Rectangular curve pipe jacking bottom curtain construction prediction method based on pushing force calculation

Abstract

The application discloses a rectangular curve jacking pipe bottom curtain construction prediction method based on pushing force calculation, and the method comprises three parts: the first part: taking the soil parameters in the field geological survey report and the geometric parameters of the rectangular curve jacking pipe as input parameters, analyzing the static balance relationship in the jacking pipe jacking process, deducing the calculation method of the pushing force in the curve jacking pipe jacking process, and calculating the corresponding pushing force data by the pushing force calculation system; the pushing force data are input into the second part as input. The second part: the analysis and prediction system calculates and outputs the displacement and deformation data of the object. The third part: the jacking pipe machine operation system displays the displacement and deformation data of the object in real time according to the prediction result of the second part, adjusts and controls the construction parameters such as the tunneling speed, the cutter head rotating speed and the slurry tank pressure, and protects the target object sensitive to displacement and deformation; when necessary, if the displacement and deformation of the target object exceed the safety threshold index, manual intervention or adjustment of the tunneling system operation is carried out.

Description

Technical Field

[0001] This invention relates to the field of research on deformation control of existing objects in the construction of rectangular curved pipe jacking bottom curtain method, specifically a method for predicting the construction of existing objects in the rectangular curved pipe jacking bottom curtain method based on the calculation of jacking force. Background Technology

[0002] Rectangular curved pipe jacking with a bottom curtain method is a relatively new engineering technology, and its application in tunnel engineering is still limited, especially for rectangular curved pipe jacking with small radii of curvature, which is still in the research and exploration stage. The rectangular curved pipe jacking method forms a bottom curtain that protects objects within its enclosed area or isolates the surrounding strata during internal operations (see...). Figure 8 (Scene illustration) This method has promising applications in underground engineering expansion, subway station renovation, and underwater salvage. However, there are currently no implementation cases of the curved pipe jacking bottom curtain method. Rectangular curved pipe jacking is characterized by its small size, rapid advancement, and complex underground environment. Furthermore, some adjacent structures (such as existing subway lines, pipelines, and ancient shipwrecks) are often extremely sensitive due to their high safety levels, and are extremely valuable and fragile due to their special significance. During the advancement process, they may fail or be damaged due to stress deformation and / or large displacement, leading to serious consequences. To guide engineering construction and maximize the preservation, safety, and stability of adjacent objects, a method is needed to predict the dynamic evolution of stress and deformation of objects during the jacking process of the rectangular curved pipe jacking bottom curtain method, identify the most unfavorable construction nodes, and guide the development of corresponding protective measures. The traditional approach in the industry for this type of problem is to establish finite element models of both the strata and the target protected object, and to conduct numerical simulations of the rectangular curved pipe jacking bottom curtain construction process. The accuracy of this method is affected by many uncertainties, such as the determination of the constitutive model and the accuracy of the input parameters, making the entire dynamic tunneling simulation difficult and computationally time-consuming. Furthermore, different types of problems in engineering require independent remodeling, lacking repeatability. Summary of the Invention

[0003] Based on the "Analysis and Prediction Method for the Impact of Rectangular Curved Pipe Jacking Method on Existing Objects", application date August 18, 2022, application number 2022109905992, this invention further discloses alternative technical solutions.

[0004] This invention first derives the formula for calculating the jacking force by deriving the force balance condition during the jacking process of a rectangular curved pipe, calculates the panel resistance data, and then, by establishing a relative coordinate system and utilizing the calculation principle of the Mindlin solution for a semi-infinite space in elasticity, calculates the additional stress at various locations in the object caused by the frontal resistance by simplifying the geometric model of the curved beam of the rectangular curved pipe. Based on the Winkler foundation model, the vertical settlement of each point of the object is calculated according to the foundation model, deformation compatibility conditions, equilibrium equations, etc., and by discretizing the geometric model of the object, the external forces acting on each point of the object are calculated to obtain the resultant force state of the object. The translational displacement and pure rotational displacement of the object during the jacking process are calculated to predict the dynamic displacement of the object's position during the jacking process of the rectangular curved pipe.

[0005] The technical solution is as follows:

[0006] A method for analyzing and predicting the impact of rectangular curved pipe jacking bottom curtain method on existing objects, applied to pipe jacking machine construction operations, characterized by comprising:

[0007] Part 1: Using the soil parameters from the on-site geological survey report and the geometric parameters of the rectangular curved pipe jacking as input parameters, and by analyzing the static equilibrium relationship during the pipe jacking process, the calculation method of the jacking force during the curved pipe jacking process is derived, and the corresponding jacking force data is calculated by the jacking force calculation system; this is then used as input for Part 2.

[0008] Part Two: The analysis and prediction system calculates and outputs predicted object displacement and deformation data;

[0009] Part Three: Based on the prediction results in Part Two, the pipe jacking machine operation system displays the displacement and deformation data of objects in real time, and adjusts and controls construction parameters such as on-site tunneling speed, cutterhead speed, and slurry chamber pressure. For target objects that are sensitive to displacement and deformation, if their displacement or deformation exceeds the safety threshold, manual intervention or adjustment of the tunneling system operation will be carried out when necessary.

[0010] Part One:

[0011] The jacking force calculation system decomposes the forces on the rectangular jacking pipe during the jacking process. By establishing mechanical equilibrium equations for the jacking force, the frictional resistance between the pipe section and the soil, the jacking pipe face resistance, the body force, and the interaction force between the pipe section and the guide frame as the curved jacking pipe enters the soil, the jacking force of the rectangular curved jacking pipe arc beam is solved to be jacked to any angle.

[0012] Part Two:

[0013] The analysis and prediction system discretizes the continuous jacking process into a superposition of several jacking angle conditions. The new position of the object after the displacement of the previous jacking angle is used as the starting position for the calculation of the next jacking angle. For the case where multiple curved beams (n beams) form the bottom curtain, after the calculation of the k-th curved beam is completed, it is regarded as a state of equilibrium of the resultant external forces. The force state of the (k+1)-th curved beam is calculated from the equilibrium state. The displacement state of the k-th curved beam after jacking is used as the initial condition to enter the calculation of the (k+1)-th curved beam. The analysis and prediction system uses the superposition principle to predict and output the displacement and deformation state of the target protected object in the construction of the rectangular curved pipe jacking bottom curtain method, providing a guarantee for the safety of the entire construction process.

[0014] This invention proposes a method for predicting the impact of rectangular curved pipe jacking construction on existing objects. The simplified object model can be applied to any object model that can be simplified to a uniform cross-section tensile body (such as a cylinder or prism) through multi-plane approximation. Therefore, the various parts of this invention are highly modular and do not depend on the shape of the object. With slight modifications, it can be applied to situations where pipe jacking construction with a small radius of curvature passes through or surrounds objects or underground pipelines of various shapes, exhibiting good scalability and portability. Attached Figure Description

[0015] Figure 1 Technical roadmap for jacking force algorithm of rectangular curved pipe jacking and arc beam

[0016] Figure 2 Schematic diagram of the stress on the rectangular curved pipe jacking arc beam

[0017] Figure 3 Schematic diagram of key parameters in the calculation model of rectangular curved pipe jacking arc beam

[0018] Figure 4 Comparison chart of theoretical calculations and experimental results in the implementation case.

[0019] Figure 5 Flowchart of the analysis and prediction method for the impact of rectangular curved pipe jacking bottom curtain method on existing objects

[0020] Figure 6 Calculation diagram (front view)

[0021] Figure 7 Top view of the calculated section

[0022] Figure 8 A schematic diagram of the construction scenario of the rectangular curved pipe jacking bottom curtain method and a three-dimensional schematic diagram of the model of the present invention. Detailed Implementation

[0023] This invention is applied to pipe jacking machine operations. A control system is installed in the operator's room of the pipe jacking machine. The system is also equipped with a sensing system and a tunneling system to support the conventional operations on site. At the same time, the control system in the operator's room has developed a thrust calculation system and an analysis and prediction system. And / or, the control system in the operator's room is connected to the back-end system, and the calculation system runs the thrust calculation system and the analysis and prediction system.

[0024] The method of the present invention comprises three parts.

[0025] Part 1: Using the soil parameters from the on-site geological survey report and the geometric parameters of the rectangular curved pipe jacking as input parameters, and by analyzing the static equilibrium relationship during the pipe jacking process, the calculation method of the jacking force during the curved pipe jacking process is derived, and the corresponding jacking force data is calculated by the jacking force calculation system; this is then used as input for Part 2.

[0026] Part Two: The analysis and prediction system calculates and outputs predicted object displacement and deformation data;

[0027] Part Three: Based on the prediction results in Part Two, the pipe jacking machine operation system displays the displacement and deformation data of objects in real time, and adjusts and controls construction parameters such as on-site tunneling speed, cutterhead speed, and slurry chamber pressure. For target objects that are sensitive to displacement and deformation, if their displacement or deformation exceeds the safety threshold, manual intervention or adjustment of the tunneling system operation will be carried out when necessary.

[0028] The first part of the solution can be summarized as follows:

[0029] like Figure 1 As shown: The jacking force calculation system decomposes the forces on the rectangular jacking pipe during the jacking process. By establishing the mechanical equilibrium equations of the jacking force, the frictional resistance between the pipe section and the soil, the jacking pipe face resistance, the body force, and the interaction force between the pipe section and the guide frame as the curved jacking pipe enters the soil, the jacking force of the rectangular curved jacking pipe arc beam is solved to be jacked to any angle.

[0030] First, the following assumptions are satisfied:

[0031] ① The initial principal stresses of the soil are along the vertical and horizontal directions;

[0032] ②The curved beam is a rigid body, meaning its deformation is negligible;

[0033] ③ Due to the limiting effect of the guide frame, it is assumed that the arc beam always moves along the predetermined trajectory, and the jacking force always moves along the tangent direction of the jacking trajectory with no lateral component.

[0034] ④ Due to the friction reduction operation of the ball bearings, it is assumed that the transmission of axial force is continuous, and the friction coefficient of the interaction force between the pipe section and the guide frame is set as small as possible;

[0035] ⑤ The shear plasticity of soil follows the Mohr-Coulomb criterion;

[0036] ⑥ During the jacking process of the pipe section, the adjacent soil is in a critical shear yielding state.

[0037] ⑦ The general formula requires that the horizontal plane of the (n+1)th layer of soil be higher than the horizontal tangent height of the lowest point of the inner arc surface when the pipe section is pushed to its deepest point.

[0038] Based on the above assumptions, considering the symmetry of the pipe section width, we only consider the tangential forces of the inner arc surface friction, outer arc surface friction, and friction on both sides. The moment of the frontal resistance at the center of the side plane is balanced due to symmetry. The normal force on the side plane is also balanced due to symmetry. After integrating the forces, the three-dimensional force model can be converted into a two-dimensional force model, where it is assumed that the pipe section rotates counterclockwise. See [link to relevant documentation]. Figure 2 .

[0039] Step 1.1: Derive the torque expressions for the inner arc surface friction, outer arc surface friction, lateral friction, and frontal resistance about the centroid of the trajectory, applicable to the entire jacking process, as well as the expressions for the horizontal and vertical concentrated forces. Integrate to obtain the concentrated force, F. 内 F 外 F 侧 F 推 See the simplified force diagram. Figure 2 .

[0040] Specifically, it includes:

[0041] Step 1.1.1 Determine the relevant expressions for the frictional resistance of the inner arc surface (1-2), (1-4), and (1-5).

[0042] Considering symmetry, the force on the inner arc surface is integrated, thereby transforming it from the inner arc surface in three dimensions to a motion trajectory plane orthogonal to it, which facilitates the establishment of the final mechanical equilibrium equation.

[0043] First, calculate the normal stress and shear stress acting on the inner curved surface. In the formula, A i =sinθ(sin 2 θ+K i cos 2 θ); i is the soil layer number; L is the width of the curved beam; γ i The unit weight of the i-th soil layer is considered as the effective unit weight when submerged in water; K i c is the lateral earth pressure coefficient of the i-th soil layer; i and These represent the cohesion and internal friction angle of the i-th soil layer, respectively. In the formula derivation, the case where the end face of the pipe section intersects the soil layer interface at an oblique angle is simplified, and different parameters θ are used in the segments before and after the jacking process. Li and θ RiThis simplifies the formula, and its specific meaning is: θ Li θ is the angle between the line connecting the intersection of the outer arc trajectory of the curved beam and the boundary line between the two soil layers, the center of the pipe section, and the horizontal plane; it is used for calculations during the downward jacking process of the pipe section. Ri θ is the angle between the line connecting the intersection of the inner arc trajectory of the curved beam and the boundary line between the two soil layers, the center of the pipe section, and the horizontal plane; it is used in calculations during the upward ejection of the pipe section. In each step, θ... Li and θ Ri The meanings are the same, see Figure 3 σ Hi τ is the normal stress exerted by the i-th layer of soil on the inner arc surface of the pipe section. Hi It is the tangential stress exerted by the i-th layer of soil on the inner arc surface of the pipe section.

[0044] σ Hi =γ i R1A i (1-1)

[0045] Assume there are n+1 layers of soil. We will discuss different cases depending on the jacking process. For the bending moment M1 generated by the frictional resistance of the inner arc surface, when θ < θ Li At times, such as Figure 2 The pipe section is pushed downwards into the soil. When it reaches the (i+1)th layer of soil (i = 0, 1, ..., n), the formula for calculating M1 is shown in Part 1 of (1-2). When θ > θ Li At this point, the pipe section enters the bottom layer of soil and gradually begins to push upwards. When it reaches the i-th layer of soil (i = 1, ..., n+1), the formula for calculating M1 is as shown in Part 2 of (1-2). θ is the angle between the end of the curved beam entering the mud surface and the horizontal mud surface, which is also the angle of rotation of the pipe section.

[0046]

[0047] in,

[0048] θ L0 =0 π-θ R(n+1) =θ Ln (1-3)

[0049] To facilitate the establishment of the equilibrium equations, the normal and tangential stresses generated by the frictional resistance of the inner arc surface are decomposed and integrated to obtain the horizontal concentrated force X1 and vertical concentrated force Y1 after the decomposition of the frictional resistance of the inner arc surface, as shown in formulas (1-4) and (1-5). The classification of formulas is the same as the analysis process of formula (1-2): when θ < θ Li At that time, the pipe section enters the soil and is pushed downwards. When it reaches the (i+1)th layer of soil (i = 0, 1, ..., n), when θ > θ LiWhen the pipe section enters the bottom layer of soil, it gradually begins to push upwards. When it reaches the i-th layer of soil (i = 1, ..., n+1), it will reach the bottom layer of soil.

[0050]

[0051]

[0052] Step 1.1.2 Determine the expressions for the frictional resistance of the outer arc surface (1-7), (1-8), and (1-9).

[0053] Specifically, the frictional resistance of the outer arc surface differs from that of the inner arc surface in two ways: the radius in the stress expression should be the outer diameter; and the direction of the normal stress in the outer arc surface frictional resistance is opposite to that in the inner arc surface frictional resistance. Therefore, the formula (1-7) for the bending moment M2 caused by the outer arc surface frictional resistance, as well as its decomposed formulas for the horizontal concentrated force X2 (1-8) and the vertical concentrated force Y2 (1-9), can be derived from the formulas (1-2), (1-4), (1-4), and (1-5) for the bending moment M1, horizontal concentrated force X1, and vertical concentrated force Y1 of the inner arc surface frictional resistance, respectively. The sign of the radius differs from that of the normal stress. The expressions for normal stress and shear stress are as follows:

[0054] σ Hi =γ i R2A i (1-6)

[0055] The meanings of the other parameters are the same as before.

[0056]

[0057]

[0058]

[0059] Step 1.1.3 Determine the expressions for the side friction resistance (1-11), (1-12), and (1-13).

[0060] Specifically, this includes: due to symmetry, the normal forces on both sides of the surface are in equilibrium, therefore the resulting lateral plane moment is not considered. τ Hi It is the tangential stress exerted by the i-th layer of soil on the side surface of the pipe section, expressed as in formula (1-10). The contact surface between the side surface and the soil is a plane, while the inner and outer arc surfaces are curved surfaces, thus the stress calculation methods differ.

[0061]

[0062] The meanings of the other parameters are the same as before. When θ < θ LiAt that time, the pipe section enters the soil and is pushed downwards. When it reaches the (i+1)th layer of soil (i = 0, 1, ..., n), when θ > θ Li At this point, the pipe section enters the bottom layer of soil and gradually begins to push upwards. When it reaches the i-th layer of soil (i = 1, ..., n+1), the expressions for its bending moment M3, horizontal concentrated force X3, and vertical concentrated force Y3 are (1-11), (1-12), and (1-13), respectively. Note that when considering two sides, the corresponding formulas in the equilibrium equations need to be multiplied by 2.

[0063]

[0064]

[0065]

[0066] Step 1.1.4 Determine the expressions for the frontal resistance (1-14), (1-15), and (1-16).

[0067] Specifically, this includes: The frontal resistance does not require separate discussion because it is independent of the movement path. There are n+1 layers in total. When the pipe jacking reaches the i-th layer of soil, the expressions for the bending moment M4, the horizontal concentrated force X4, and the vertical concentrated force Y4 are (1-14)(1-15)(1-16), as follows. Where i = 1, ..., n+. Where D... i =(cos 2 θ+K i sin 2 θ), where i is the soil layer number.

[0068]

[0069]

[0070]

[0071] Step 1.2: Derive the torque expressions (1-18) of the tube segment body forces about the trajectory centroid during the entire jacking process, as well as the expressions (1-19) and (1-20) of the horizontal and vertical concentrated forces. See Figure 2 .

[0072] Specifically, it includes:

[0073] Step 1.2.1 The distance h between the centroid and center of the annulus can be obtained from the formula for the distance between the centroid and center of the circle. c , such as (1-17).

[0074]

[0075] In the formula, R1 is the inner radius of the curved beam, R2 is the outer radius of the curved beam, S1 is the area of ​​the inner semicircle, and S2 is the area of ​​the outer semicircle.

[0076] Step 1.2.2 Determine the expression for body force.

[0077] The moment M5 caused by the self-weight of the curved beam is:

[0078] M5=G B h c sinθ (1-18)

[0079] In the formula, G B Let θ be the self-weight of the curved beam, and θ be the angle between the end of the curved beam entering the mud surface and the horizontal mud surface.

[0080] Its own weight constitutes a vertical force, with no horizontal component. The expressions for its horizontal concentrated force X5 and vertical concentrated force Y5 are equations (1-11), (1-19), and (1-20) respectively, as follows:

[0081] X5 = 0 (1-19)

[0082] Y5 = -G B (1-20)

[0083] Step 1.3: Assume the interaction force between the pipe section and the guide frame is a concentrated force with an unknown location, and the direction of the interaction force is the tangential and normal directions of the running trajectory. Based on the construction conditions, set the friction coefficient to establish the normal concentrated force N and the tangential concentrated force Nt. t Relationship K t The expression for the moment M6 of the interaction force between the pusher section and the guide frame about the centroid of the trajectory is given in equation (1-22), as are the expressions for the horizontal concentrated force X6 (1-23) and the vertical concentrated force Y6 (1-24). In equation (1-21), N... t The tangential force in the interaction forces, when taken as its absolute value, represents a direction that remains constant and is opposite to the direction of the pipe joint's movement. p represents the angle between the point of application of the interaction force and the horizontal plane containing the center of the circle, see... Figure 2 .

[0084] N t =|K t N| (1-21)

[0085] M6=N t R1 (1-22)

[0086] X6 = N t sin(p) - Ncos(p) (1-23)

[0087] Y6 = N t cos(p) + Nsin(p) (1-24)

[0088] Step 1.4: Set the jacking force as an unknown force T, and derive the expression (1-25) for the moment M7 of the jacking force about the centroid of the trajectory, as well as the expressions (1-26) for the horizontal concentrated force X7 and (1-27) for the vertical concentrated force Y7. See Figure 2 .

[0089] M7=-T(R1+R2) / 2 (1-25)

[0090] X7=-Tsinθ (1-26)

[0091] Y7=Tcosθ (1-27)

[0092] Step 1.5: Establish a system of three quadratic equations based on the above expressions. Ensure static equilibrium for bending moment, horizontal concentrated force, and vertical concentrated force, respectively, yielding the bending moment equilibrium equation (1-28), the horizontal concentrated force equilibrium equation (1-29), and the vertical concentrated force equilibrium equation (1-30). Obtain the corresponding jacking force, the normal force in the interaction force between the pipe section and the guide frame, and the position of action of the interaction force between the pipe section and the guide frame at different propulsion angles.

[0093] 0=M1+M2+M3+M4+M5+M6+M7 (1-28)

[0094] 0 = X1 + X2 + X3 + X4 + X5 + X6 + X7 (1-29)

[0095] 0=Y1+Y2+Y3+Y4+Y5+Y6+Y7 (1-30)

[0096] Output parameters: The jacking force T (used to supply the second part) corresponding to different propulsion angles, the normal force N in the interaction force between the tube section and the guide frame, and the position p in the interaction force between the tube section and the guide frame.

[0097] To demonstrate the practicality of the jacking force calculation system in Part One of this invention and to provide a more intuitive introduction to the invention, a set of model test jacking force results are used as a reference for comparison with theoretical calculation results. When calculating the theoretical solution, it is assumed that there are two soil layers: a layer of iron-plate sand and a layer of bluish-gray mud. The iron-plate sand layer is 3.2 meters thick, and the bluish-gray mud layer is more than 4.3 meters thick. The main physical and mechanical properties of the two soil layers are shown in Table 1. The pipe section is a hollow arc-shaped structure with a density of 7850 kg / m³. 3 The inner diameter is 7.5 meters, the outer diameter is 8.5 meters, the width is 2 meters, and the plate thickness is 0.1 meters. The coefficient of friction K between the frame and the pipe section is... t Set it to 0.01. The comparison results are as follows: Figure 4 .

[0098] Table 1. Main physical and mechanical parameters of the formation

[0099]

[0100] The second part of the plan can be summarized as follows:

[0101] The system discretizes the continuous jacking process into a superposition of several jacking angle conditions, using the new position of the object after the displacement of the previous jacking angle as the starting position for the calculation of the next jacking angle. For the case where the bottom curtain consists of multiple curved beams (n beams), after the calculation of the k-th curved beam is completed, it is considered to be in a state of equilibrium of the net external forces. The stress state of the (k+1)-th curved beam is calculated from this equilibrium state. The displacement state of the k-th curved beam after jacking is used as the initial condition for the calculation of the (k+1)-th curved beam. Using the superposition principle, the system predicts and outputs the displacement and deformation state of the target protected object during the construction of the rectangular curved pipe jacking bottom curtain method, providing a guarantee for the safety of the entire construction process.

[0102] The entire prediction process in Part Two, the algorithm flow is as follows: Figure 5 As shown.

[0103] Step 2.1: Calculate the vertical and horizontal thrust of the kth curved beam using the jacking force data provided by the sensing system during the jacking process of the rectangular curved pipe jacking arc beam.

[0104] Specifically, it includes:

[0105] Step 2.1.1: Obtain the jacking force data F of the j-th jacking step of the k-th curved beam. j .

[0106] Step 2.1.2: Apply the jacking force F j The thrust is decomposed into horizontal and vertical components, and the horizontal and vertical components p of the j-th jacking thrust are obtained through equation (2-1). h,j p v,j ;

[0107]

[0108] In the formula, Fj is the measured total jacking force, and θj is the current jacking angle of the pipe.

[0109] Step 2.2: Based on the calculation principle of the Mindlin solution for a semi-infinite space in elasticity, the geometric model of the curved beam of the jacking pipe is simplified. On the basis of reasonable assumptions such as the geometric model being closed, continuous, homogeneous, and having small deformation, the additional stress at each position in the object caused by the frontal resistance is calculated.

[0110] Specifically, it includes:

[0111] Step 2.2.1: As Figure 6 , Figure 7As shown, the target protected object is simplified into a cylindrical geometric model of equal length and volume, with its surface region being Г. For other models, the cross-section can be approximated using a multi-section method according to their different geometric shapes, transforming them into other equal-section tensile bodies. The calculation method remains unchanged (the same geometric model is used in subsequent working conditions, but the position changes). The jacking force is considered to be entirely applied to the end face of the curved beam as a uniformly distributed load in the form of frontal resistance. The frontal resistance is approximately equal to the magnitude of the jacking force, applied to the end face as a uniformly distributed load.

[0112] Step 2.2.2 Based on the Mindlin solution, establish a spatial coordinate system with the center of the curved jacking pipe circle as the origin, and the long and short axes of the object and the positive directions of the vertical axis as the x, y, and z axes, respectively. Calculate the frontal resistance at any point Q(x) on the object's surface. q ,y q ,z q The additional stress ∈ Г. The vertical and horizontal loads p in the j-th apex advance are obtained according to equations (2-2) and (2-3), respectively. v dξdη and p h dξdη causes any point Q(x) on the object q ,y q ,z q Additional stress σ at ∈ Г zv σ zh :

[0113]

[0114]

[0115] Where, σ z =σ zv +σ zh .

[0116] In the formula, dξdη is a infinitesimal element on the jacking surface Ω of the curved beam (the same below), ξ and η are mutually perpendicular local coordinates on the jacking surface, and ν is Poisson's ratio. For the burial depth of the j-th jacking pipe end face, R 梁 The radius of the arc-shaped beam is denoted by . The top surface of the arc-shaped beam is the facing surface. Wherein,

[0117]

[0118] Step 2.3: Based on the Winkler foundation model, Figure 8 With the center of the arc beam k as the origin O, the x, y, and z axes of the spatial coordinate system are determined by the cylindrical axis of the target protected object and the horizontal and vertical directions of the section where the arc beam k is located. Under this spatial coordinate system, the vertical deformation w of each point of the object is calculated based on the foundation model, deformation compatibility conditions, equilibrium equations, etc.

[0119] Specifically, it includes:

[0120] Step 2.3.1 Based on the Winkler foundation model, establish the deformation compatibility conditions and equilibrium equations between the object and the foundation, and determine the deformation control differential equations of the object;

[0121] When analyzing the additional stress perpendicular to the cylinder caused by pipe jacking, the cylinder can be considered as an infinitely long beam on a Winkler elastic foundation under distributed load. Thus, the governing equation for the influence of the additional stress on the object is obtained:

[0122]

[0123] EI is the bending stiffness of the object, P Z (x)=σ z D represents the additional load on the object.

[0124] D is the diameter of the object (equivalent to a circle of the same area, the same below).

[0125] K is the subgrade coefficient, calculated according to the formula proposed by Vesic.

[0126]

[0127] Step 2.3.2 Solve the deformation control differential equation to obtain the vertical deformation data w at each point of the object.

[0128] The solution for the object under the action of a concentrated force P0 is:

[0129]

[0130] in,

[0131] Treating the uniformly distributed load as an integral of the concentrated load P(ξ)dξ, we calculate it according to equation (2-6) and integrate it within the uniformly distributed load range to obtain the analytical formula for the vertical deformation of the object (ξ is the integration variable):

[0132]

[0133] The obtained vertical deformation w can be output in real time for dynamic monitoring of the deformation of the protected object during the tunneling process, and the system can adjust the operation parameters and operation mode in a timely manner when the deformation exceeds the threshold range.

[0134] Step 2.3.3 For each working condition in the calculation of the same curved beam, based on the previous working condition, determine the initial position for the deformation calculation of the object, that is, based on the calculation results of the previous stage, set the current vertical coordinates of each point. The values ​​are updated according to the vertical deformation.

[0135]

[0136] Where k is the current sequence number of the curved beam advancement, and j is the top advancement number.

[0137] Step 2.4: Based on the additional stress at each position in the object caused by the frontal resistance obtained in Step 2, determine the resultant external force state and displacement of the object during the jacking process, and update the object position;

[0138] Step 2.4.1 Calculate the net external force on the j-th apex of the k-th pipe segment: The external force within each calculation region is calculated according to formula P. k,j =σ zk,j A is calculated, where A is the area of ​​the region.

[0139] The net external force F acting on the center of gravity of an object 合k,j =∑ Γ P k,j Γ represents the total calculation area of ​​the object.

[0140] The resultant torque T acting on the object k,j =∑ Γ P k,j ·l,l represents the distance from the centroid of each calculation region to the centroid of the object.

[0141] Step 2.4.2 Based on the external force state (resultant force and resultant torque), according to Newton's second law F=ma and the kinematic formula, the displacement δ of the object during the j-th apex advance of the k-th tube segment is obtained according to equation (9). k,j and rotation angle θ k,j ;

[0142]

[0143]

[0144] Where a k,j For acceleration, ω k,j Let ω be the angular acceleration, J be the moment of inertia, m be the mass, and t be the jacking time per jacking step.

[0145] The rigid body displacement and rotation data δ obtained in this step k,j and θ k,j It can output data in real time, enabling real-time monitoring of the protected object during the tunneling process, and timely adjustment of operating parameters and methods when the limits are exceeded.

[0146] Step 2.4.3 Based on the displacement obtained in Step 2.4.2, update the position coordinates of each calculated point of the object. If this is not the last working condition, continue to calculate the next working condition (return to Step 2.1) until all the curved beams have been advanced.

[0147] Thus, the analysis and prediction system calculates and outputs predicted object displacement and deformation data; then, the pipe jacking machine operation system displays the object displacement and deformation data in real time based on the prediction results in the second part, and adjusts and controls construction parameters such as on-site tunneling speed, cutterhead speed, and slurry chamber pressure. For target objects that are sensitive to displacement and deformation, if it is necessary for their displacement and deformation to exceed the safety threshold, manual intervention or adjustment of the tunneling system operation will be carried out.

Claims

1. A prediction method for rectangular curve pipe jacking bottom curtain construction based on jacking force calculation, applied to pipe jacking machine construction operations, characterized in that, include: Part 1: Using the soil parameters from the on-site geological survey report and the geometric parameters of the rectangular curved pipe jacking as input parameters, and by analyzing the static equilibrium relationship during the pipe jacking process, the calculation method for the jacking force during the curved pipe jacking process is derived. The corresponding jacking force is then calculated by the jacking force calculation system. T The data; used as input for the second part; Part Two: The analysis and prediction system calculates and outputs predicted object displacement and deformation data; Part Three: The analysis and prediction system displays the displacement and deformation data of objects in real time based on the prediction results of Part Two. It adjusts and controls the construction parameters such as the tunneling speed, cutterhead speed, and slurry chamber pressure on site. For target objects that are sensitive to displacement and deformation, if their displacement or deformation exceeds the safety threshold, manual intervention or adjustment of the tunneling system operation will be carried out. Step 1.1: Derive the torque expressions for the inner arc surface friction, outer arc surface friction, side friction, and frontal resistance about the centroid of the trajectory, applicable to the entire jacking process; and the expressions for the horizontal and vertical concentrated forces. Integral force is obtained. , , , ； Step 1.2: Derive the torque expression (1-18) of the tube segment body force about the trajectory centroid during the entire jacking process, as well as the expressions (1-19) and (1-20) of the horizontal and vertical concentrated forces. Step 1.3: The moment of the interaction force between the guide joint and the guide frame about the centroid of the trajectory. Expression (1-22), and horizontal concentrated force Expression (1-23) and vertical concentrated force Expression (1-24); Step 1.4: Set the jacking force as an unknown force. T Derive the torque of the top thrust about the centroid of the trajectory. Expression (1-25), and horizontal concentrated force Expression (1-26) and vertical concentrated force Expression (1-27); Step 1.5: Establish a system of three quadratic equations. Ensure static equilibrium for bending moment, horizontal concentrated force, and vertical concentrated force, respectively. Obtain the bending moment equilibrium equation (1-28), the horizontal concentrated force equilibrium equation (1-29), and the vertical concentrated force equilibrium equation (1-30). Then, obtain the corresponding jacking force for different thrust angles. T Normal force in the interaction force between pipe section and guide frame N The position of action in the interaction force between the pipe section and the guide frame p； Step 1.1 specifically includes: Step 1.1.1 Determine the relevant expressions for the frictional resistance of the inner arc surface (1-2), (1-4), and (1-5). （1-2） in, （1-3） （1-4） （1-5） Step 1.1.2 Determine the expressions for the frictional resistance of the outer arc surface (1-7), (1-8), and (1-9); （1-7） （1-8） （1-9） Step 1.1.3 Determine the expressions for the side friction resistance (1-11), (1-12), and (1-13); （1-11） （1-12） （1-13） Step 1.1.4 Determine the expressions for the frontal resistance (1-14), (1-15), and (1-16); （1-14） （1-15） （1-16）； Step 1.2 specifically includes: Step 1.2.1 The distance between the centroid and center of the annulus can be obtained from the formula for the distance between the centroid and center of the circle. For example (1-17); (1-17) In the formula R 1 is the inner radius of the curved beam. R 2 is the outer radius of the curved beam. S 1 represents the area of ​​the inner semicircle. S 2 represents the area of ​​the outer semicircle; Step 1.2.2 Determine the expression for body force; Moment caused by the self-weight of the curved beam for: (1-18) In the formula, G B For the self-weight of the curved beam, θ The angle between the end of the curved beam entering the mud surface and the horizontal mud surface; Its own weight is a vertical force, and there is no horizontal component; its concentrated horizontal force is... Vertical concentrated force The expressions are (1-11), (1-19), and (1-20) respectively, as follows: (1-19) (1-20)； Step 1.3 specifically includes: (1-22) (1-23) (1-24)； Step 1.4: (1-25) (1-26) (1-27)； Step 1.5: Establish a system of three quadratic equations based on the above expression: (1-28) (1-29) (1-30) Output parameters: Obtain the jacking force corresponding to different thrust angles. T Normal force in the interaction force between pipe section and guide frame N The position of action in the interaction force between the pipe section and the guide frame p .

2. The method as described in claim 1, characterized in that, Part One: The jacking force calculation system decomposes the forces on the rectangular jacking pipe during the jacking process. By establishing mechanical equilibrium equations for the jacking force, the frictional resistance between the pipe section and the soil, the jacking pipe face resistance, the body force, and the interaction force between the pipe section and the guide frame as the curved jacking pipe enters the soil, the jacking force of the rectangular curved jacking pipe arc beam is solved to be jacked to any angle.

3. The method as described in claim 1, characterized in that, in, Part Two: The analysis and prediction system discretizes the continuous jacking process into a superposition of several jacking angle conditions. The new position of the object after the displacement of the previous jacking angle is used as the starting position for the calculation of the next jacking angle. For the case where multiple curved beams (n) form the bottom curtain, after the calculation of the kth curved beam is completed, it is regarded as a state of equilibrium of the resultant external forces. The stress state of the (k+1)th curved beam is calculated from the equilibrium state. The displacement state of the kth curved beam after jacking is used as the initial condition to enter the calculation of the (k+1)th curved beam. The analysis and prediction system uses the superposition principle to predict and output the displacement and deformation state of the target protected object in the construction of the rectangular curved pipe jacking bottom curtain method, providing a guarantee for the safety of the entire construction process.

4. The method as described in claim 3, characterized in that, The second part, the entire prediction process, includes: Step 1: Calculate the vertical and horizontal thrust of the k-th curved beam using the jacking force data provided by the sensing system during the jacking process of the rectangular curved pipe jacking arc beam; Step 2: Based on the calculation principle of the Mindlin solution for a semi-infinite space in elasticity, the additional stress at each position in the object caused by the frontal resistance is calculated by simplifying the geometric model of the curved beam of the jacking pipe. Step 3: Based on the Winkler foundation model, with the center of the arc beam k as the origin O, determine the x, y, and z axes of the spatial coordinate system with the cylindrical axis of the target protected object and the horizontal and vertical directions of the section where the arc beam k is located. Under this spatial coordinate system, calculate the vertical deformation w of each point of the object according to the foundation model, deformation compatibility conditions, and equilibrium equations. Step 4: Based on the additional stress at various locations in the object caused by the frontal resistance obtained in Step 2, determine the resultant external force state and displacement of the object during the jacking process, and update the object position. Step 1 specifically includes: Step 1.1: Obtain the jacking force data for the j-th jacking step of the k-th curved beam. F j ; Step 1.2: Apply top thrust F j The thrust is decomposed into horizontal and vertical components, and the horizontal and vertical components p of the j-th jacking thrust are obtained through equation (1). h,j p v,j ; (1) In the formula Fj To measure the total thrust, θj This represents the current jacking angle of the pipe; Step 2 specifically includes: Step 2.1: Simplify the target protected object into a cylindrical geometric model of equal length and volume, with its surface region being Г; the jacking force is regarded as being applied to the end face of the arc-shaped beam as a uniformly distributed load in the form of frontal resistance; the frontal resistance is approximately equal to the magnitude of the jacking force and is applied to the end face as a uniformly distributed load. Step 2.2 Based on the Mindlin solution, establish a spatial coordinate system with the center of the curved jacking pipe circle as the origin, and the long and short axes of the object and the positive directions of the x, y, and z axes, respectively. Calculate the impact of the frontal resistance on any point on the object's surface. Additional stress; the vertical and horizontal loads in the j-th apex advance are obtained according to equations (2) and (3), respectively. and Cause any point on the object Additional stress at the location : （2） （3） in, ; In the formula, Let Ω be a micro-element on the jacking surface of the curved beam. and Let be the mutually perpendicular local coordinates on the jacking surface, and ν be Poisson's ratio. R represents the burial depth of the j-th jacking pipe end face. 梁 The radius of the arc-shaped beam; the top surface of the arc-shaped beam, i.e., the facing surface; wherein, ； Step 3 specifically includes: Step 3.1 Based on the Winkler foundation model, establish the deformation compatibility conditions and equilibrium equations between the object and the foundation, and determine the deformation control differential equations of the object; When analyzing the additional stress perpendicular to the cylinder caused by pipe jacking, the cylinder is considered as an infinitely long beam on a Winkler elastic foundation under distributed load; the governing equation for the influence of the additional stress on the object is obtained: （4） ； （5） Step 3.2 Solve the deformation control differential equation to obtain the vertical deformation data w at each point of the object; An object is subjected to concentrated force P The solution under the action of 0 is: （6） in, ; Treat uniformly distributed loads as concentrated loads. P ( ξ )d ξ The integral form of the equation (12) is used to calculate and integrate within the uniformly distributed load range to obtain the analytical formula for the vertical deformation of the object, where ξ is the integration variable: （7） The obtained vertical deformation amount w is output in real time and used for dynamic monitoring of the deformation of the protected object during the tunneling process. When the deformation exceeds the threshold range, the system adjusts the operation parameters and operation mode in a timely manner. Step 3.3 For each working condition in the calculation of the same curved beam, based on the previous working condition, determine the initial position for the deformation calculation of the object, that is, based on the calculation results of the previous stage, set the current vertical coordinates of each point. The values ​​are updated according to the vertical deformation. （8） Where k is the current sequence number of the curved beam advancement, and j is the step-up advancement number; Step 4 specifically includes Step 4.1 Calculate the net external force on the j-th apex of the k-th pipe segment: The external force within each calculation region is calculated according to the formula... Calculate, where A is the area of ​​the region; The net external force acting on the center of gravity of an object , ; Resultant torque acting on an object ; Step 4.2 Based on the external force state, and according to Newton's second law F=ma and the kinematic formula, the displacement δ of the object during the j-th apex advance of the k-th tube segment is obtained according to equation (9). k,j and rotation angle θ k,j ; （9） Where a k,j For acceleration, ω k,j ω is angular acceleration, J is moment of inertia, m is mass, and t is the jacking time per jacking step. The rigid body displacement and rotation data δ obtained in this step k,j and θ k,j Real-time output is used for real-time monitoring of the protected object during the tunneling process, and timely adjustment of operating parameters and operating methods when the allowable range is exceeded. Step 4.3 Based on the displacement obtained in Step 4.2, update the position coordinates of each calculated point of the object. If this is not the last working condition, continue to calculate the next working condition and return to Step 1 until all the curved beams have been advanced.

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