WO2023241356A1 - 一种地铁隧道冻结法施工地层三维冻胀变形的预测方法 - Google Patents

一种地铁隧道冻结法施工地层三维冻胀变形的预测方法 Download PDF

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WO2023241356A1
WO2023241356A1 PCT/CN2023/097355 CN2023097355W WO2023241356A1 WO 2023241356 A1 WO2023241356 A1 WO 2023241356A1 CN 2023097355 W CN2023097355 W CN 2023097355W WO 2023241356 A1 WO2023241356 A1 WO 2023241356A1
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freezing
soil
frozen
radius
predicting
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蔡海兵
李孟凯
洪荣宝
姚方兴
胡时
杨哲
庞昌强
黄献文
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安徽理工大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/14—Pipes
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/08—Thermal analysis or thermal optimisation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

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  • the invention relates to the technical field of subway tunnel construction, and in particular to a method for predicting three-dimensional frost heave deformation of subway tunnel construction stratum using freezing method.
  • the analytical method based on strict mathematical derivation can quantitatively consider the influence of geological parameters and freezer parameters, and is a practical method to predict stratigraphic deformation caused by freezing construction of tunnels; however, the stratum uplift obtained from current research on stratum deformation caused by frost heave is the final The formation uplift value does not consider the time effect and actual conditions such as soil temperature, and cannot accurately predict the formation freezing speed and frost heave displacement.
  • Embodiments of the present invention provide a method for predicting three-dimensional frost heave deformation of subway tunnel construction strata constructed using the freezing method. This method can effectively solve the problem of uneven frost heaving of the ground caused by frozen construction of subway tunnels, and at the same time avoid adverse deformation of existing building foundations and tunnel linings around it.
  • a method for predicting three-dimensional frost heaving deformation of subway tunnel construction stratum using freezing method including the following steps:
  • t is the freezing time
  • ⁇ f is the frost heave rate of the soil under load
  • ⁇ f0 is the frost heave rate of the soil under no load
  • P is the load of the layer where the frost heave influence range is located, kPa
  • b is the constant 0.001
  • B is the coefficient
  • r is the freezing radius
  • the present invention discloses the following technical effects:
  • the prediction method of the present invention integrates the thermophysical and mechanical properties of the soil, takes into account factors such as the freezing time effect, soil freezing temperature and soil load, and calculates the unsteady temperature field and freezing front r(t) of a single frozen pipe. Then, based on the shape of the frozen area, calculate the inner radius R 1 (t), outer radius R 2 (t) and frost heave area ⁇ (t) of the freezing front after the frozen wall intersects, determine the frost heave influence range and calculate the frost heave impact.
  • the range is frozen
  • the expansion displacement can be used to determine the evolution rules of frozen curtain and frost heave deformation at different stages, improve the reliability and accuracy of three-dimensional frost heave prediction of the ground caused by freezing construction of subway tunnels, and ensure that the prediction results are more conducive to providing reliable data reference for actual construction. and theoretical basis.
  • Figure 1 is a schematic diagram of frost heave layering according to the present invention.
  • Figure 2 is a diagram of the unsteady freezing front pattern of a single frozen pipe of the present invention
  • Figure 3 is a regular diagram of the unsteady freezing front after the freezing wall of the present invention intersects
  • Figure 4 is a schematic diagram of the formation uplift caused by frost heaving in the unit of the present invention.
  • Figure 1 is a schematic diagram of the frost heave layering of the present invention.
  • Figure 2 is a diagram of the unsteady freezing front pattern of a single frozen pipe of the present invention.
  • Figure 3 is a diagram of the unsteady freezing front pattern of the frozen wall after the intersection of the present invention.
  • Figure 4 is a diagram of the present invention.
  • Invention sheet Schematic diagram of formation uplift caused by frost heaving. Based on the above four drawings, the present invention's method for predicting three-dimensional frost heaving deformation of strata constructed using the freezing method of subway tunnels includes the following steps:
  • T f is the differential equation of the temperature field in the frozen area
  • T u is the differential equation of the temperature field in the unfrozen area
  • T c is the temperature of the frozen pipe wall
  • T d is the freezing temperature of the soil. If the soil layer is homogeneous, it is a single soil.
  • the freezing temperature of the body if the soil layer is uneven, is the freezing temperature of the soil where the freezing front radius is located; Ei represents the exponential integral function well known in this field; r 0 is the diameter of the frozen pipe; T 0 is the initial ambient temperature; k f is the frozen Soil thermal conductivity; k u is the thermal conductivity of unfrozen soil; A is the coefficient; L w is the latent heat of water; ⁇ d is the dry density of soil; w 0 is the moisture content; w u is the moisture content of unfrozen soil.
  • ⁇ f is the thermal diffusion coefficient of the frozen area
  • ⁇ u is the thermal diffusion coefficient of the unfrozen area
  • k f represents the thermal conductivity of the frozen area
  • c f represents the specific heat of the frozen area
  • ⁇ f represents the density of the soil in the frozen area
  • k u represents the thermal conductivity of the unfrozen area
  • c u represents the unfrozen area.
  • the specific heat, ⁇ u represents the density of the soil in the unfrozen area.
  • t is the freezing time
  • ⁇ f is the frost heave rate of the soil under load
  • ⁇ f0 is the frost heave rate of the soil under no load
  • P is the load of the layer, kPa
  • b is the constant 0.001
  • B is the coefficient
  • r is the freezing radius
  • R d is the distribution radius of the frozen tubes
  • T c ' is the average temperature of the frozen wall after the intersection
  • eta is the ordinate direction of the frozen tubes in the cylindrical coordinate system.
  • h i is the height of the layer where the frost heave influence range is located from the tunnel; ⁇ is the main influence angle of the overlying soil layer on the frozen wall; ⁇ is the polar angle in the polar coordinate system; z is the z-direction coordinate of the spatial coordinate system; x is the x-direction coordinate of the spatial coordinate system; y is the y-direction coordinate of the spatial coordinate system; ⁇ is the length direction of the frozen tube in the cylindrical coordinate system; is the circumferential angle in the cylindrical coordinate system.
  • This embodiment 1 selects the shallow-buried large-section tunnel project on the south side of the section from ssenyao to Thermal Power Plant on the Fu (Xingmen)-Ba (Wangfen) Line of the Beijing Metro in China. This project is located directly from Dayao Bridge to Guomao Bridge. Below, there are many criss-crossing underground pipelines in the ground. Due to their age and disrepair, water seepage and other phenomena often occur. For this reason, artificial freezing method is used for construction. In order to predict the three-dimensional frost heave deformation of the stratum in the frozen construction section, and taking into account the scope of influence of the frozen construction, the model size was selected to be 40.0m long, 6.0m wide, and the tunnel burial depth was 10m.
  • the prediction method of the present invention can determine the frost heave impact
  • the response range and the frost heave displacement of specific soil layers are calculated to determine the evolution rules of the freezing curtain and frost heave deformation at different stages, improve the reliability and accuracy of the three-dimensional frost heave prediction of the ground caused by freezing construction of the subway tunnel, and ensure that the prediction results are more beneficial Provide reliable data reference and theoretical basis for actual construction.

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Abstract

本发明公开了一种地铁隧道冻结法施工地层三维冻胀变形的预测方法，涉及地铁隧道施工领域，方法包括：首先确定冻结施工位置，获得冻结壁范围内原状土的土层参数，确定土体的热物理及力学参数，对冻结壁上方土层按其土层性质及既有建(构)筑物进行分层并确定冻胀影响范围所在层；随后计算单根冻结管的非稳态温度场及冻结锋面半径；再根据隧道开挖类型，计算冻结壁交圈后冻结锋面内圈半径、外圈半径，计算冻胀区域；最后计算冻胀位移。本发明综合土体的热物理及力学性能、冻结时间效应、土层结冰温度及土层荷载因素，以确定冻结帷幕及冻胀变形在不同阶段的演化规律，提高冻结施工引起地层三维冻胀预测的可靠性和准确性。

Description

一种地铁隧道冻结法施工地层三维冻胀变形的预测方法
本申请要求于2022年6月13日提交中国专利局、申请号为202210660022.5、发明名称为“一种地铁隧道冻结法施工地层三维冻胀变形的预测方法”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本发明涉及地铁隧道施工技术领域，尤其涉及一种地铁隧道冻结法施工地层三维冻胀变形的预测方法。
背景技术
随着社会的快速发展，城市地下轨道交通得到快速发展。冻结法作为地层加固的重要手段，在城市轨道交通工程中被广泛使用，特别是在富水量大、淤泥质、砂质地层等复杂地质下，该方法加固效果显著。但人工冻结使得地层温度急剧降低，地铁隧道冻结施工所诱发的地层变形主要表现为地层的冻胀所引起得周围建筑基础、隧道衬砌、车站底板等的不良变形。因此，准确可靠地预测冻结法施工引起地层的三维冻胀对于冻结壁设计及既有建筑保护至关重要。研究地层变形一般有以下几种方法：经验法、数值模拟法和解析法，而对于常用的是解析法。基于严格数学推导的解析法可以定量地考虑地质参数和冻结器参数的影响，是预测隧道冻结施工引起地层变形的实用方法；但是目前对冻胀引起的地层变形的研究得到的地层隆起都是最终的地层隆起值，并未考虑时间效应及土层温度等实际条件，不能准确预测地层冻结速度以及冻胀位移。
发明内容
本发明实施例提供一种地铁隧道冻结法施工地层三维冻胀变形的预测方 法，有效解决地铁隧道冻结施工导致地层不均匀冻胀的问题，同时避免对周围既有建筑物基础、隧道衬砌造成不良变形。
为实现上述目的，本发明实施例提供了如下方案：
一种地铁隧道冻结法施工地层三维冻胀变形的预测方法，包括如下步骤：
(1)确定冻结施工位置，获得冻结壁范围内原状土的土层参数，确定土体的热物理及力学参数，对冻结壁上方土层进行分层并确定冻胀影响范围所在层；
(2)计算单根冻结管的非稳态温度场及冻结锋面半径r(t)；
(3)根据隧道开挖类型，计算冻结壁交圈后冻结锋面内圈半径R1(t)、外圈半径R2(t)，并由下式计算冻胀区域Δ(t)：

εf＝εf0exp(-bP)；
式中：t为冻结时间；εf为荷载下的土体冻胀率；εf0为无荷载下的土体冻胀率；P为冻胀影响范围所在层的荷载，kPa；b为常数0.001；B为系数；r为冻结半径；
(4)计算冻胀位移Wi(t)。
根据本发明提供的具体实施例，本发明公开了以下技术效果：
本发明预测方法综合土体的热物理及力学性能，考虑冻结时间效应、土层结冰温度及土层荷载等因素，通过计算单根冻结管非稳态温度场及冻结锋面r(t)，进而根据冻结区域形状，计算冻结壁交圈后冻结锋面内圈半径R1(t)、外圈半径R2(t)和冻胀区域Δ(t)，确定冻胀影响范围并计算冻胀影响范围所在层冻 胀位移，以确定冻结帷幕及冻胀变形在不同阶段得演化规律，提高地铁隧道冻结施工引起地层三维冻胀预测的可靠性和准确性，保证预测结果更有利于为实际施工提供可靠的数据参考和理论依据。
附图说明
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动性的前提下，还可以根据这些附图获得其他的附图。
图1为本发明冻胀分层示意图；
图2为本发明单根冻结管非稳态冻结锋面规律图；
图3为本发明冻结壁交圈后非稳态冻结锋面规律图；
图4为本发明单元冻胀引起地层隆起示意图；
图5为本发明冻结施工t＝60天地层冻胀示意图；
图6为本发明冻结施工t＝90天地层冻胀示意图。
具体实施方式
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
图1为本发明冻胀分层示意图，图2为本发明单根冻结管非稳态冻结锋面规律图，图3为本发明冻结壁交圈后非稳态冻结锋面规律图，图4为本发明单 元冻胀引起地层隆起示意图，基于上述四幅附图，本发明地铁隧道冻结法施工地层三维冻胀变形的预测方法，包括如下步骤：
(1)确定冻结施工位置，获得冻结壁范围内原状土的土层参数，确定土体的热物理及力学参数土体的密度ρ、热扩散系数α、导热系数k、比热c、相变潜热L及无荷载下的土体冻胀率εf0，对冻结壁上方土层按其土性及建筑物位置进行分层并确定冻胀影响范围所在层。
其中，
(2)由下式(1)、式(2)、式(3)、式(4)、式(5)、式(6)计算单根冻结管的非稳态温度场及冻结锋面半径r(t)：





L＝Lwρd(w0-wu)           (6)
式中：Tf为已冻区温度场微分方程；Tu为未冻区温度场微分方程；Tc为冻结管管壁温度；Td为土体冻结温度，土层均质则为单一土体冻结温度，土层不均匀则为冻结锋面半径所在土体的冻结温度；Ei表示本领域公知的指数积分函数；r0为冻结管管径；T0为初始环境温度；kf为已冻土导热系数；ku为未冻土导热系数；A为系数；Lw为水的潜热；ρd为土体干密度；w0为含水率；wu为未冻土含水率。
αf为已冻结区域的热扩散系数，αu为未冻结区域的热扩散系数，计算公式如下：
其中，kf表示已冻结区域的导热系数，cf表示已冻结区域的比热，ρf表示已冻结区域的土体的密度，ku表示未冻结区域的导热系数，cu表示未冻结区域的比热，ρu表示未冻结区域的土体的密度。
(3)根据隧道开挖类型，由下式(7)、式(8)、式(9)、式(10)、式(11)计算冻结壁交圈后冻结锋面内圈半径R1(t)、外圈半径R2(t)，并由下式计算冻胀区域Δ(t)：




εf＝εf0exp(-bP)           (11)
式中：t为冻结时间；εf为荷载下的土体冻胀率；εf0是无荷载下的土体冻胀率；P为该层的荷载，kPa；b为常数0.001；B为系数；r为冻结半径；Rd为冻结管分布半径；Tc’为交圈后冻结壁的平均温度；η为圆柱坐标系中冻结管的纵坐标方向。
(4)由下式(12)计算冻胀影响范围所在层的冻胀位移Wi(t)：
式中：hi为冻胀影响范围所在层位距隧道的高度；β为冻结壁上覆土层的主要影响角；θ为极坐标系下的极角；z为空间坐标系的z方向坐标；x为空间坐标系的x方向坐标；y为空间坐标系的y方向坐标；ζ为圆柱坐标系中冻结管长度方向；为圆柱坐标系中环向角度。
实施例1
本实施例1选取中国北京地铁复(兴门)--八(王坟)线，大北窑至热电厂区间段南侧的浅埋大断面隧道工程，该工程因位于大窑桥至国贸桥正下方，地层中分布多条纵横交错地下管道，因年久失修，常出现渗水等现象。为此，采用人工冻结法进行施工。为对该冻结施工段地层进行三维冻胀变形预测，同时考虑到冻结施工的影响范围，选取模型尺寸选为长40.0m，宽6.0m，隧道埋深为10m。并根据实际工况获取土体参数，如下表1所示，并由式(1)至式(12)构建的三维冻胀预测方法，分别模拟获得冻胀60天及90天的地层冻胀隆起云图，如图5及图6所示。由该实施例可知，本发明的预测方法能够确定冻胀影 响范围并计算特定土层冻胀位移，以确定冻结帷幕及冻胀变形在不同阶段得演化规律，提高地铁隧道冻结施工引起地层三维冻胀预测的可靠性和准确性，保证预测结果更有利于为实际施工提供可靠的数据参考和理论依据。
表1土体及冻结管参数表

本说明书中各个实施例采用递进的方式描述，每个实施例重点说明的都是与其他实施例的不同之处，各个实施例之间相同相似部分互相参见即可。
本文中应用了具体个例对本发明的原理及实施方式进行了阐述，以上实施例的说明只是用于帮助理解本发明的方法及其核心思想；同时，对于本领域的一般技术人员，依据本发明的思想，在具体实施方式及应用范围上均会有改变之处。综上所述，本说明书内容不应理解为对本发明的限制。

Claims (8)

  1. 一种地铁隧道冻结法施工地层三维冻胀变形的预测方法，其特征在于，包括如下步骤：
    (1)确定冻结施工位置，获得冻结壁范围内原状土的土层参数，确定土体的热物理及力学参数，对冻结壁上方土层进行分层并确定冻胀影响范围所在层；
    (2)计算单根冻结管的非稳态温度场及冻结锋面半径r(t)；
    (3)根据隧道开挖类型，计算冻结壁交圈后冻结锋面内圈半径R1(t)、外圈半径R2(t)，并由下式计算冻胀区域Δ(t)：

    εf＝εf0exp(-bP)；
    式中：t为冻结时间；εf为荷载下的土体冻胀率；εf0为无荷载下的土体冻胀率；P为冻胀影响范围所在层的荷载，kPa；b为常数0.001；B为系数；r为冻结半径；
    (4)计算冻胀位移Wi(t)。
  2. 根据权利要求1所述地铁隧道冻结法施工地层三维冻胀变形的预测方法，其特征在于：步骤(1)中，所述土体的热物理及力学参数为土体的密度ρ、热扩散系数α、导热系数k、比热c、相变潜热L及无荷载下的土体冻胀率εf0，其中，
  3. 根据权利要求1所述地铁隧道冻结法施工地层三维冻胀变形的预测方法，其特征在于：步骤(2)中，所述单根冻结管的非稳态温度场由下式获得：

    式中：Tf为已冻区温度场微分方程；Tu为未冻区温度场微分方程；Tc为冻结管管壁温度；Td为土体冻结温度，土层均质则为单一土体冻结温度，土层不均匀则为冻结锋面半径所在土体的冻结温度；Ei表示指数积分函数；r0为冻结管管径；αf为已冻结区域的热扩散系数；T0为初始环境温度；αu为未冻结区域的热扩散系数。
  4. 根据权利要求3所述地铁隧道冻结法施工地层三维冻胀变形的预测方法，其特征在于：步骤(2)中，所述冻结锋面半径r(t)由下式获得：

    式中：kf为冻土导热系数；ku为未冻土导热系数；A为系数，L表示相变潜热。
  5. 根据权利要求4所述地铁隧道冻结法施工地层三维冻胀变形的预测方法，其特征在于：步骤(3)中，所述冻结壁交圈后冻结锋面内圈半径R1(t)、外圈半径R2(t)由下式获得：


    式中：Rd为冻结管分布半径；Tc’为交圈后冻结管管壁的平均温度；η为圆柱坐标系中冻结管的纵坐标方向。
  6. 根据权利要求1所述地铁隧道冻结法施工地层三维冻胀变形的预测方法，其特征在于：步骤(4)中，所述冻胀位移Wi(t)由下式获得：
    式中：hi为冻胀影响范围所在层位距隧道的高度；β为冻结壁上覆土层的主要影响角；θ为极坐标系下的极角；z为空间坐标系的z方向坐标；x为空间坐标系的x方向坐标；y为空间坐标系的y方向坐标；ζ为圆柱坐标系中冻结管长度方向；为圆柱坐标系中环向角度。
  7. 根据权利要求3所述地铁隧道冻结法施工地层三维冻胀变形的预测方法，其特征在于：所述
    其中，kf表示已冻结区域的导热系数，cf表示已冻结区域的比热，ρf表示已冻结区域的土体的密度，ku表示未冻结区域的导热系数，cu表示未冻结区域的比热，ρu表示未冻结区域的土体的密度。
  8. 根据权利要求2所述地铁隧道冻结法施工土地层三维冻胀变形的预测方 法，其特征在于：所述相变潜热L由下式获得：
    L＝Lwρd(w0-wu)；
    式中：Lw为水的潜热；ρd为土体干密度；w0为含水率；wu为未冻土含水率。
PCT/CN2023/097355 2022-06-13 2023-05-31 一种地铁隧道冻结法施工地层三维冻胀变形的预测方法 WO2023241356A1 (zh)

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