道超挖对拱部塌方影响的方法如下。Referring to FIG. 1 , the method for evaluating the influence of over-excavation of shallow tunnels on arch collapse in this embodiment is as follows.
（1）根据浅埋隧道超挖情况，确定超挖形状以及超挖面积；超挖形状简化为三角形，其超挖面积由下式确定。(1) According to the over-excavation situation of the shallow-buried tunnel, determine the over-excavation shape and over-excavation area; the over-excavation shape is simplified to a triangle, and its over-excavation area is determined by the following formula.
式中，Sc为超挖区面积；R为隧道拱部半径；θ为超挖角度；h为超挖高度；π为圆周率。In the formula, S c is the area of the over-excavation area; R is the radius of the tunnel arch; θ is the over-excavation angle; h is the over-excavation height; π is the pi.
（2）计算浅埋隧道塌方体重力做功，其由下式确定。(2) Calculate the gravity work of the collapse of the shallow tunnel, which is determined by the following formula.
式中，Pγ为浅埋隧道塌方体重力做功；L1为浅埋隧道地表塌方区宽度的一半，L2为浅埋隧道洞内塌方区宽度的一半；γ为围岩重度；g(x)为隧道拱部轮廓函数；f(x)为塌方形状函数；v为机动容许速度场；x为直角坐标系中x轴坐标值。In the formula, P γ is the gravity work done by the collapse of the shallow tunnel; L 1 is half the width of the surface collapse area of the shallow tunnel; L 2 is half the width of the collapse area in the shallow tunnel; γ is the weight of the surrounding rock; g(x ) is the profile function of the tunnel arch; f(x) is the collapse shape function; v is the maneuvering allowable velocity field; x is the x-axis coordinate value in the Cartesian coordinate system.
其中，隧道拱部轮廓函数g(x)，具体由下式进行确定。Among them, the tunnel arch contour function g(x) is specifically determined by the following formula.
式中，H为浅埋隧道埋深。In the formula, H is the depth of the shallow tunnel.
（3）计算浅埋隧道塌方体内能耗散，其由下式确定。(3) Calculate the energy dissipation in the collapse of the shallow tunnel, which is determined by the following formula.
式中，PD为浅埋隧道塌方体内能耗散；
（4）根据最小能耗原理以及边界条件，求解塌方范围以及塌方量大小，其包括如下步骤。(4) According to the principle of minimum energy consumption and boundary conditions, solve the range of collapse and the magnitude of collapse, which includes the following steps.
（Ⅰ）由浅埋隧道塌方体重力做功与内能耗散，构建如下函数。(I) The following functions are constructed from the gravity work and internal energy dissipation of the collapse of the shallow tunnel.
式中：
（Ⅱ）由泛函数的变分原理，可得其对应的欧拉方程为。(II) According to the variational principle of functional functions, the corresponding Euler equation can be obtained as .
结合边界条件，求解可得：
式中，c1为系数。In the formula, c 1 is the coefficient.
（Ⅲ）由几何条件可知。(III) It can be known from the geometric conditions.
由此可以得到以下式。Thereby, the following formula can be obtained.
（Ⅳ）由能量守恒定律，即浅埋隧道塌方体重力做功与内能耗散相等，可得。 (IV) According to the law of conservation of energy, that is, the gravity work of a shallow buried tunnel collapse is equal to the internal energy dissipation, and can be obtained.
（Ⅴ）联合步骤（Ⅲ）与（Ⅳ）的公式，可构成一个方程组，从而可以解得浅埋隧道地表塌方区宽度2L1和洞内塌方区宽度2L2的值，塌方大小即塌方面积可由下式求得。(V) Combine the formulas of steps (III) and (IV) to form a system of equations, so that the values of the width 2L 1 of the surface collapse area of the shallow buried tunnel and the width 2L 2 of the collapse area in the tunnel can be solved, and the size of the collapse is the area of the collapse. It can be obtained by the following formula.
（Ⅵ）根据上述，结合实际超挖情况，即可求得超挖引起的浅埋隧道塌方范围，包括塌方面积、塌方高度以及塌方宽度等；改变超挖高度、超挖角度等相关参数，即可求得超挖高度、超挖角度以及超挖面积对浅埋隧道拱部塌方的影响，从而为评估超挖影响以及浅埋隧道塌方的加固与防治提供理论方法指导。(VI) According to the above, combined with the actual over-excavation situation, the collapse range of the shallow tunnel caused by over-excavation can be obtained, including the area of the collapse, the height of the collapse, and the width of the collapse; The influence of over-excavation height, over-excavation angle and over-excavation area on the collapse of the arch of the shallow tunnel can be obtained, so as to provide theoretical method guidance for evaluating the impact of over-excavation and the reinforcement and prevention of the collapse of the shallow tunnel.
根据上述方法步骤，可以得到不同超挖高度与超挖角度对塌方高度、塌方宽度、塌方面积的影响，如图2与图3所示。从图中可以看出，随着超挖高度h与超挖角度θ的增大，塌落面形状有所扩大，塌落宽度逐渐增大，塌落高度也逐渐增大，导致塌落面的面积呈增大趋势。According to the above method steps, the effects of different over-excavation heights and over-excavation angles on the collapse height, collapse width, and collapse area can be obtained, as shown in FIG. 2 and FIG. 3 . It can be seen from the figure that with the increase of the overcut height h and the overcut angle θ , the shape of the slump surface expands, the width of the slump increases gradually, and the height of the slump increases gradually, resulting in The area is increasing.
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