WO2023226237A1 - 一种垂直顶升法施工过程中顶力的修正剪切理论计算方法 - Google Patents

一种垂直顶升法施工过程中顶力的修正剪切理论计算方法 Download PDF

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WO2023226237A1
WO2023226237A1 PCT/CN2022/117727 CN2022117727W WO2023226237A1 WO 2023226237 A1 WO2023226237 A1 WO 2023226237A1 CN 2022117727 W CN2022117727 W CN 2022117727W WO 2023226237 A1 WO2023226237 A1 WO 2023226237A1
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jacking
soil
riser
shear
weight
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PCT/CN2022/117727
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French (fr)
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王霄
魏新江
魏纲
朱成伟
章丽莎
章书远
马靖昊
张泽楠
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浙大城市学院
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    • 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
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • 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
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

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  • the invention belongs to the technical field of underground tunnel engineering, and in particular relates to a theoretical calculation method of jacking force during the construction process of the vertical jacking method based on a modified shear failure model.
  • the theoretical calculation of jacking force in the vertical jacking method mainly includes the following four research methods: (1) Theoretical calculation method of earth pressure (document [1]); (2) Soil punching and shear failure method (document [2]) ; (3) Foundation bearing capacity method (document [3]); (4) Influencing factor analysis method (document [4]).
  • F sl is the jacking force during vertical jacking (kN)
  • G sl is the self-weight of the riser (kN)
  • W sl is The water pressure above the standpipe (kN)
  • R sl is the friction resistance between the pipe and soil (kN)
  • S sl is the head-on resistance (kN).
  • the existing method compares the calculated maximum jacking force and the measured maximum jacking force, it does not include the calculated value of the jacking force during the entire riser jacking process. Compare with actual measured values;
  • existing methods can calculate the jacking force, some methods can only calculate the maximum value of the jacking force (document [3]). Although other methods can calculate the jacking force during the entire jacking process. value, but the components of the jacking force are not completely considered.
  • the present invention proposes a modified shear theory calculation method of jacking force during the construction process of vertical jacking method.
  • the present invention proposes a modified shear theory calculation method for jacking force during the construction process of the vertical jacking method.
  • the method specifically includes the following steps:
  • Step 1 Analyze the components of the jacking force: According to the construction process of the vertical jacking method, it is determined that the jacking force should be equal to the sum of the head-on resistance, the friction resistance between the pipe and soil, the self-weight of the riser, and the water pressure above the riser;
  • Step 2 Use the soil shear failure method to back-calculate the n value at different jacking distances.
  • the n value is the ratio of the top radius R c of the truncated cone-shaped damage zone to the outer radius r of the riser. According to the n value, The changing rule of increasing jacking distance corrects the shear failure model area in the soil shear failure method;
  • Step 3 Determine the head-on resistance based on the n value calculated in step 2 and the modified shear failure model combined with the jacking force of the vertical jacking method;
  • Step 4 Determine the dead weight of the riser, the water pressure above the riser and the frictional resistance between the pipe and soil according to the soil shear failure method
  • Step 5 Correct the jacking force in the formation stage of the damage zone, use the measured data back-analysis method, and use the average jacking force when the construction time is 2 and 3 days as the measured data to determine the correction coefficient m;
  • Step 6 Calculate the corrected jacking force based on the head-on resistance obtained in step 3, the dead weight of the riser obtained in step 4, the water pressure above the riser, the friction resistance between the pipe and soil, and the correction coefficient m obtained in step 5.
  • the development stage of the truncated cone-shaped damage zone is specifically: Stage I is the regional soil extrusion stage, corresponding to the jacking distance range of 0.04L 0 ⁇ 0.2L 0 , and the L 0 is the total riser pipe Length; Stage II is the extensional shear failure stage, corresponding to the jacking distance range of 0.2L 0 ⁇ 0.68L 0 ; Stage III is the failure surface penetration stage, corresponding to the jacking distance range of 0.68L 0 ⁇ 0.84L 0 ; Stage IV is the soil weight In the distribution stage, the corresponding jacking distance range is 0.84L 0 ⁇ L 0 .
  • step 2 when the construction time is 3 days, the change of n value with jacking distance L is:
  • step 2 when the construction time is 2 days, the change of n value with jacking distance L is:
  • step 3 is specifically:
  • the head-on resistance S sl satisfies:
  • G e is the self-weight of the soil within the shear failure line
  • V sl is the shear force between the pipeline and the soil
  • the self-weight of the soil within the range of the shear failure line and the shear force between the pipeline and the soil are corrected on the basis of the soil shear failure method
  • the diameter of the top of the truncated cone-shaped failure zone changes with the change of jacking distance L, and the self-weight G e of the soil within the shear failure line is corrected as:
  • ⁇ i is the weight of the i-th layer of soil that changes with the jacking distance L;
  • V i (L) is the truncated cone volume of the i-th layer of soil that changes with the jacking distance L;
  • h si is the i-th layer in the damage zone
  • R i (L) is the radius of the top of the circular cone of the i-th layer of soil that changes with the jacking distance L;
  • r i is the radius of the bottom of the circular cone of the i-th layer of soil;
  • V sl is corrected to:
  • c i is the cohesion of the i-th layer of soil in the damage zone; is the internal friction angle of the i-th layer of soil in the damage zone; ⁇ i is the normal stress on the sliding surface of the i-th layer of soil in the damage zone; K 0 is the static earth pressure coefficient; sin ⁇ 0 (L) is the jacking distance L The changing sin ⁇ 0 value; cos ⁇ 0 (L) is the cos ⁇ 0 value that changes with the jacking distance L.
  • step 4 is specifically:
  • G sl G 1 +G 2 +n sl G 3
  • G 1 is the self-weight of the top cover
  • G 2 is the self-weight of the first riser pipe section
  • n sl is the number of riser pipe sections being jacked
  • G 3 is the self-weight of the standard pipe section
  • ⁇ w is the weight of water
  • h w is the height above the top cover from the sea level during the jacking process
  • D is the outer diameter of the riser (m)
  • a s is the cross-sectional area of the riser
  • R sl refers to the friction resistance between the outer surface of the riser and the soil.
  • the calculation formula is:
  • M sl is the friction force per unit area on the outer surface of the riser, and L is the jacking distance.
  • step 5 when the construction time is 3 days, the jacking distance is 0 ⁇ 0.088L.
  • m satisfies:
  • step 5 when the construction time is 2 days, the jacking distance is 0 ⁇ 0.088L.
  • m satisfies:
  • G sl is the self-weight of the riser
  • W sl is the water pressure above the riser
  • R sl is the friction resistance between the pipe and soil
  • S sl is the head-on resistance
  • G e is the self-weight of the soil within the shear failure line
  • V sl is the shear force between the pipe and the soil.
  • the invention innovatively considers the impact of the construction time of each standpipe on the jacking force during the construction process of the vertical jacking method, and re-summarizes the vertical jacking construction method on the basis of the soil shear failure method.
  • the modified shear failure method proposed by the present invention has a simple calculation process, can be used to predict the jacking force in actual vertical jacking projects in advance, and has strong practicability. It has been verified that the vertical jacking method construction process calculated by this patented method The jacking force in is consistent with the measured value, and the jacking force first increases to the maximum value and then gradually decreases.
  • Figure 1 shows the variation pattern of the n value of the riser with the jacking distance for a construction period of 3 days;
  • Figure 2 shows the variation pattern of the n value of the riser with the jacking distance for a construction period of 2 days;
  • Figure 3 shows the variation pattern of the average value of n with the jacking distance
  • Figure 4 shows the variation pattern of the correction coefficient m with the jacking distance
  • Figure 5 is a flow chart for solving the jacking force during vertical jacking construction using the modified shear failure method
  • Figure 6 shows the comparison between the calculated values of the modified soil shear failure method and existing methods (construction time is 3 days);
  • Figure 7 shows the comparison between the calculated values of the modified soil shear failure method and existing methods (construction time is 2 days).
  • the present invention proposes a modified shear theoretical calculation method for jacking force during the construction process of the vertical jacking method, which specifically includes the following steps:
  • Step 1 Determine the components of the jacking force according to the vertical jacking method construction process.
  • the jacking force F sl should be equal to the sum of the head-on resistance S sl , the friction resistance between the pipe and soil R sl , the self-weight of the riser G sl and the water pressure W sl above the riser, which can be expressed as:
  • Step 2 Modify the shear failure model area in the soil shear failure method.
  • the soil shear failure area above the riser is regarded as a circular cone with a larger top and a smaller bottom, and the width of the top of the cone is 1.2 D ⁇ 1.5D, D is the diameter of the standpipe.
  • Stage I is the regional soil extrusion stage, corresponding to the jacking distance range of 0.04L 0 ⁇ 0.2L 0 (L 0 is the total length of the riser).
  • Stage II is the extensional shear failure stage, corresponding to the jacking distance range of 0.2L 0 ⁇ 0.68L 0 .
  • Stage III is the failure surface penetration stage.
  • the corresponding jacking distance range is 0.68L 0 ⁇ 0.84L 0 .
  • This stage is the transition stage from the "small truncated cone shape” to the "large truncated cone shape” damage zone;
  • Stage IV is the soil weight distribution stage, corresponding to the jacking distance range 0.84L 0 ⁇ L 0. In this stage, the "great truncated cone-shaped" damage zone continues to develop.
  • the maximum jacking force of the riser is related to the number of construction days.
  • the maximum jacking force value is small, between 1280kN and 1520kN; when the construction days are 3 days, the maximum jacking force value is between 1640kN and 2040kN; when the construction days are 4 days, the maximum jacking force value is is 2160kN, which is the maximum value among the 8 risers.
  • the normal construction time for a riser is 2 days. During this period, if the welds are unqualified and reworked, the construction time will be increased. It is speculated that the No.
  • Figure 3 shows the variation curve of the average value of n with the jacking distance under different construction times.
  • the value of n is expressed as a piecewise function.
  • n is 1.01;
  • the change of n with the jacking distance Linear fitting was performed, and the correlation coefficients of the linear fitting when the construction time was 3 days and 2 days were 0.9697 and 0.9728 respectively, indicating that the jacking distance L can be used to better fit the n value when the jacking distance is 1.1m to 4.7m. . Therefore, in the vertical jacking project selected in this patent, the change of n with L when the construction time is 3 days can be expressed as:
  • Step 3 Based on the n value calculated in step 2, combined with the modified shear failure model of the jacking force of the vertical jacking method, determine the calculation formula of the head-on resistance S sl
  • the head-on resistance S sl satisfies:
  • G e is the self-weight of the soil within the range of the shear failure line
  • V sl is the shear force between the pipeline and the soil.
  • G e Since the diameter of the top of the truncated cone-shaped damage zone changes with the change of the jacking distance L, G e can be modified as:
  • ⁇ i is the weight of the i-th layer of soil that changes with the jacking distance L;
  • V i (L) is the truncated cone volume of the i-th layer of soil that changes with the jacking distance L, related to the n value;
  • h si is the damage The radius of the circular cone bottom corresponding to the i-th layer of soil in the area;
  • R i (L) is the radius of the circular cone top of the i-th layer of soil that changes with the jacking distance L;
  • V sl can be modified as:
  • c i is the cohesion of the i-th layer of soil in the damage zone; is the internal friction angle of the i-th layer of soil in the damage zone; ⁇ i is the normal stress on the sliding surface of the i-th layer of soil in the damage zone; K 0 is the static earth pressure coefficient; sin ⁇ 0 (L) is the jacking distance L The changing sin ⁇ 0 value; cos ⁇ 0 (L) is the cos ⁇ 0 value that changes with the jacking distance L.
  • Step 4 Determine the self-weight of the riser G sl , the water pressure above the riser W sl , and the frictional resistance between the pipe and soil R sl (kN) based on the soil shear failure method.
  • G 1 is the self-weight of the top cover (kN)
  • G 2 is the self-weight of the first riser section (kN)
  • n sl is the number of riser sections being jacked
  • G 3 is the self-weight of the standard pipe section (kN)
  • ⁇ w is the weight of water (kN ⁇ m 3 )
  • h w is the height above the top cover from the sea level during the jacking process (m)
  • D is the outer diameter of the riser (m)
  • a s is the cross section of the riser Area (m 2 ).
  • R sl refers to the friction resistance between the outer surface of the standpipe and the soil, and is calculated using the following formula:
  • M sl is the friction force per unit area on the outer surface of the riser (kN/m 2 ), and L is the jacking distance (m).
  • Step 5 Correction of the jacking force during the formation stage of the damage zone
  • n can only be 1.01. Since the truncated cone-shaped failure zone is still in the formation stage within the range of 0m to 1.1m jacking distance, setting n to 1.01 obviously over-calculates the self-weight of the soil G e and the shear between the pipe and the soil within the range of the shear failure line. Force V. Therefore, it is necessary to correct the jacking force in the range of 0m to 1.1m, that is, the range of 0 to 0.088L 0 .
  • the correction coefficient m is used to correct the jacking force when the jacking distance is 0m to 1.1m. It is assumed that the corrected calculated jacking force F m is:
  • the measured data back-analysis method is used, and the average jacking force when the construction time is 2 and 3 days is used as the basic data to back-calculate the correction coefficient of the jacking force when the jacking distance is 0m to 1.1m. m, the results are shown in Figure 4. As shown in Figure 4, when the construction time is 3 days and the jacking distance is 0m to 1.1m, m satisfies:
  • the jacking distance is 0 ⁇ 0.088L.
  • the jacking distance is 0 ⁇ 0.088L.
  • Step 6 Determine the calculation formula of jacking force F sl during vertical jacking construction according to steps 1 to 5.
  • the method of the present invention is used to calculate the jacking force during the construction process of the vertical jacking method in the project, and is combined with the soil shear failure method ([Document 2]), Yang Chunshan modified Wang Shousheng method ( Reference [5]) and the actual measured jacking force can be compared, and Figures 6 to 7 can be obtained.
  • the measured jacking force in Figure 6 refers to the average measured jacking force of the standpipe during the construction period of 3 days.
  • the measured jacking force in Figure 7 refers to the average measured jacking force of the riser during the construction period of 2 days.
  • Table 3 The specific values are shown in Table 3.
  • the calculated jacking force of the soil shear failure method is far less than the measured jacking force when the jacking distance is 2 to 10m, which is quite different from the actual situation.
  • the reason is that the range of 1.2D to 1.5D for the diameter of the top of the truncated cone is too small, which is consistent with the conclusion obtained by Yang Chunshan (document [5]).
  • the calculated jacking force of Yang Chunshan's modified Wang Shousheng method is greater than the measured jacking force when the jacking distance is about 0m to 3m, and is smaller than the measured jacking force when the jacking distance is 3m to 12.5m.
  • the calculated jacking force by Yang Chunshan's modified Wang Shousheng method is closer to the measured average jacking force value when the construction time is 2 days. It can be seen that the influence of construction time cannot be ignored when calculating the jacking force.
  • the modified shear failure method proposed in this patent for calculating the jacking force during vertical jacking construction can consider the impact of construction time, is simple in calculation, easy to apply, and has technical significance and application value.

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Abstract

本发明公开了一种垂直顶升法施工过程中顶力的修正剪切理论计算方法，所述方法首先分析顶力的组成部分：根据垂直顶升法施工过程确定顶力应等于迎面阻力、管土间的摩擦阻力、立管的自重以及立管上方的水压力之和；采用土体剪切破坏法反算不同顶进距离处的n值，所述n值为圆台形破坏区的顶面半径Rc与立管的外半径r的比值，根据n值随顶进距离增加的变化规律对土体剪切破坏法中剪切破坏模型区域进行修正；根据计算得到的n值，结合垂直顶升法顶力的修正剪切破坏模型确定迎面阻力；根据土体剪切破坏法确定立管自重、立管上方的水压力和管土间的摩擦阻力；对破坏区形成阶段的顶力进行修正，确定修正系数m；最后计算修正后的顶力。

Description

一种垂直顶升法施工过程中顶力的修正剪切理论计算方法 技术领域
本发明属于地下隧道工程技术领域，尤其涉及一种基于修正剪切破坏模型的垂直顶升法施工过程中顶力的理论计算方法。
背景技术
目前，垂直顶升法中顶力的理论计算主要为以下四种研究方法：(1)土压力理论计算法(文献[1])；(2)土体冲剪破坏法(文献[2])；(3)地基承载力法(文献[3])；(4)影响因素分析法(文献[4])。
对现有顶力的理论方法进行总结和分析(见表1)，表1中，F sl为垂直顶升过程中的顶力(kN)，G sl为立管自重(kN)，W sl为立管上方的水压力(kN)，R sl为管土间的摩擦阻力(kN)，S sl为迎面阻力(kN)。
由表1可知，现有方法的不足之处主要有：(1)现有方法虽然比较了计算最大顶力和实测最大顶力，但并没有在立管顶进全过程中将顶力计算值与实测值进行比较；(2)现有方法虽然可以计算顶力，但一些方法仅可计算顶力的最大值(文献[3])，另一些方法虽然可以计算顶力在整个顶进过程中的值，但顶力的组成部分考虑不完全，例如仅考虑顶力组成部分中的管土摩擦力(文献[4])，仅考虑管土摩擦力与立管上方水压力(文献[1])等；(3)现有方法中，土体剪切破坏法虽然较为全面地考虑了顶力的四个影响因素，但王寿生和葛春晖(文献[2])在土体剪切破坏法(下文将此法简称土体剪切破坏法)中并未对比该方法的计算值与实测值间的差别。因此，需要对现有方法进行修正和改进，并将计算结果与实测值进行对比研究，以获得准确、可靠的顶力理论计算公式。
表1现有的四种垂直顶升法顶力的计算方法
Figure PCTCN2022117727-appb-000001
Figure PCTCN2022117727-appb-000002
发明内容
针对现有技术不足，本发明提出了一种垂直顶升法施工过程中顶力的修正剪切理论计算方法。
本发明的技术方案为：本发明提出了一种垂直顶升法施工过程中顶力的修正剪切理论计算方法，所述方法具体包括以下步骤：
步骤1：分析顶力的组成部分：根据垂直顶升法施工过程确定顶力应等于迎面阻力、管土间的摩擦阻力、立管的自重以及立管上方的水压力之和；
步骤2：采用土体剪切破坏法反算不同顶进距离处的n值，所述n值为圆台形破坏区的顶面半径R c与立管的外半径r的比值，根据n值随顶进距离增加的变化规律对土体剪切破坏法中剪切破坏模型区域进行修正；
步骤3：根据步骤2计算得到的n值，结合垂直顶升法顶力的修正剪切破坏模型确定迎面阻力；
步骤4：根据土体剪切破坏法确定立管自重、立管上方的水压力和管土间的摩擦阻力；
步骤5：对破坏区形成阶段的顶力进行修正，采用实测数据反分析法，以施工时间为2天和3天时的平均顶力作为实测数据，确定修正系数m；
步骤6：根据步骤步骤3得到的迎面阻力、步骤4得到的立管自重、立管上方的水压力和管土间的摩擦阻力及步骤5得到的修正系数m计算修正后的顶力。
进一步地，所述步骤2中，圆台形破坏区的发展阶段具体为：阶段Ⅰ为区域土体挤压阶段，对应顶进距离范围0.04L 0～0.2L 0，所述L 0为立管总长度；阶段Ⅱ为延伸剪切破坏阶段，对应顶进距离范围0.2L 0～0.68L 0；阶段Ⅲ为破坏面贯通阶段，对应顶进距离范围0.68L 0～0.84L 0；阶段Ⅳ为土体重分布阶段，对应顶进距离范围0.84L 0～L 0。
进一步地，所述步骤2中，施工时间为3天时n值随顶进距离L的变化为：
Figure PCTCN2022117727-appb-000003
进一步地，所述步骤2中，施工时间为2天时n值随顶进距离L的变化为：
Figure PCTCN2022117727-appb-000004
进一步地，所述步骤3具体为：
迎面阻力S sl满足：
S sl＝G e+V sl
式中：G e为剪切破坏线范围内的土体自重，V sl为管道与土体间的剪切力；
对所述剪切破坏线范围内的土体自重及管道与土体间的剪切力在土体剪切破坏法的基础上进行修正；
圆台形破坏区顶部直径随顶进距离L的变化而变化，剪切破坏线范围内的土体自重G e修正为：
Figure PCTCN2022117727-appb-000005
式中：γ i为随顶进距离L变化的第i层土的重度；V i(L)为随顶进距离L变化的第i层土的圆台体积；h si为破坏区内第i层土对应的圆台底面半径；R i(L)为随顶进距离L变化的第i层土的圆台顶部半径；r i为第i层土的圆台底部半径；
V sl修正为：
Figure PCTCN2022117727-appb-000006
式中：c i为破坏区内第i层土的粘聚力；
Figure PCTCN2022117727-appb-000007
为破坏区内第i层土的内摩擦角；σ i为破坏区内第i层土滑动面上的法向应力；K 0为静止土压力系数；sinα 0(L)为随顶进距离L变化的sinα 0值；cosα 0(L)为随顶进距离L变化的cosα 0值。
进一步地，所述步骤4具体为：
立管管节自重G sl及立管上方的水重W sl的计算公式为：
G sl＝G 1+G 2+n slG 3
W sl＝γ wh wA s＝γ wh wπD 2/4
式中：G 1为顶盖自重，G 2为立管首节管节自重，n sl为正在顶进的立管管节数量，G 3为标准管节自重，γ w为水的重度，h w为顶升过程中顶盖上方距海平面的高度，D为立管外径(m)，A s为立管横截面面积；
R sl指立管外表面与土体之间的摩擦阻力，计算公式为：
R sl＝M sl×D×π×L
式中：M sl为立管外表面的单位面积摩擦力，L为顶进距离。
进一步地，所述步骤5中，施工时间为3天时，则顶进距离为0～0.088L 0时，m满足：
Figure PCTCN2022117727-appb-000008
进一步地，所述步骤5中，施工时间为2天时，则顶进距离为0～0.088L 0时，m满足：
Figure PCTCN2022117727-appb-000009
进一步地，修正后的顶力的计算公式为：
F m＝m(G sl+W sl+R sl+G e+V sl)＝m(G sl+W sl+R sl+S sl)
其中，G sl为立管的自重，W sl为立管上方的水压力，R sl为管土间的摩擦阻力，S sl为迎面阻力，G e为剪切破坏线范围内的土体自重，V sl为管道与土体间的剪切力。
本发明的有益效果为：本发明创新性地考虑了垂直顶升法施工过程中每根立管施工时间对顶升力的影响，在土体剪切破坏法的基础上，重新总结了垂直顶升施工过程中立管上方破坏区的变化规律，并首次对破坏区及其对应的顶升距离进行了定量分析。本发明提出的修正剪切破坏法计算过程简单，可用于实际的垂直顶升工程中顶升力的提前预测，具有较强的实用性，且验证发现本专利方法计算得到的垂直顶升法施工过程中的顶力与实测值较为吻合，顶力均呈现先增加到最大值后逐渐减小的趋势。
附图说明
图1为施工时间为3天的立管n值随顶进距离的变化规律；
图2为施工时间为2天的立管n值随顶进距离的变化规律；
图3为n的平均值随顶进距离的变化规律；
图4为修正系数m随顶进距离的变化规律；
图5为修正剪切破坏法求解垂直顶升施工过程中顶力的流程图；
图6为修正土体剪切破坏法计算值与已有方法的比较(施工时间为3天)；
图7为修正土体剪切破坏法计算值与已有方法的比较(施工时间为2天)。
具体实施方式
下面结合附图，对本发明的一种垂直顶升法施工过程中顶力的修正剪切理论计算方法进行详细说明。在不冲突的情况下，下述的实施例及实施方式中的特征可以相互组合。
如图1所示，本发明提出了一种垂直顶升法施工过程中顶力的修正剪切理论计算方法，具体包括以下步骤：
步骤1：根据垂直顶升法施工过程确定顶力的组成部分。
在垂直顶升施工过程中，顶力F sl应等于迎面阻力S sl、管土间的摩擦阻力R sl、立管的自重G sl以及立管上方的水压力W sl之和，可表示为：
F sl＝G sl+W sl+R sl+S sl     (1)
步骤2：对土体剪切破坏法中剪切破坏模型区域进行修正。
土体剪切破坏法中，首次提出垂直顶升过程中土体发生剪切破坏，并将立管上方的土体剪切破坏区域视作上大下小的圆台，且圆台上部的宽度为1.2D～1.5D，D为立管直径。
随着顶进距离的增加，“圆台形”破坏区顶面的宽度大致为从0开始不断增加，其后保持不变，而非一直保持在同一个值不变。本发明将破坏区的发展分为四个阶段：阶段Ⅰ为区域土体挤压阶段，对应顶进距离范围0.04L 0～0.2L 0(L 0为立管总长度)，此阶段中形成“小圆台形”破坏区；阶段Ⅱ为延伸剪切破坏阶段，对应顶进距离范围0.2L 0～0.68L 0，此阶段中“小圆台形”破坏区不断发展；阶段Ⅲ为破坏面贯通阶段，对应顶进距离范围0.68L 0～0.84L 0，此阶段为“小圆台形”到“大圆台形”破坏区的过渡阶段；阶段Ⅳ为土体重分布阶段，对应顶进距离范围0.84L 0～L 0，此阶段中“大圆台形”破坏区不断发展。
以某垂直顶升工程中在均质立管中顶进的8根立管(3～8号，10号，13号立管)为工程背景，采用土体剪切破坏法反算不同顶进距离处的n值(n为圆台形破坏区的顶面半径R c与立管的外半径r的比值)，最后获得n随顶进距离增加的变化规律，并据此对土体剪切破坏法进行修正。
根据工程的顶力监测记录，8根立管的施工时间及最大顶力见表2。
表2某工程中均质土层中顶进的8根立管施工时间及最大顶力
立管 施工日期 施工时间(天) 最大顶力(kN)
3 20161110-20161112 3 1920
4 20161112-20161114 3 2040
5 20161114-20161116 3 1760
6 20161116-20161118 3 1640
13 20161129-20161201 3 1760
7 20161118-20161119 2 1280
10 20161124-20161125 2 1520
8 20161119-20161122 4 2160
由表2可知，立管的最大顶力与施工天数有关。当施工天数为2天时，最大顶力数值较小，在1280kN～1520kN之间；当施工天数为3天时，最大顶力数值在1640kN～2040kN之间；当施工天数为4天时，最大顶力数值为2160kN，是8根立管中的最大值。该垂直顶升工程中，一根立管的正常施工时间为2天，期间若焊缝不合格返工会导致施工时间增加。推测8号立管在施工过程中有非正常停工或其他原因造成施工时间过长。土体剪切破坏法没有将非正常停工时间这一因素考虑在内，因此下文分析时将8号立管排除在外，采用土体剪切破坏法对另外7根立管进行n的反分析计算，结果见图1～图2。
由图1～图2可知，施工时间为2天及3天时反算得到的n值均呈现先增加后保持不变的趋势。此外，整体而言，施工时间为3天的n值比施工时间为2天的n值大。
图3为不同施工时间情况下，n的平均值随顶进距离的变化曲线。根据图3，将n的取值表示为分段函数，当顶进距离为0～1.1m时，n取1.01；当顶进距离为1.1m～4.7m时，对n随顶进距离的变化进行线性拟合，施工时间为3天和2天时线性拟合的相关系数分别为0.9697和0.9728，说明采用顶进距离L可较好地拟合顶进距离为1.1m～4.7m时的n值。因此，在本专利选取的垂直顶升工程中，施工时间为3天时n随L的变化可以表示为：
Figure PCTCN2022117727-appb-000010
若将之推广到其他工程，有：
Figure PCTCN2022117727-appb-000011
在本专利选取的垂直顶升工程中，施工时间为2天时n随L的变化可以表示为：
Figure PCTCN2022117727-appb-000012
若将之推广到其他工程，有：
Figure PCTCN2022117727-appb-000013
步骤3：根据步骤2计算得到的n值，结合垂直顶升法顶力的修正剪切破坏模型确定迎面阻力S sl的计算公式
将式(3)，式(5)中的n值计算公式修正迎面阻力S sl。
迎面阻力S sl满足：
S sl＝G e+V sl     (6)
式中：G e为剪切破坏线范围内的土体自重，V sl为管道与土体间的剪切力，这两个参数与圆台形破坏区的形状有关，需要在土体剪切破坏法的基础上进行修正。
由于圆台形破坏区顶部直径随顶进距离L的变化而变化，所以G e可修正为：
Figure PCTCN2022117727-appb-000014
式中：γ i为随顶进距离L变化的第i层土的重度；V i(L)为随顶进距离L变化的第i层土的圆台体积，与n值有关；h si为破坏区内第i层土对应的圆台底面半径；R i(L)为随顶进距离L变化的第i层土的圆台顶部半径；r i为第i层土的圆台底部半径；均质粗砾砂层中，满足R i(L)＝nr；r i＝r。
V sl可修正为：
Figure PCTCN2022117727-appb-000015
式中：c i为破坏区内第i层土的粘聚力；
Figure PCTCN2022117727-appb-000016
为破坏区内第i层土的内摩擦角；σ i为破坏区内第i层土滑动面上的法向应力；K 0为静止土压力系数；sinα 0(L)为随顶进距离L变化的sinα 0值；cosα 0(L)为随顶进距离L变化的cosα 0值。
步骤4：根据土体剪切破坏法确定立管自重G sl，立管上方的水压力W sl，管土间的摩擦阻力R sl(kN)的计算公式
由于立管管节自重G sl、立管上方的水重W sl、管节四周与土体的摩擦阻力R sl不受土体剪切破坏区域的影响，计算公式与剪切破坏法相同，保持不变，即：
G sl＝G 1+G 2+n slG 3     (9)
W sl＝γ wh wA s＝γ wh wπD 2/4       (10)
式中：G 1为顶盖自重(kN)，G 2为立管首节管节自重(kN)，n sl为正在顶进的立管管节数量，G 3为标准管节自重(kN)，γ w为水的重度(kN·m 3)，h w为顶升过程中顶盖上方距海平面的高度(m)，D为立管外径(m)，A s为立管横截面面积(m 2)。
R sl指立管外表面与土体之间的摩擦阻力，采用下式进行计算：
R sl＝M sl×D×π×L       (11)
式中：M sl为立管外表面的单位面积摩擦力(kN/m 2)，L为顶进距离(m)。
步骤5：破坏区形成阶段顶力的修正
由于土体剪切破坏法假定破坏区为上大下小的圆台，n的最小值只能取1.01。由于在0m～1.1m顶进距离范围内，圆台形破坏区仍处于形成阶段，n取1.01显然过大地计算了剪切破坏线范围内的土体自重G e和管道与土体间的剪切力V。因此，需要对0m～1.1m范围内即0～0.088L 0范围内的顶力进行修正。
为了更准确地计算圆台形破坏区形成阶段的顶力，采用修正系数m对顶进距离为0m～1.1m时的顶力进行修正，假设修正后的计算顶力F m为：
F m＝mF sl      (12)
基于本专利选取的垂直顶升工程，采用实测数据反分析法，以施工时间为2天和3天时的平均顶力作为基础数据，反算顶进距离为0m～1.1m时顶力的修正系数m，结果见图4。如图4所示，施工时间为3天时，顶进距离为0m～1.1m时的m满足：
Figure PCTCN2022117727-appb-000017
若将之推广到其他工程，则顶进距离为0～0.088L 0时，m满足：
Figure PCTCN2022117727-appb-000018
施工时间为2天时，顶进距离为0～1.1m时的m满足：
Figure PCTCN2022117727-appb-000019
若将之推广到其他工程，则顶进距离为0～0.088L 0时，m满足：
Figure PCTCN2022117727-appb-000020
步骤6：根据步骤1～5确定垂直顶升施工过程中顶力F sl的计算公式
将公式(14)或公式(16)代入公式(12)中，可以得到修正土体剪切破坏法的顶力F m计算公式如下：
F m＝m(G sl+W sl+R sl+G e+V sl)＝m(G sl+W sl+R sl+S sl)    (17)
总结来讲，本专利计算垂直顶升法施工过程中顶力的流程图见图5。
实施例1
杨春山等(2020)(文献[5]，杨春山,何娜,刘力英,等.垂直顶升施工上覆土层破坏形态的颗粒流模拟[J].公路,2020,65(3):356-360.)通过对垂直顶升施工过程进行颗粒流模拟，指出管道上覆土层剪切破坏面具有非线性特征，满足三次函数分布。同时，指出土体剪切破坏区域的顶部破坏范围为2.97D，与王寿生和葛春晖(2009)提出的1.2D～1.5D存在较大的差距。将杨春山等(2020)(文献[5])提出的剪切破坏区域顶部破坏范围2.97D代入到土体剪切破坏法公式中，并将之称为“杨春山修正王寿生法”。
基于某垂直顶升工程，采用本发明方法对该工程中垂直顶升法施工过程中的顶升力进行计算，并与土体剪切破坏法([文献2])、杨春山修正王寿生法(文献[5])以及实测顶力进行比较，可以得到图6～图7。图6中的实测顶力指施工时间为3天立管的实测顶力平均值，图7中的实测顶力指施工时间为2天立管的实测顶力平均值，具体数值见表3。
表3均质土层中顶进的7根立管顶力随顶进距离的变化
Figure PCTCN2022117727-appb-000021
Figure PCTCN2022117727-appb-000022
由图6～图7可知，可以得到土体剪切破坏法，杨春山修正王寿生法的计算顶力随顶进距离的变化函数均为单调递减的凹函数，当顶进距离为0m时顶力为最大值，其后随着顶进距离的增加，顶力不断减小，与实际情况相差较大。本文的修正剪切破坏法与实测值较为吻合，顶力均呈现先增加到最大值后逐渐减小的趋势。
土体剪切破坏法的计算顶力在顶进距离为2～10m时远远小于实测顶力，与实际情况相差较大。其原因是圆台顶部直径取值范围1.2D～1.5D偏小，这与杨春山(文献[5])得到的结论一致。
杨春山修正王寿生法的计算顶力在顶进距离约0m～3m时大于实测顶力，在顶进距离为3m～12.5m时比实测顶力小。杨春山修正王寿生法的计算顶力与施工时间为2天的平均顶力实测值更接近，可见在计算顶力时施工时间的影响不可忽略。
综上所述，本专利提出的用于计算垂直顶升施工过程中顶升力的修正剪切破坏法可以考虑施工时间的影响，且计算简单，便于应用，具有技术意义与应用价值。
本实施例表明，本发明方法提出的修正剪切破坏法可以考虑施工时间的影响，且计算简单，便于应用，可为垂直顶升施工过程中顶升力计算提供理论参考。
以上实施例仅用于说明本发明的设计思想和特点，其目的在于使本领域内的技术人员能够了解本发明的内容并据以实施，本发明的保护范围不限于上述实施例。所以，凡依据本发明所揭示的原理、设计思路所作的等同变化或修饰，均在本发明的保护范围之内。

Claims (9)

  1. 一种垂直顶升法施工过程中顶力的修正剪切理论计算方法，其特征在于，所述方法具体包括以下步骤：
    步骤1：分析顶力的组成部分：根据垂直顶升法施工过程确定顶力应等于迎面阻力、管土间的摩擦阻力、立管的自重以及立管上方的水压力之和；
    步骤2：采用土体剪切破坏法反算不同顶进距离处的n值，所述n值为圆台形破坏区的顶面半径R c与立管的外半径r的比值，根据n值随顶进距离增加的变化规律对土体剪切破坏法中剪切破坏模型区域进行修正；
    步骤3：根据步骤2计算得到的n值，结合垂直顶升法顶力的修正剪切破坏模型确定迎面阻力；
    步骤4：根据土体剪切破坏法确定立管自重、立管上方的水压力和管土间的摩擦阻力；
    步骤5：对破坏区形成阶段的顶力进行修正，采用实测数据反分析法，以施工时间为2天和3天时的平均顶力作为实测数据，确定修正系数m；
    步骤6：根据步骤3得到的迎面阻力、步骤4得到的立管自重、立管上方的水压力和管土间的摩擦阻力及步骤5得到的修正系数m计算修正后的顶力。
  2. 根据权利要求1所述的垂直顶升法施工过程中顶力的修正剪切理论计算方法，其特征在于，所述步骤2中，圆台形破坏区的发展阶段具体为：阶段Ⅰ为区域土体挤压阶段，对应顶进距离范围0.04L 0～0.2L 0，所述L 0为立管总长度；阶段Ⅱ为延伸剪切破坏阶段，对应顶进距离范围0.2L 0～0.68L 0；阶段Ⅲ为破坏面贯通阶段，对应顶进距离范围0.68L 0～0.84L 0；阶段Ⅳ为土体重分布阶段，对应顶进距离范围0.84L 0～L 0。
  3. 根据权利要求1所述的垂直顶升法施工过程中顶力的修正剪切理论计算方法，其特征在于，所述步骤2中，施工时间为3天时n值随顶进距离L的变化为：
    Figure PCTCN2022117727-appb-100001
  4. 根据权利要求1所述的垂直顶升法施工过程中顶力的修正剪切理论计算方法，其特征在于，所述步骤2中，施工时间为2天时n值随顶进距离L的变化为：
    Figure PCTCN2022117727-appb-100002
  5. 根据权利要求3或4所述的垂直顶升法施工过程中顶力的修正剪切理论计算方法，其特征在于，所述步骤3具体为：
    迎面阻力S sl满足：
    S sl＝G e+V sl
    式中：G e为剪切破坏线范围内的土体自重，V sl为管道与土体间的剪切力；
    对所述剪切破坏线范围内的土体自重及管道与土体间的剪切力在土体剪切破坏法的基础上进行修正；
    圆台形破坏区顶部直径随顶进距离L的变化而变化，剪切破坏线范围内的土体自重G e修正为：
    Figure PCTCN2022117727-appb-100003
    式中：γ i为随顶进距离L变化的第i层土的重度；V i(L)为随顶进距离L变化的第i层土的圆台体积；h si为破坏区内第i层土对应的圆台底面半径；R i(L)为随顶进距离L变化的第i层土的圆台顶部半径；r i为第i层土的圆台底部半径；
    V sl修正为：
    Figure PCTCN2022117727-appb-100004
    式中：c i为破坏区内第i层土的粘聚力；
    Figure PCTCN2022117727-appb-100005
    为破坏区内第i层土的内摩擦角；σ i为破坏区内第i层土滑动面上的法向应力；K 0为静止土压力系数；sinα 0(L)为随顶进距离L变化的sinα 0值；cosα 0(L)为随顶进距离L变化的cosα 0值。
  6. 根据权利要求1所述的垂直顶升法施工过程中顶力的修正剪切理论计算方法，其特征在于，所述步骤4具体为：
    立管管节自重G sl及立管上方的水重W sl的计算公式为：
    G sl＝G 1+G 2+n slG 3
    W sl＝γ wh wA s＝γ wh wπD 2/4
    式中：G 1为顶盖自重，G 2为立管首节管节自重，n sl为正在顶进的立管管节数量，G 3为标准管节自重，γ w为水的重度，h w为顶升过程中顶盖上方距海平面的高度，D为立管外径(m)，A s为立管横截面面积；
    R sl指立管外表面与土体之间的摩擦阻力，计算公式为：
    R sl＝M sl×D×π×L
    式中：M sl为立管外表面的单位面积摩擦力，L为顶进距离。
  7. 根据权利要求1所述的垂直顶升法施工过程中顶力的修正剪切理论计算方法，其特征在于，所述步骤5中，施工时间为3天时，顶进距离为0m～1.1m时的m满足：
    Figure PCTCN2022117727-appb-100006
  8. 根据权利要求1所述的垂直顶升法施工过程中顶力的修正剪切理论计算方法，其特征在于，所述步骤5中，施工时间为2天时，顶进距离为0～1.1m时的m满足：
    Figure PCTCN2022117727-appb-100007
  9. 根据权利要求7或8所述的垂直顶升法施工过程中顶力的修正剪切理论计算方法，其特征在于，修正后的顶力的计算公式为：
    F m＝m(G sl+W sl+R sl+G e+V sl)＝m(G sl+W sl+R sl+S sl)
    其中，G sl为立管的自重，W sl为立管上方的水压力，R sl为管土间的摩擦阻力，S sl为迎面阻力，G e为剪切破坏线范围内的土体自重，V sl为管道与土体间的剪切力。
PCT/CN2022/117727 2022-05-23 2022-09-08 一种垂直顶升法施工过程中顶力的修正剪切理论计算方法 WO2023226237A1 (zh)

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