An optimization method for the closure thrust of a continuous rigid frame bridge with unequal height piers

Abstract

The invention discloses an optimization method for the closure thrust of a continuous rigid frame bridge with unequal-height piers on a curve, which belongs to the technical field of bridge construction and comprises the following steps: step 1, establishing a finite element model according to construction, and splitting the closure thrust into four component forces; step 2, using the finite element model, determining a number of influence coefficients under the condition of applying a transverse unit jacking force and a longitudinal unit jacking force; step 3, according to the finite element model, under the condition of not applying a jacking force, calculating the longitudinal horizontal displacement of the pier top under the action of other loads ten years after the bridge is completed, the lateral horizontal displacement of the pier top under the action of other loads ten years after the bridge is completed, and the stress of the pier bottom during the construction stage; step 4, under the action of the four component forces, calculating the longitudinal horizontal displacement and the lateral horizontal displacement of two piers; step 5, constructing an objective function; step 6, setting constraint conditions of the objective function; step 7, performing iterative solution to obtain the optimal jacking force under the condition of minimum objective function value.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge construction, and in particular relates to a method for optimizing the closure thrust of a curved unequal-height pier continuous rigid frame bridge. Background Art

[0002] Continuous rigid frame bridge is a common type of bridge with advantages such as strong spanning capacity, mature construction technology, reduced support setting, low maintenance cost and good economy. Due to shrinkage creep, loss of prestress and temperature effects, the top of the pier of the continuous rigid frame bridge will be displaced. Therefore, it is necessary to apply a top thrust during the closure stage to minimize the impact of these displacements on the piers.

[0003] Due to the special geological conditions in the western mountainous areas, the form of the continuous rigid frame bridge must change with the terrain, and the layout of the continuous rigid frame bridge sometimes needs to adopt the form of curved unequal height piers. Figure 1 , Figure 2 If no top thrust is applied to the joint, the continuous rigid frame bridge with curved unequal-height piers will not only produce longitudinal displacement toward the mid-span, but also transverse displacement along the radius. These displacements will gradually increase with the shrinkage and creep of concrete, causing the piers to be non-vertical, the pier tops to have large displacements, and the pier bottom stress to be excessive, resulting in cracks.

[0004] Public document CN107977498A constructs a characteristic energy function that introduces the combined action of the top thrust of each pier at each closure mouth under a certain closure sequence. The difference in the pier bottom stress of the pier bottom section in the completed state includes both the displacement factor and the stress factor of the pier bottom. It is better adapted to the situation of uneven pier heights of continuous rigid frame bridges and the characteristics of its curves, and improves the accuracy of the top thrust calculation. However, for curved continuous rigid frame bridges with unequal height piers, the different stiffnesses lead to different horizontal displacements on both sides of the pier tops and different corresponding effects on the top thrust. Applying asymmetric top thrusts for closure can effectively solve the problem of different pier stiffness caused by unequal height piers, and can also effectively reduce the lateral horizontal displacement of the pier tops caused by the curvature, so that the stress and deformation after the bridge is completed are more reasonable.

[0005] The current scheme lacks calculation of the asymmetric closure thrust of a continuous rigid frame bridge with curved unequal height piers. Generally, finite element calculation is used to simulate the size of the symmetrical closure thrust, which cannot accurately reduce the problem of asymmetric displacement caused by the unequal height piers. Summary of the invention

[0006] The purpose of the present invention is to provide a method for optimizing the closure thrust of a continuous rigid frame bridge with curved unequal height piers, so as to solve the problem of low precision of the closure thrust simulated by finite element calculation in the prior art.

[0007] To achieve the above object, the present invention provides a method for optimizing the closure thrust of a curved unequal height pier continuous rigid frame bridge, comprising the following steps:

[0008] Step 1: Establish a finite element model based on the construction and split the closure thrust into four components F z1 、F z2 、F h1 、F h2 ;

[0009] Step 2: Using the finite element model, determine the influence coefficient c of the lateral horizontal displacement of the pier top under the conditions of applying the lateral unit thrust and the longitudinal unit thrust. ij , influence coefficient of longitudinal horizontal displacement of pier top a ij , Bridge pier bottom stress influence coefficient b ijk , mid-span main beam deflection influence coefficient d ijk , mid-span main beam lateral displacement influence coefficient e ijk ;

[0010] Step 3: According to the finite element model, calculate ∑a without applying thrust i ,Σc i and Σb jk , where Σa i , i = 1, 2, the longitudinal horizontal displacement of the top of the i-th pier under other loads ten years after the completion of the bridge without applying top thrust; ∑c i , i = 1, 2, represents the lateral displacement of the top of the i-th pier under other loads ten years after the completion of the bridge without applying top thrust; ∑b jk , j = 1, 2, k = 1 to 4 represents the stress at the kth position of the bottom of the jth pier during the construction stage;

[0011] Step 4: In the four components F z1 、F z2 、F h1 、F h2 Under the action of , calculate the longitudinal horizontal displacement and transverse horizontal displacement of the two piers;

[0012] Step 5: Construct the objective function M;

[0013] Step 6, set the constraint conditions of the objective function, with the stress of the pier during the construction period not exceeding the allowable stress as the first constraint condition; the resultant force of the jacking force along the tangent direction of the curved joint mouth as the second constraint condition; the vertical deflection and transverse horizontal displacement deviation of the mid-span main beam joint not exceeding the allowable deviation as the third constraint condition;

[0014] Step 7: Perform an iterative solution through the quadprog function in the MATLAB optimization toolbox to obtain the optimal thrust force under the condition of minimum objective function value.

[0015] Preferably, the expressions for calculating the longitudinal horizontal displacement and the transverse horizontal displacement of the two piers in step 4 are as follows:

[0016]

[0017] In the formula, Δz i represents the longitudinal horizontal displacement of the i-th bridge pier; Δh i represents the horizontal displacement of the i-th bridge pier, i = 1, 2; F z1 、F z2 、F h1 、F h2 They represent the left longitudinal component, the right longitudinal component, the left lateral component, and the right lateral component respectively; a z1 represents the influence coefficient of the longitudinal horizontal displacement of Pier 1 under the unit thrust in the longitudinal direction of the bridge; a z2 represents the influence coefficient of the longitudinal horizontal displacement of Pier 2 under the unit thrust in the longitudinal direction of the bridge; c z1 represents the influence coefficient of the lateral horizontal displacement of Pier 1 under the unit thrust in the longitudinal direction of the bridge; c z2 represents the influence coefficient of the lateral horizontal displacement of Pier 2 under the unit thrust in the longitudinal direction of the bridge; a h1 represents the influence coefficient of the longitudinal horizontal displacement of Pier 1 under the unit thrust in the transverse direction of the bridge; a h2 represents the influence coefficient of the longitudinal horizontal displacement of Pier 2 under the unit thrust in the transverse direction of the bridge; c h1 represents the influence coefficient of the lateral displacement of Pier 1 under the unit thrust in the transverse direction of the bridge; c h2 It represents the influence coefficient of the lateral horizontal displacement of Pier 2 under the unit thrust in the transverse direction of the bridge.

[0018] Preferably, the objective function M constructed in step 5 is specifically as follows:

[0019]

[0020] Preferably, the expression of the first constraint is as follows:

[0021]

[0022] In the formula, [σ c ] is the allowable compressive stress, [σ t ] is the allowable tensile stress; in the finite element model analysis, compressive stress is negative and tensile stress is positive; b ijk It represents the stress influence coefficient at the kth position of the bottom of the jth pier under the action of i-unit jacking force, i indicates that the jacking force is in the longitudinal direction z or the transverse direction h, j=1, 2, k=1~4.

[0023] Preferably, the expression of the second constraint is as follows:

[0024]

[0025] Where θ represents the angle between the tangent direction of the joint and the horizontal direction.

[0026] Preferably, the expression of the third constraint is as follows:

[0027]

[0028] Where, d z左 It represents the influence coefficient of the vertical deflection of the left side of the main beam under the unit thrust in the longitudinal direction of the bridge; d h左 It represents the influence coefficient of the vertical deflection of the left side of the main beam under the unit thrust in the transverse direction of the bridge; d z右 It represents the influence coefficient of the vertical deflection of the right side of the main beam under the unit thrust in the longitudinal direction of the bridge; d h右 It represents the influence coefficient of the vertical deflection of the right side of the main beam under the unit thrust in the transverse direction of the bridge; e z左 It represents the horizontal influence coefficient of the left side of the main beam under the unit thrust of the longitudinal bridge; e h左 It represents the horizontal influence coefficient of the left side of the main beam under the unit thrust force in the transverse direction of the bridge; e z右 It represents the horizontal influence coefficient of the right side of the main beam under the unit top thrust of the longitudinal bridge; e h右 It represents the horizontal influence coefficient of the right side of the main beam under the unit thrust in the transverse direction of the bridge; ∑d 左 Indicates the vertical deflection of the left side of the main beam under other loads without applying top thrust; ∑d 右 It represents the vertical deflection of the right side of the main beam under other loads without applying top thrust; ∑e 左 It represents the horizontal displacement of the left side of the main beam under other loads without applying top thrust; ∑e 右 It represents the horizontal displacement of the right side of the main beam under other loads without applying top thrust; [Δ 1 ] represents the allowable error of cantilever joint deflection during the joint construction stage; [Δ 2 ] indicates the allowable error of the lateral horizontal displacement of the cantilever closure during the closure construction phase.

[0029] Therefore, the present invention adopts the above-mentioned optimization method for the closure thrust of a continuous rigid frame bridge with curved unequal height piers. By constructing an objective function and setting corresponding constraints, the objective function is minimized under the three constraints, and the accurate closure thrust is iteratively obtained, thereby improving the internal force and displacement state of the continuous rigid frame bridge with curved unequal height piers.

[0030] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is the longitudinal horizontal displacement direction diagram of the continuous rigid frame bridge with unequal height piers without applying the closure top thrust in the background technology;

[0032] Figure 2 It is the lateral horizontal displacement direction diagram of the continuous rigid frame bridge with unequal height piers without applying the closure top thrust curve in the background technology;

[0033] Figure 3 It is an overall flow chart of a method for optimizing the closure thrust of a continuous rigid frame bridge with curved unequal height piers according to the present invention;

[0034] Figure 4 A flow chart for determining the objective function of an embodiment of the present invention;

[0035] Figure 5 A stress constraint condition flow chart of an embodiment of the present invention;

[0036] Figure 6 It is a schematic diagram of the process of splitting the asymmetric joint jacking force into four component forces according to an embodiment of the present invention;

[0037] Figure 7 It is a schematic diagram of the positions of four stresses in the cross section of the bottom of a pier according to an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] See also Figure 3-7 , a method for optimizing the closure thrust of a continuous rigid frame bridge with curved unequal height piers, comprising the following steps:

[0040] Step 1: Establish a finite element model based on the construction and split the closure thrust into four components F z1 、F z2 、F h1 、F h2 ;

[0041] Step 2: Using the finite element model, determine the influence coefficient c of the lateral horizontal displacement of the pier top under the conditions of applying the lateral unit thrust and the longitudinal unit thrust. ij , influence coefficient of longitudinal horizontal displacement of pier top a ij , Bridge pier bottom stress influence coefficient b ijk , mid-span main beam deflection influence coefficient d ijk, mid-span main beam lateral displacement influence coefficient e ijk ;

[0042] Step 3: According to the finite element model, calculate ∑a without applying thrust i ,∑c i and ∑b jk , where ∑a i , i = 1, 2, the longitudinal horizontal displacement of the top of the i-th pier under other loads ten years after the completion of the bridge without applying top thrust; ∑c i , i = 1, 2, represents the lateral displacement of the top of the i-th pier under other loads ten years after the completion of the bridge without applying top thrust; ∑b jk , j = 1, 2, k = 1 to 4 represents the stress at the kth position of the bottom of the jth pier during the construction stage;

[0043] Step 4: In the four components F z1 、F z2 、F h1 、F h2 Under the action of , the longitudinal horizontal displacement and transverse horizontal displacement of the two piers are calculated, and the expressions are as follows:

[0044]

[0045] In the formula, Δz i represents the longitudinal horizontal displacement of the i-th bridge pier; Δh i represents the horizontal displacement of the i-th bridge pier, i = 1, 2; F z1 、F z2 、F h1 、F h2 They represent the left longitudinal component, the right longitudinal component, the left lateral component, and the right lateral component respectively; a z1 represents the influence coefficient of the longitudinal horizontal displacement of Pier 1 under the unit thrust in the longitudinal direction of the bridge; a z2 represents the influence coefficient of the longitudinal horizontal displacement of Pier 2 under the unit thrust in the longitudinal direction of the bridge; c z1 represents the influence coefficient of the lateral horizontal displacement of Pier 1 under the unit thrust in the longitudinal direction of the bridge; c z2 represents the influence coefficient of the lateral horizontal displacement of Pier 2 under the unit thrust in the longitudinal direction of the bridge; a h1 represents the influence coefficient of the longitudinal horizontal displacement of Pier 1 under the unit thrust in the transverse direction of the bridge; a h2 represents the influence coefficient of the longitudinal horizontal displacement of Pier 2 under the unit thrust in the transverse direction of the bridge; c h1 represents the influence coefficient of the lateral displacement of Pier 1 under the unit thrust in the transverse direction of the bridge; c h2 It represents the influence coefficient of the lateral horizontal displacement of Pier 2 under the unit thrust in the transverse direction of the bridge.

[0046] Step 5: Construct the objective function M, taking the sum of the squares of the longitudinal horizontal displacement and the transverse horizontal displacement of the pier top as the objective function, stipulating that the longitudinal horizontal displacement pointing to the mid-span direction is positive, and the transverse horizontal displacement pointing to the center of the circle is positive. i and Δh i The positive and negative values ​​cannot be directly added together to find the minimum value of the sum, so the objective function is as follows:

[0047]

[0048] Step 6, set the constraints of the objective function, with the stress of the pier during the construction phase not exceeding the allowable stress as the first constraint; the resultant force of the top thrust is along the tangent direction of the curve joint mouth as the second constraint; the vertical deflection and lateral horizontal displacement deviation of the mid-span main beam joint not exceeding the allowable deviation as the third constraint; among them, in order to ensure the safety of the construction phase, the stress at each position of the pier bottom section during the construction phase should not exceed the limit. The expression of the first constraint is as follows:

[0049]

[0050] In the formula, [σ c ] is the allowable compressive stress, [σ t ] is the allowable tensile stress; in the finite element model analysis, compressive stress is negative and tensile stress is positive; b ijk It represents the stress influence coefficient at the kth position of the bottom of the jth pier under the action of i-unit jacking force, i indicates that the jacking force is in the longitudinal direction z or the transverse direction h, j=1, 2, k=1~4.

[0051] For curved unequal-height pier continuous rigid frame bridges, the direction of the resultant force of the joint thrust must be consistent with the axis of the main beam, otherwise it will generate redundant additional force. Therefore, the expression of the second constraint condition is as follows:

[0052]

[0053] Where θ represents the angle between the tangent direction of the joint and the horizontal direction.

[0054] Since an asymmetric thrust force is applied, the vertical deflection and lateral displacement of the main beams on both sides of the mid-span should be controlled within the specified range when the joint is closed to ensure the accuracy of the joint. Therefore, the expression of the third constraint condition is as follows:

[0055]

[0056] Where, d z左 It represents the influence coefficient of the vertical deflection of the left side of the main beam under the unit thrust in the longitudinal direction of the bridge; d h左It represents the influence coefficient of the vertical deflection of the left side of the main beam under the unit thrust in the transverse direction of the bridge; d z右 It represents the influence coefficient of the vertical deflection of the right side of the main beam under the unit thrust in the longitudinal direction of the bridge; d h右 It represents the influence coefficient of the vertical deflection of the right side of the main beam under the unit thrust in the transverse direction of the bridge; e z左 It represents the horizontal influence coefficient of the left side of the main beam under the unit thrust of the longitudinal bridge; e h左 It represents the horizontal influence coefficient of the left side of the main beam under the unit thrust force in the transverse direction of the bridge; e z右 It represents the horizontal influence coefficient of the right side of the main beam under the unit top thrust of the longitudinal bridge; e h右 It represents the horizontal influence coefficient of the right side of the main beam under the unit thrust in the transverse direction of the bridge; ∑d 左 Indicates the vertical deflection of the left side of the main beam under other loads without applying top thrust; ∑d 右 It represents the vertical deflection of the right side of the main beam under other loads without applying top thrust; ∑e 左 It represents the horizontal displacement of the left side of the main beam under other loads without applying top thrust; ∑e 右 It represents the horizontal displacement of the right side of the main beam under other loads without applying top thrust; [Δ 1 ] represents the allowable error of cantilever joint deflection during the joint construction stage; [Δ 2 ] indicates the allowable error of the lateral horizontal displacement of the cantilever closure during the closure construction phase.

[0057] Step 7: Perform an iterative solution through the quadprog function in the MATLAB optimization toolbox to obtain the optimal thrust force under the condition of minimum objective function value.

[0058] Example

[0059] Taking a curved unequal height pier in a mountainous area as an example, the top thrust of the bridge is calculated. The upper structure adopts 101+140+55m prestressed concrete continuous rigid frame with a curvature of 1150m. The lower structure 1# pier adopts a uniform cross-section double-limb thin wall with a pier height of 50m; 2# adopts a variable cross-section rectangular hollow pier with a pier height of 127m.

[0060] Because there is only one joint mouth, the joint thrust of the joint mouth is divided into four components F z1 、F z2 、F h1 、F h2 ; Without applying the closure thrust, the ∑a under other loads ten years after the completion of the bridge is obtained 1 =16.55mm,∑a 2 =-20.32mm,∑c 1 =3.89mm,∑c 2=7.62mm, apply unit thrust, take unit thrust as 200kN, and get a z1 =-4.76mm, a h1 =-0.35mm, a z2 =4.55mm, a h2 =0.28mm, c z1 =0.18mm, c h1 =0.56mm, c z2 =0.19mm, c h2 =0.68mm,

[0061]

[0062] So the objective function can be obtained

[0063] Without applying the jacking force, the ∑b under other loads during the construction stage is obtained. 11 =-2.56MPa,∑b 12 =-2.05MPa,∑b 13 =-3.02MPa,∑b 14 =-3.52MPa,∑b 21 =-7.05MPa,∑b 22 =-7.78MPa,∑b 23 =-6.87MPa,∑b 24 =-7.62MPa. Applying unit thrust to obtain the stress influence coefficient, the first constraint equation is:

[0064]

[0065] The second constraint equation is

[0066]

[0067] Without applying the jacking force, the ∑d under other loads in the closure stage is obtained. 左 =3.24mm,

[0068] ∑d 右 =-5.41mm,∑e 左 =0.654mm,∑e 右 =4.03mm, apply unit thrust to get the corresponding influence coefficient, and the third constraint condition can be obtained as follows:

[0069]

[0070] The quadprog function in the MATLAB optimization toolbox is used to iteratively solve the problem.

[0071] [3.4857, 0.1827, 4.5029, 0.2360]

[0072] F h1 =3.4857×200=697.14kN F z1 =0.1827×200=36.54kN

[0073] F h2 =4.5029×200=900.58kN F h2 =0.2360×200=47.2kN

[0074] After applying the optimized top thrust, the longitudinal horizontal displacement of pier 1# was reduced from 16.55mm to 0.101mm, the longitudinal horizontal displacement of pier 2# was reduced from -20.32mm to 0.234mm, the transverse horizontal displacement of pier 1# was reduced from 3.89mm to 3.36mm, and the transverse horizontal displacement of pier 2# was reduced from 7.62mm to 6.92mm. Under the asymmetric top thrust of the joint, the displacement of the tops of the two unequal-height piers was significantly reduced ten years after the completion of the bridge, and the stress at the bottom of the piers was more uniform and reasonable. At the same time, the stress at the bottom of the piers during the construction process was also guaranteed, ensuring that the stress at the bottom of the piers would not be too large during the joint.

[0075] Therefore, the present invention adopts the above-mentioned optimization method for the closure thrust of a continuous rigid frame bridge with piers of unequal heights on a curve. By constructing an objective function and setting corresponding constraints, the objective function is minimized under the three constraints, and the accurate closure thrust is iteratively obtained. Under the action of the asymmetric closure thrust, the internal force and displacement state of the piers of the continuous rigid frame bridge with piers of unequal heights on the curve are improved.

[0076] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for optimizing the closure thrust of a continuous rigid frame bridge with curved unequal height piers, characterized in that: The following steps are involved: Step 1: Establish a finite element model based on the construction and split the closure thrust into four components F z1 、F z2 、F h1 、F h2 ; Step 2: Using the finite element model, determine the influence coefficient c of the lateral horizontal displacement of the pier top under the conditions of applying the lateral unit thrust and the longitudinal unit thrust. ij , influence coefficient of longitudinal horizontal displacement of pier top a ij , Bridge pier bottom stress influence coefficient b ijk , mid-span main beam deflection influence coefficient d ijk , mid-span main beam lateral displacement influence coefficient e ijk ; Step 3: According to the finite element model, calculate ∑a without applying thrust i ,∑c i and ∑b jk , where ∑a i , i = 1, 2, the longitudinal horizontal displacement of the top of the i-th pier under other loads ten years after the completion of the bridge without applying top thrust; ∑c i , i = 1, 2, represents the lateral displacement of the top of the i-th pier under other loads ten years after the completion of the bridge without applying top thrust; ∑b jk , j = 1, 2, k = 1 to 4 represents the stress at the kth position of the bottom of the jth pier during the construction stage; Step 4: In the four components F z1 、F z2 、F h1 、F h2 Under the action of , calculate the longitudinal horizontal displacement and transverse horizontal displacement of the two piers; Step 5: Construct the objective function M; Step 6: Set the constraint conditions of the objective function, with the stress of the piers during the construction phase not exceeding the allowable stress as the first constraint condition; the resultant force of the jacking force along the tangent direction of the curved joint mouth as the second constraint condition; the vertical deflection of the mid-span main beam joint and the horizontal displacement deviation not exceeding the allowable deviation as the third constraint condition; Step 7: Perform an iterative solution through the quadprog function in the MATLAB optimization toolbox to obtain the optimal thrust force under the condition of minimum objective function value.

2. The optimization method for the closure thrust of a continuous rigid frame bridge with curved unequal height piers according to claim 1 is characterized in that: The expressions for calculating the longitudinal horizontal displacement and transverse horizontal displacement of the two piers in step 4 are as follows: In the formula, Δz i represents the longitudinal horizontal displacement of the i-th bridge pier; Δh i represents the horizontal displacement of the i-th bridge pier, i = 1, 2; F z1 、F z2 、F h1 、F h2 They represent the left longitudinal component, the right longitudinal component, the left lateral component, and the right lateral component respectively; a z1 represents the influence coefficient of the longitudinal horizontal displacement of Pier 1 under the unit thrust in the longitudinal direction of the bridge; a z2 represents the influence coefficient of the longitudinal horizontal displacement of Pier 2 under the unit thrust in the longitudinal direction of the bridge; c z1 represents the influence coefficient of the lateral horizontal displacement of Pier 1 under the unit thrust in the longitudinal direction of the bridge; c z2 represents the influence coefficient of the lateral horizontal displacement of Pier 2 under the unit thrust in the longitudinal direction of the bridge; a h1 represents the influence coefficient of the longitudinal horizontal displacement of Pier 1 under the unit thrust in the transverse direction of the bridge; a h2 represents the influence coefficient of the longitudinal horizontal displacement of Pier 2 under the unit thrust in the transverse direction of the bridge; c h1 represents the influence coefficient of the lateral displacement of Pier 1 under the unit thrust in the transverse direction of the bridge; c h2 It represents the influence coefficient of the lateral horizontal displacement of Pier 2 under the unit thrust in the transverse direction of the bridge.

3. The method for optimizing the closure thrust of a curved unequal height pier continuous rigid frame bridge according to claim 2 is characterized in that: The objective function M constructed in step 5 is as follows:

4. The method for optimizing the closure thrust of a curved unequal height pier continuous rigid frame bridge according to claim 3 is characterized in that: The expression of the first constraint is as follows: In the formula, [σ c ] is the allowable compressive stress, [σ t ] is the allowable tensile stress; in the finite element model analysis, compressive stress is negative and tensile stress is positive; b ijk It represents the stress influence coefficient at the kth position of the bottom of the jth pier under the action of i-unit jacking force, i indicates that the jacking force is in the longitudinal direction z or the transverse direction h, j=1, 2, k=1~4.

5. The method for optimizing the closure thrust of a curved unequal height pier continuous rigid frame bridge according to claim 4 is characterized in that: The expression of the second constraint is as follows: Where θ represents the angle between the tangent direction of the joint and the horizontal direction.

6. The method for optimizing the closure thrust of a curved unequal height pier continuous rigid frame bridge according to claim 5 is characterized in that: The expression of the third constraint is as follows: Where, d z左 It represents the influence coefficient of the vertical deflection of the left side of the main beam under the unit thrust in the longitudinal direction of the bridge; d h左 It represents the influence coefficient of the vertical deflection of the left side of the main beam under the unit thrust in the transverse direction of the bridge; d z右 It represents the influence coefficient of the vertical deflection of the right side of the main beam under the unit thrust in the longitudinal direction of the bridge; d h右 It represents the influence coefficient of the vertical deflection of the right side of the main beam under the unit thrust in the transverse direction of the bridge; e z左 It represents the horizontal influence coefficient of the left side of the main beam under the unit thrust of the longitudinal bridge; e h左 It represents the horizontal influence coefficient of the left side of the main beam under the unit thrust force in the transverse direction of the bridge; e z右 It represents the horizontal influence coefficient of the right side of the main beam under the unit top thrust of the longitudinal bridge; e h右 It represents the horizontal influence coefficient of the right side of the main beam under the unit thrust in the transverse direction of the bridge; ∑d 左 Indicates the vertical deflection of the left side of the main beam under other loads without applying top thrust; ∑d 右 It represents the vertical deflection of the right side of the main beam under other loads without applying top thrust; ∑e 左 It represents the horizontal displacement of the left side of the main beam under other loads without applying top thrust; ∑e 右 It indicates the lateral horizontal displacement of the right side of the main beam under other loads without applying jacking force; [Δ1] indicates the allowable error of the cantilever closure deflection during the closure construction stage; [Δ2] indicates the allowable error of the lateral horizontal displacement of the cantilever closure during the closure construction stage.

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