Analytical prediction method for the impact of rectangular curve pipe jacking bottom curtain construction on existing objects

Abstract

A method for analyzing and predicting the impact of rectangular curve jacking bottom curtain method construction on existing objects is proposed. The present invention proposes a method capable of predicting the impact of rectangular curve jacking bottom curtain method construction on existing objects. Panel resistance data is calculated from the jacking thrust data during the rectangular curve jacking process. By establishing a relative coordinate system and utilizing the calculation principle of the Mindlin solution of a semi-infinite space in elastic mechanics, the geometric model of the rectangular curve jacking arc beam is simplified to calculate the additional stress at each position in the object caused by the head-on resistance. Based on the Winkler foundation model, the vertical settlement of each point on the object is calculated according to the foundation model, deformation coordination conditions, equilibrium equations, etc. The external force acting on each point on the object is calculated by discretizing the geometric model of the object 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 during the rectangular curve jacking process.

Description

Technical Field

[0001] The present invention relates to the research field of deformation control of existing objects during construction using a rectangular curve pipe jacking and bottom curtain method. Background Art

[0002] The rectangular curve jacking bottom curtain method is a relatively new engineering technology and its application in tunnel engineering is still relatively rare, especially the small curvature radius rectangular curve jacking, which is still in the research and exploration stage. The rectangular curve jacking is used to form a bottom curtain to protect the objects within the enclosed area or to isolate the strata outside the enclosed area during internal operations (see Figure 3 Scenario diagram), it has good prospects for expansion and application in underground engineering expansion, subway underground station renovation and underwater salvage. However, there are currently no implementation cases of the curved pipe jacking bottom curtain method. The rectangular curve pipe jacking is small in size, advances quickly, and has a complex underground environment. In addition, some adjacent object structures (such as existing subway lines, pipelines, ancient shipwrecks, etc.) are often extremely sensitive due to their high security level, and are extremely valuable and fragile due to their special value. During the advancement process, they may fail and be damaged due to stress deformation and / or large displacement, resulting in serious consequences. In order to guide engineering construction and maximize the originality, safety and stability of adjacent objects, it is necessary to propose a method that can predict the dynamic evolution of stress and deformation caused by the rectangular curve pipe jacking bottom curtain method during the jacking process, determine the most unfavorable construction nodes, and guide and formulate corresponding protection measures. For such problems, the traditional approach in the industry is to establish finite element models of both the stratum and the target protection object, and perform numerical simulation of the rectangular curve pipe jacking bottom curtain construction process. The accuracy of this method is limited by numerous uncertainties, including the determination of the constitutive model and the accuracy of input parameters. This makes dynamic tunneling simulation difficult and computationally time-consuming. Furthermore, each different type of engineering problem requires independent re-modeling, resulting in a lack of repeatability. Summary of the Invention

[0003] The present invention calculates panel resistance data from the thrust data during the rectangular curve jacking process, establishes a relative coordinate system, utilizes the calculation principle of the Mindlin solution of a semi-infinite space in elastic mechanics, and simplifies the geometric model of the rectangular curve jacking arc beam to calculate the additional stress at each position in the object caused by the head-on resistance. Based on the Winkler foundation model, the vertical settlement of each point of the object is calculated according to the foundation model, deformation coordination conditions, equilibrium equations, etc., and through the discretization of the object's geometric model, the external force acting on each point of the object is calculated to obtain the object's resultant force state, calculate the object's translational displacement and pure rotational displacement during the jacking process, and predict the dynamic displacement of the object's position during the rectangular curve jacking process.

[0004] The technical solution is:

[0005] A method for analyzing and predicting the impact of rectangular curve pipe jacking bottom curtain construction on existing objects, applied to pipe jacking machine construction operations, is characterized by comprising:

[0006] Part 1: During the jacking process, the tunneling system calculates the corresponding thrust data based on the hydraulic cylinder pressure of the jacking machine jack for each rectangular curved jacking beam through the sensing system; this data is used as input to the second part.

[0007] Part 2: By way of example and not limitation, the control system of the pipe jacking machine (or the backend computing system, referred to as the "analysis and prediction system") may calculate and output predicted object displacement and deformation data;

[0008] Part 3: The analysis and prediction system displays the displacement and deformation data of the object in real time based on the prediction results of the second part, and adjusts and controls the on-site excavation speed, cutterhead speed, and mud chamber pressure construction parameters. For target protection objects that are sensitive to displacement and deformation, if their displacement and deformation exceed the safety threshold indicators, manual intervention or adjustment of the excavation system operation will be carried out when necessary.

[0009] Among them, the second part:

[0010] The analysis and prediction system discretizes the continuous jacking process into the superposition of several jacking angle conditions, and uses 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 multiple curved beams (n beams) form a bottom curtain, after the calculation of the kth curved beam is completed, it is regarded as a state of balance of the resultant external force, and the force state of the k+1th curved beam is calculated from the equilibrium state; the displacement state of the kth curved beam after the jacking is completed is used as the initial condition to enter the calculation of the k+1th curved beam, and the superposition principle is used to analyze and predict the output of the displacement and deformation state of the target protection object in the construction of the rectangular curve jacking bottom curtain method, providing protection for the safety of the entire construction process.

[0011] This invention proposes a method for predicting the impact of rectangular curve pipe jacking on existing objects. This simplified model of existing objects can be applied to any object model that can be simplified to a uniform cross-sectional tensile body (such as a cylinder or prism) through multi-plane approximation or other methods. Therefore, the various components of this invention are fully modular and independent of the object's shape. With minor modifications, they can be applied to situations involving pipe jacking on small-radius curves, crossing or surrounding a variety of differently shaped objects or underground pipelines, demonstrating excellent scalability and portability. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 Process flow chart of the method of the present invention

[0013] Figure 2Calculation diagram (front view)

[0014] Figure 3 Schematic diagram of top view of calculation section

[0015] Figure 4 Schematic diagram of the rectangular curve pipe jacking bottom curtain method construction scene and the three-dimensional schematic diagram of the model of the present invention

[0016] Figure 5 Vertical displacement data of the first curved beam of the full-scale model of the hypothetical object in the application example

[0017] Figure 6 Vertical deformation of the full-scale model of the hypothetical object in the application example after all jacking is completed DETAILED DESCRIPTION

[0018] The method of the present invention comprises three parts

[0019] Part 1: During the jacking process, the tunneling system calculates the corresponding thrust data based on the hydraulic cylinder pressure of the jacking machine jack for each rectangular curved jacking beam through the sensing system; this data is used as input to the second part.

[0020] Part 2: Calculate and output predicted object displacement and deformation data;

[0021] Part 3: Based on the prediction results of Part 2, the system displays the displacement and deformation data of the object in real time, adjusts and controls construction parameters such as on-site excavation speed, cutterhead speed, and mud chamber pressure. For target protection objects that are sensitive to displacement and deformation, if their displacement and deformation exceed the safety threshold indicators, manual intervention or adjustment of the excavation system operation will be carried out when necessary.

[0022] Among them, the second plan is summarized as follows:

[0023] The system discretizes the continuous jacking process into a superposition of several jacking angle conditions, using the new position of the object after the previous jacking angle displacement as the starting position for the calculation of the next jacking angle. In the case of a bottom curtain composed of multiple curved beams (n beams), after the calculation of the kth curved beam is completed, it is regarded as a state of equilibrium of the resultant external force, and the force state of the k+1th curved beam is calculated starting from this equilibrium state. The displacement state of the kth curved beam after jacking is used as the initial condition for entering the calculation of the k+1th curved beam. The superposition principle is used to systematically predict and output the displacement and deformation state of the target protection object during the rectangular curve jacking bottom curtain construction method, providing safety guarantees for the entire construction process.

[0024] The whole prediction process of the second part, the algorithm flow is as follows Figure 1 shown.

[0025] Step 1: Calculate the vertical and horizontal thrusts of the kth curved beam based on the thrust data provided by the sensor system during the jacking process of the rectangular curved pipe jacking beam.

[0026] Specifically include:

[0027] Step 1.1: Obtain the jacking force data F of the jth jacking step of the kth curved beam j .

[0028] Step 1.2: Set the thrust force F j Decomposed into horizontal and vertical components, the horizontal and vertical components p of the jacking force of the j-th jacking step are obtained by formula (1): h,j 、p v,j ;

[0029] p v,j =F j sinθ j

[0030] p h,j =F j cosθ j (1)

[0031] Where Fj is the measured total jacking force, and θj is the current jacking angle of the jacking pipe.

[0032] Step 2: Based on the calculation principle of the Mindlin solution for semi-infinite spaces in elastic mechanics, by simplifying the geometric model of the curved jacking pipe arc beam, and on the basis of reasonable assumptions such as the closed continuity, homogeneity, and small deformation of the geometric model, the additional stress at each position in the object caused by the head-on resistance is calculated.

[0033] Specifically include:

[0034] Step 2.1: If Figure 2 、 Figure 3 As shown, the target protected object is simplified into a cylindrical geometric model of equal length and volume, with a surface area of ​​Γ. For other models, a multi-section approximation method can be used to transform them into other tensile bodies of equal cross-section, depending on their geometric shapes. The calculation method remains unchanged (the same geometric model is used in subsequent working conditions, but the position is changed). The thrust force is considered to be applied entirely as a uniformly distributed load in the form of head-on resistance on the end face of the curved beam. The head-on resistance is approximately equal to the thrust force and is applied to the end face as a uniformly distributed load.

[0035] Step 2.2 Based on Mindlin's solution, a spatial coordinate system is established with the center of the curved pipe as the origin, the long axis, the short axis, and the vertical direction of the object as the positive direction of the x, y, and z axes, respectively. The Q(x q ,y q ,z q)∈Г. According to formulas (2) and (3), the vertical and horizontal loads p in the jth top step are obtained respectively: v dξdη and p h dξdη causes any point Q(x q ,y q ,z q )∈Г additional stress σ zv , σ zh :

[0036]

[0037]

[0038] Among them, σ z =σ zv +σ zh .

[0039] Where dξdη is the infinitesimal element on the top surface Ω of the curved beam (the same below), ξ and η are local coordinates perpendicular to each other on the top surface, ν is the Poisson's ratio, is the buried depth of the top pipe end face in the jth top pipe jacking step, R 梁 is the radius of the arc beam. The arc beam top surface is the front surface.

[0040]

[0041] Step 3: Based on the Winkler foundation model, Figure 4 In the equation, the center of the arc-shaped beam k is taken as the coordinate origin O, and 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 cross section of the arc-shaped beam k, respectively. In this spatial coordinate system, the vertical deformation w of each point of the object is calculated based on the foundation model, deformation coordination conditions, equilibrium equations, etc.

[0042] Specifically include:

[0043] Step 3.1 Based on the Winkler foundation model, establish the deformation coordination conditions and equilibrium equations of the object and foundation, and determine the deformation control differential equation of the object;

[0044] When analyzing the additional stress perpendicular to the cylinder caused by pipe jacking, the cylinder can be regarded as an infinite-length beam on a Winkler elastic foundation under a distributed load. Thus, the governing equation for the effect of the additional stress on the object is obtained:

[0045]

[0046] EI is the bending stiffness of the object, P Z (x)=σ z D is the additional load on the object,

[0047] D is the diameter of the object (equivalent to a circle of the same area, the same below).

[0048] K is the foundation bed coefficient. According to the formula proposed by Vesic,

[0049]

[0050] Step 3.2: Solve the deformation control differential equation to obtain the vertical deformation data w of each point on the object.

[0051] The solution for an object subjected to a concentrated force P0 is:

[0052]

[0053] in,

[0054] The uniformly distributed load is regarded as the integral form of the concentrated load P(ξ)dξ, and is calculated according to formula (12) and integrated within the uniformly distributed load range to obtain the analytical formula for the vertical deformation of the object (ξ is the integral variable):

[0055]

[0056] The obtained vertical deformation w can be output in real time for dynamic monitoring of the deformation of the protected object during excavation. When the threshold range is exceeded, the system can promptly adjust the operating parameters and operating methods.

[0057] Step 3.3 For each working condition in the calculation of the same curved beam, determine the initial position of the object deformation calculation based on the previous working condition, that is, according to the calculation results of the previous stage, the current vertical coordinates of each point are The value is updated according to the vertical deformation amount.

[0058]

[0059] Among them, k is the current arc beam advancement sequence number, and j is the top step number.

[0060] Step 4: Based on the additional stress at each position of the object caused by the head-on resistance obtained in step 2, determine the net external force state and displacement of the object during the jacking process, and update the object position;

[0061] Step 4.1 Calculate the total external force of the object at the jth apex of the kth root canal segment: The external force in each calculation area is calculated according to the formula P k，j =σ zk， j A is calculated, where A is the area of ​​the region.

[0062] The net external force F acting on the object's center of gravity 合k，j =∑ Γ Pk，j , Γ is the total calculation area of ​​the object.

[0063] The resultant moment T acting on the object k，j =∑ Γ P k，j l, l is the distance from the center of gravity of each calculation area to the center of gravity of the object.

[0064] Step 4.2 Based on the external force state (resultant force and torque), Newton's second law F = ma and the kinematic formula, the displacement δ of the object in the jth apical step of the kth root canal segment is obtained according to formula (9): k，j and the rotation angle θ k，j ;

[0065]

[0066]

[0067] where a k，j is the acceleration, ω k，j is the angular acceleration, J is the moment of inertia, m is the mass, and t is the duration of each advancement.

[0068] The rigid body displacement and rotation angle data δ obtained in this step k，j and θ k，j It can output in real time and be used for real-time monitoring of the protected objects during the excavation process, and timely adjust the operating parameters and operating methods when they exceed the allowable range.

[0069] Step 4.3 updates the position coordinates of each calculation point of the object according to the displacement obtained in step 4.2. If this is not the last working condition, continue to calculate the next working condition (return to step 1) until all curved beams are advanced.

[0070] Example

[0071] When the technical solution of the present invention is specifically applied, the algorithm is embedded in the curved pipe jacking tunneling system.

[0072] The prediction method of the present invention is intended to be applied to a salvage project, wherein: the rectangular curve jacking pipe bottom curtain method has a total of 15 arc beams in the whole construction process, the buried depth of the object to be salvaged is 2.5m, the total length is 38.6m, and the diameter D is 2.7m; the radius of the arc beam R 梁 =8.5m, density ρ is 0.6×10 3 kg / m 3 , bending stiffness EI=2.6×10 10 N·m 2 ; The Poisson's ratio of soil is ν 0.4, the elastic modulus E s =19.5MPa.

[0073] Model diagram as shown Figure 4 As shown in the figure, the vertical displacement of the first curved beam after jacking and the vertical deformation of the 15 curved beams after jacking are obtained by using the prediction method of the present invention. Figure 5 、 Figure 6 As shown:

[0074] from Figure 5 As can be seen from the figure, during the jacking of a single curved beam, the overall displacement of the target salvage object gradually increases from its initial position, reaching a maximum of approximately 25 mm upon completion. The deformation growth rate is fastest when the jacking angle is between 90° and 150°. Therefore, it is important to closely monitor the displacement of the target salvage object during the later stages of the jacking process. If it exceeds the allowable value, the excavation operation method must be adjusted or manual intervention must be performed.

[0075] from Figure 6 As can be seen in the figure, after the 15 curved beams were installed, the vertical deformation of the object formed a double-peaked "M" shape with high symmetry. The maximum deformation occurred at approximately 1 / 4 of the length on the left and right sides, measuring approximately 2 mm. During the tunneling process, it is important to pay special attention to areas with large deformation, as these areas are prone to exceeding the allowable range. If the deformation exceeds the threshold, manual intervention or adjustment of the operation method is required.

Claims

1. A method for analyzing and predicting the impact of rectangular curve pipe jacking bottom curtain construction on existing objects, applied to pipe jacking machine construction operations, characterized in that: include: Part 1: During the jacking process, the tunneling system calculates the corresponding thrust data based on the hydraulic cylinder pressure of the jacking machine jack for each rectangular curved jacking beam through the sensing system; this data is used as input to the second part. Part 2: The analysis and prediction system calculates and outputs the predicted object displacement and deformation data; Part 3: Based on the prediction results from Part 2, the analysis and prediction system displays the displacement and deformation data of the object in real time, and adjusts and controls the on-site excavation speed, cutterhead speed, and slurry chamber pressure construction parameters. For target protection objects that are sensitive to displacement and deformation, if their displacement and deformation exceed the safety threshold, manual intervention or adjustment of the excavation system operation will be carried out when necessary; The second part of the forecast process includes: Step 1: Calculate the vertical and horizontal thrusts of the kth curved beam based on the thrust data provided by the sensor system during the jacking process of the rectangular curved pipe jacking beam; Step 2: Based on the calculation principle of the Mindlin solution for semi-infinite space in elastic mechanics, the geometric model of the curved jacking pipe arc beam is simplified to calculate the additional stress at each position in the object caused by the head-on resistance. Step 3: Based on the Winkler foundation model, with the center of the curved beam k as the coordinate 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 cross section of the curved beam k, respectively. In this spatial coordinate system, the vertical deformation w of each point on the object is calculated based on the foundation model, deformation coordination conditions, and equilibrium equations. Step 4: Based on the additional stress at each position of the object caused by the head-on resistance obtained in step 2, determine the net external force state and displacement of the object during the jacking process, and update the object position; Step 2 specifically includes: Step 2.1: Simplify the target protected object into a cylindrical geometric model of equal length and volume, with a surface area of ​​Γ. The thrust force is considered to be applied entirely on the end face of the curved beam in the form of a uniformly distributed load in the form of a head-on resistance. The head-on resistance is approximately equal to the thrust force and is applied on the end face as a uniformly distributed load. Step 2.2 Based on Mindlin's solution, a spatial coordinate system is established with the center of the curved pipe as the origin, the long axis, short axis, and vertical direction of the object as the positive direction of the x, y, and z axes, respectively, to calculate the head-on resistance at any point on the surface of the object. The additional stress of the j-th top step is obtained by using formula (2) and (3) respectively: and Cause any point on the object Additional stress at : （2） （3） in, ; Where, is the infinitesimal element on the top surface of the curved beam, and are local coordinates perpendicular to each other on the jacking surface, ν is the Poisson's ratio, , is the buried depth of the top pipe end face in the jth top step, R 梁 is the radius of the arc beam; the arc beam top surface, that is, the front surface; wherein, 。 2. The method according to claim 1, wherein in, Part 2: The analysis and prediction system discretizes the continuous jacking process into the superposition of several jacking angle conditions, and uses 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 multiple curved beams (n beams) form a bottom curtain, after the calculation of the kth curved beam is completed, it is regarded as a state of balance of the resultant external force, and the force state of the k+1th curved beam is calculated from the equilibrium state; the displacement state of the kth curved beam after jacking is completed is used as the initial condition to enter the calculation of the k+1th curved beam, and the superposition principle is used to analyze and predict the output of the displacement and deformation state of the target protection object in the construction of the rectangular curve jacking bottom curtain method, providing protection for the safety of the entire construction process.

3. The method according to claim 1, wherein Step 1 specifically includes: Step 1.1: Obtain the jacking force data of the jth jacking step of the kth curved beam F j ; Step 1.2: Apply the top thrust F j Decomposed into horizontal and vertical components, the horizontal and vertical components p of the j-th jacking step thrust are obtained by formula (1): h,j 、p v,j ; (1) In the formula Fj is the measured total thrust, θj The current jacking angle of the jacking pipe.

4. The method according to claim 1, wherein Step 3 specifically includes: Step 3.1 Based on the Winkler foundation model, establish the deformation coordination conditions and equilibrium equations of the object and foundation, and determine the deformation control differential equation of the object; When analyzing the additional stress perpendicular to the cylinder caused by pipe jacking, the cylinder is regarded as an infinite-length beam on a Winkler elastic foundation under a distributed load. The governing equation for the effect 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 of each point on the object; Objects subject to concentrated forces 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 is calculated according to formula (12) and integrated within the uniformly distributed load range to obtain the analytical formula for the vertical deformation of the object (ξ is the integral variable): （7） The vertical deformation w is output in real time and used to dynamically monitor the deformation of the protected object during excavation. When the threshold value is exceeded, the system can adjust the operation parameters and operation mode in time. Step 3.3 For each working condition in the calculation of the same curved beam, determine the initial position of the object deformation calculation based on the previous working condition, that is, according to the calculation results of the previous stage, the current vertical coordinates of each point are The value is updated according to the vertical deformation; （8） Among them, k is the current arc beam advancement sequence number, and j is the top step number.

5. The method according to claim 1, wherein Step 4 specifically includes Step 4.1 Calculate the total external force on the object at the jth top of the kth root canal segment: The external force in each calculation area is calculated according to the formula Calculate, where A is the area of ​​the region; The net external force acting on the object's center of gravity , ; The net torque acting on the object ; Step 4.2 Based on the external force state, Newton's second law F=ma and the kinematic formula, the displacement δ of the object in the jth apical step of the kth root canal segment is obtained according to formula (9): k,j and the rotation angle θ k,j ; （9） where a k,j is the acceleration, ω k,j is the angular acceleration, J is the moment of inertia, m is the mass, and t is the duration of each advancement; The rigid body displacement and rotation angle data δ obtained in this step k,j and θ k,j Real-time output is used to monitor the protected object in real time during the excavation process, and to adjust the operating parameters and operation methods in a timely manner when the allowable range is exceeded; Step 4.3: Update the position coordinates of each calculation point of the object according to the displacement obtained in step 4.

2. If this is not the last working condition, continue to calculate the next working condition and return to step 1 until all curved beams are advanced.

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