Composite lining joint surface calculation model

Abstract

The invention relates to the technical field of building construction calculation models, in particular to a composite lining joint surface calculation model which comprises an outer lining model and an inner lining model, the outer lining model adopts a beam-spring model for simulation, the inner lining model adopts a beam unit for simulation, and prestress is applied to the inner lining model. Prestress is applied to joints of the lining beam units in a concentrated force mode by adopting an equivalent loading method; according to the composite lining joint surface calculation model provided by the invention, the multi-directional combined springs are arranged between the composite lining joint surfaces, and the value basis or calculation method of the key parameters of each spring is given; by activating the corresponding springs, simulation of various different joint surface treatment modes such as direct bonding between the composite linings, laying of a waterproof layer and arrangement of joint bars can be achieved.

Description

Technical Field

[0001] The invention relates to the field of building construction calculation models, in particular to a composite lining joint surface calculation model. Background Art

[0002] Composite lining usually refers to a tunnel support method formed by combining primary support and secondary lining. This structural form is also called "composite lining". There are usually many different surface treatment methods between the two layers of lining, such as direct bonding, laying waterproof layer, and inserting reinforcement.

[0003] At present, two modeling methods, contact analysis or setting pressure relief spring, are usually used to numerically simulate the interface of composite lining. These two calculation models mainly consider the contact friction and extrusion slip problems of the composite lining interface, and it is difficult to simulate a variety of different interface treatment methods between composite linings at the same time.

[0004] Therefore, it is necessary to propose a composite lining joint surface calculation model to simultaneously simulate a variety of different joint surface treatment methods between composite linings. Summary of the invention

[0005] The purpose of the present invention is to provide a composite lining joint surface calculation model to solve the problems raised in the above background technology.

[0006] To achieve the above-mentioned purpose, the present invention provides the following technical solutions: a composite lining joint surface calculation model, the model includes an outer lining model and an inner lining model, the outer lining model is simulated by a beam-spring model, the inner lining model is simulated by a beam unit, and prestress is applied to the inner lining model, and the prestress is applied to the nodes of the inner lining beam unit in the form of concentrated force using the equivalent load method.

[0007] Preferably, the model further comprises a stratum spring, which is used to simulate the resistance of the soil layer to the outer lining.

[0008] Preferably, the composite lining interface is simulated by a combined spring model, which includes a normal spring K n 、Stiffener spring K s and tangential spring K τ , normal spring K n Used to simulate the interaction between the inner and outer lining concrete, the reinforcing bar spring K s Set at the position corresponding to the bolt hand hole to simulate the force transmission of the inserted reinforcement. The tangential spring K τ Used to simulate the force transmission of composite lining in the tangential direction.

[0009] Preferably, when simulating the cushion mode, the reinforcing bar spring K s and tangential spring K τ Failure, normal spring Kn It is only compressed but not pulled, and is composed of three springs K1, K2 and K3, which represent the concrete columns in the compression zone of the inner lining, cushion layer and outer lining respectively. The series relationship of the three normal springs is calculated by the following formula:

[0010]

[0011]

[0012]

[0013] D n =x1+x2+x3

[0014] Where: x1, x2 are the compression deformations of the inner lining concrete column, the outer lining concrete column and the cushion layer respectively; F n K is the spring n The force; E1, E2, E3 are the elastic moduli of the inner lining concrete, outer lining concrete and cushion layer respectively; t1, t2, t3 are the thickness of the inner lining, outer lining and cushion layer respectively; A n K is the spring n The effective area of ​​D n K is the spring n The deformation of the spring K is calculated by combining the above formula. n Force (F n )-Deformation(D n )relation:

[0015]

[0016] Preferably, when simulating the bonding mode, the reinforcing spring K s Failure, normal spring K n Can transmit compressive stress and certain tensile stress, tangential spring K τ Transfer shear stress.

[0017] Preferably, when the normal spring K n When in compression, the stiffness calculation method is consistent with the cushion mode; when the normal spring K n In the tensile state, if the force is less than or equal to the product of the normal bond strength and the effective area, the stiffness calculation method is still consistent with the cushion mode. If the force is greater than the product of the normal bond strength and the effective area, the normal spring K n Invalid.

[0018] Preferably, when the shear stress of the composite lining joint surface is less than the tangential bonding strength, the tangential spring K τ The stiffness is calculated based on the series relationship of the two tangential springs; when the shear stress on the composite lining interface is greater than the tangential bond strength, the tangential spring K τThe applied force is always the product of the tangential bond strength and the applied area.

[0019] Preferably, when simulating the inserted reinforcement mode, the normal spring K is also activated. n , Tangential spring K τ And the reinforcing spring K s , and the normal spring K n and tangential spring K τ The stiffness calculation method is the same as the bonding mode, the reinforcing bar spring K s The stiffness of the spring is obtained from the bond stress-slip curve between concrete and steel bars; s The force F s -Deformation D s The relationship is expressed as:

[0020] F s =τ(s)·A s

[0021] Where: τ(s) is the bond stress between concrete and steel bar when the slip is s; A s K is the spring s The area of ​​effect.

[0022] Preferably, it also includes working condition simulation and solution steps, which include assembly conditions, tensioning conditions and water filling conditions. By solving the model, some calculation results of different interlayer treatment methods under different working conditions are extracted.

[0023] Preferably, under water-filled conditions, the effects of different interlayer treatment methods on the lining stress increment are simulated by adjusting the cushion layer compression stiffness, bonding force and inserted reinforcement dosage parameters.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] The composite lining joint surface calculation model proposed in the present invention sets a multi-directional combined spring between the composite lining joint surfaces, and provides the basis for or calculation method of the key parameters of each spring. By activating the corresponding spring, the simulation of various joint surface treatment methods such as direct bonding between composite linings, laying of waterproof layer, and setting of inserted reinforcement can be realized. The calculation model proposed in the present invention is simple in modeling, clear in the values ​​of relevant parameters, has little dependence on the mesh division of the lining model, and has good calculation convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a schematic diagram of the cross-sectional structure of the composite lining of the present invention;

[0027] Figure 2 It is a schematic diagram of the combined spring model of the composite lining joint surface of the present invention;

[0028] Figure 3 It is a schematic diagram of the normal spring model of the cushion mode bonding surface of the present invention;

[0029] Figure 4 It is the bond-slip curve diagram of the concrete and the steel bar of the present invention;

[0030] Figure 5 It is a schematic diagram of the spring force-displacement relationship of the present invention;

[0031] Figure 6 It is a schematic diagram of the overall calculation model of the present invention;

[0032] Figure 7 It is a schematic diagram of the load condition combination of the present invention;

[0033] Figure 8 It is a schematic diagram of the influence of different cushion compression stiffness on the liner stress increment in the cushion mode of the present invention;

[0034] Fig. 9 Schematic diagram of the influence of different bonding forces on the lining stress increment under the bonding mode of the present invention;

[0035] Fig.10 This is a schematic diagram of the effect of different amounts of inserted reinforcement on the lining stress increment in the reinforcement insertion mode of the present invention. DETAILED DESCRIPTION

[0036] In order to make the purpose and technical solution of the present invention clearly and completely described, and the advantages more clearly understood, the embodiments of the present invention are further described in detail with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are part of the embodiments of the present invention, rather than all of the embodiments, and are only used to explain the embodiments of the present invention, and are not used to limit 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.

[0037] See also Figure 1-Figure 10 The present invention provides a technical solution: a composite lining joint surface calculation model, the model includes an outer lining model and an inner lining model, the outer lining model is simulated by a beam-spring model, the inner lining model is simulated by a beam unit, and prestress is applied to the inner lining model, and the prestress is applied to the nodes of the inner lining beam unit in the form of concentrated force using an equivalent load method.

[0038] The specific implementation is as follows:

[0039] like Figure 1The composite lining of a water diversion tunnel is a prestressed composite lining. The outer lining is a segment lining assembled with staggered joints. The segment concrete strength is C50, the lining thickness is 0.4m, and the lining center ring radius is 4.1m. The inner lining is a ring-anchor prestressed lining with anchor grooves at 135° and 225°. The lining concrete strength is C40, the lining thickness is 0.45m, and the lining center ring radius is 3.725m. The composite spring model of the composite lining joint surface proposed in the present invention can simulate different interlayer interface treatment methods of the inner and outer linings of the composite lining, such as: ① cushion layer mode, that is, laying a soft cushion layer to completely separate the inner lining from the outer lining; ② bonding mode, that is, the inner lining is directly cast on the inner surface of the outer lining, and there is a certain bonding force between the inner and outer linings; ③ rebar mode, that is, the entire ring of the inner lining is directly cast on the inner surface of the outer lining and the inner and outer linings are connected by rebars. The specific implementation method is as follows:

[0040] (1) Establish the inner lining and outer lining models. The beam-spring model is used to simulate the outer lining segment lining, the stratum spring is used to simulate the resistance of the soil layer to the outer lining, and the beam unit is used to simulate the prestressed lining of the inner lining. The prestress is applied to the nodes of the inner lining beam unit in the form of concentrated force using the equivalent load method.

[0041] (2) Establish a composite spring model for the composite lining interface. Figure 2 The force transmission of the composite lining joint surface in the normal direction can be achieved through two types of springs K n and K s For simulation, spring K n Simulating the interaction between the inner and outer lining concrete, the spring K s Set at the position corresponding to the bolt hand hole to simulate the force transmission of the inserted reinforcement. The force transmission in the tangential direction can be achieved through the spring K τ Perform a simulation.

[0042] Through different spring combinations, the simulation of various joint surface treatment methods such as cushion mode, bonding mode, and reinforcing bar mode between composite linings can be realized. The details are as follows:

[0043] ① For the cushion mode, the reinforcing bar spring K s and tangential spring K τ Failure, normal spring K n It is only subjected to compression but not tension, and can be regarded as a series of three springs K1, K2, and K3, which respectively represent the concrete columns of the inner lining, cushion layer, and outer lining compression zone. Therefore, its equivalent stiffness can be calculated according to Figure 3 The series relationship of the three normal springs is calculated using the following formula:

[0044]

[0045]

[0046]

[0047] D n =x1+x2+x3

[0048] Where: x1, x2 are the compression deformations of the inner lining concrete column, the outer lining concrete column and the cushion layer respectively; F n K is the spring n The force; E1, E2, E3 are the elastic moduli of the inner lining concrete, outer lining concrete and cushion layer respectively; t1, t2, t3 are the thickness of the inner lining, outer lining and cushion layer respectively; A n K is the spring n The effective area of ​​D n K is the spring n The deformation of the spring can be calculated by combining the above formula: n Force (F n )-Deformation(D n )relation:

[0049]

[0050] According to the above formula, when the cushion modulus is infinite or the thickness is zero in the cushion mode, it can be regarded as a special case of direct contact between composite lining layers.

[0051] ②For the bonding mode, the reinforcing spring K s Failure, normal spring K n Can transmit compressive stress and certain tensile stress, tangential spring K τ Assuming that the normal bond strength of the composite lining joint surface is σ0, when the spring K n When in compression, the stiffness calculation method is consistent with the cushion mode; when the spring K n In the stretched state, if F n ≤σ0A n , spring K n The stiffness calculation method is still consistent with the cushion model. If F n >σ0A n , spring K n Invalid.

[0052] Assuming that the tangential bond strength of the composite lining joint surface is τ0, when the shear stress of the joint surface is less than the tangential bond strength, it can be assumed that the bond between the inner and outer lining concrete is intact and no relative sliding occurs. The tangential spring K τ The stiffness can be determined based on Figure 3 The series relationship of two similar tangential springs is calculated using the following formula:

[0053]

[0054]

[0055] D τ =y1+y2

[0056] Where: y1 and y2 are the shear deformations of the inner lining concrete column and the outer lining concrete column respectively; G1 and G2 are the shear moduli of the inner lining concrete and the outer lining concrete respectively; t1 and t2 are the thickness of the inner lining and the outer lining respectively; A τ K is the spring τ The effective area of ​​D τ K is the spring τ The deformation of the spring can be calculated by combining the above formula: τ Force (F τ )-Deformation(D τ )The relationship is:

[0057]

[0058] When the shear stress of the composite lining interface is greater than the tangential bond strength, relative sliding occurs between the inner and outer lining concretes. It can be approximately considered that the shear stress between the inner and outer lining concretes is no longer related to the shear displacement at this stage. At this time, the spring K τ The force acting on is always:

[0059] F τ =τ0A τ

[0060] It should be noted that the existence of tangential force between composite linings is premised on the inner lining and the outer lining not being separated from each other, that is, the normal spring K between the inner and outer linings n In a compressed state, once the normal spring K n In tension state, the shear spring K at the corresponding position τ will become invalid.

[0061] ③ For the inserting mode, an inserting spring K is added on the basis of the bonding mode. s , and the normal spring K n and tangential spring K τ The stiffness calculation method is exactly the same as that of the bonded mode. s The stiffness can be calculated based on the bond stress-slip curve between concrete and steel bars in the Code for Design of Concrete Structures ( Figure 4 ) is obtained, where d is the diameter of the steel bar (mm), and f t，r is the characteristic value of concrete tensile strength (MPa). Spring K s Force (F s )-Deformation(D s ) relationship can be expressed as:

[0062] Fs =τ(s)·A s

[0063] Where: τ(s) is the bond stress between concrete and steel bar when the slip is s; A s K is the spring s The area of ​​effect.

[0064] (3) Activate the corresponding springs and define the spring properties. Activate only the normal spring K n Can simulate cushion mode, spring K n The force-displacement relationship is as follows Figure 5 As shown in (a), the overall calculation model is as follows Figure 6 (a) shows; while activating the normal spring K n and tangential spring K τ Can simulate bonding mode, spring K n The force-displacement relationship is as follows Figure 5 As shown in (b), spring K τ The force-displacement relationship is as follows Figure 5 (c) shows the overall calculation model. Figure 6 (b) shows that the normal spring K is activated at the same time. n , Tangential spring K τ And the reinforcing spring K s Can simulate the insertion mode, spring K n The force-displacement relationship is the same as Figure 5 As shown in (b), spring K τ The force-displacement relationship is the same as Figure 5 (c) As shown, spring K s The force-displacement relationship is as follows Figure 5 (d) shows the overall calculation model. Figure 6 (c) as shown.

[0065] (4) Simulation and solution of applied working conditions According to the construction process of the inner and outer linings of the prestressed composite lining in this embodiment and its load characteristics, it can be divided into the following three load working conditions.

[0066] ① Assembly conditions. That is, after the outer lining segments are assembled, the outer lining has borne part or all of the external water and soil loads, such as Figure 7 (a) shown.

[0067] ② Tensioning condition. That is, the inner lining is poured and the prestressed anchor cables are tensioned. At this time, the inner lining and the outer lining jointly bear the remaining external water and soil loads and the prestressed load of the inner lining. Figure 7 (b) as shown.

[0068] ③ Water filling condition. That is, the tunnel construction is completed and has been filled with water. At this time, the inner lining and the outer lining jointly bear the internal water pressure. Figure 7 (c) as shown.

[0069] The model is solved to extract some calculation results of different interlayer treatment methods under water-filled conditions:

[0070] Figure 8 The figure shows the influence of different cushion compression stiffness on the lining stress increment under cushion mode. The lining concrete produces a tensile stress increment of more than 4MPa under water-filled conditions, and the tensile stress increment increases with the increase of cushion stiffness. However, it can be seen that the influence of cushion compression stiffness is not obvious in general, and the stress increment of the lining changes by less than 5% under different cushion stiffness.

[0071] Fig. 9 The effect of different bonding forces on the stress increment of the lining under the bonding mode. When σ0=0.35MPa, the inner and outer liners jointly bear the water pressure, and the tensile stress increment of the lining is less than 3MPa. When σ0=0.25MPa and σ0=0MPa, since the inner and outer liners are basically completely separated from the outer lining, the internal water pressure is almost entirely borne by the inner lining, and the tensile stress increment generated is above 4MPa. When σ0=0.3MPa, since the inner lining is separated from the outer lining above the anchor groove, the tensile stress increment of this part is basically the same as that of σ0=0.25MPa and σ0=0MPa, while the part below the anchor groove is still bonded to the outer lining, and the tensile stress increment of this part is basically the same as that of σ0=0.35MPa. Fig.10 The influence of different amounts of inserted bars on the stress increment of the inner lining under the inserted bar mode. Assuming that the number of inserted bars in each bolt hand hole is n and the diameter of the inserted bar is d, the results are calculated for different combinations of n = 1, n = 2 and d = 8mm and d = 16mm. It can be seen that the stress increment of the inner lining is basically not affected by the change in the amount of inserted bars, while the tensile stress increment of the rest of the parts generally decreases with the increase in the amount of inserted bars, indicating that more internal water compression is transmitted to the outer lining along with the inserted bars.

[0072] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A composite lining joint surface calculation model, characterized in that: The model includes an outer lining model and an inner lining model. The outer lining model is simulated using a beam-spring model, and the inner lining model is simulated using a beam unit. Prestress is applied to the inner lining model, and the prestress is applied to the nodes of the inner lining beam unit in the form of concentrated force using the equivalent load method.

2. A composite lining joint surface calculation model according to claim 1, characterized in that: The model also includes ground springs, which are used to simulate the resistance of the soil layer to the outer lining.

3. The composite lining joint surface calculation model according to claim 1 is characterized in that: The composite lining interface is simulated by a combined spring model, which includes the normal spring K n 、Stiffener spring K s and tangential spring K τ , normal spring K n Used to simulate the interaction between the inner and outer lining concrete, the reinforcing bar spring K s Set at the position corresponding to the bolt hand hole to simulate the force transmission of the inserted reinforcement. The tangential spring K τ Used to simulate the force transmission of composite lining in the tangential direction.

4. A composite lining joint surface calculation model according to claim 3, characterized in that: When simulating the cushion mode, the reinforcing bar spring K s and tangential spring K τ Failure, normal spring K n It is only compressed but not pulled, and is composed of three springs K1, K2 and K3, which represent the concrete columns in the compression zone of the inner lining, cushion layer and outer lining respectively. The series relationship of the three normal springs is calculated by the following formula: D n =x1+x2+x3 Where: x1, x2 are the compression deformations of the inner lining concrete column, the outer lining concrete column and the cushion layer respectively; F n K is the spring n The force; E1, E2, E3 are the elastic moduli of the inner lining concrete, outer lining concrete and cushion layer respectively; t1, t2, t3 are the thickness of the inner lining, outer lining and cushion layer respectively; A n K is the spring n The effective area of ​​D n K is the spring n The deformation of the spring K is calculated by combining the above formula. n Force (F n )-Deformation(D n )relation:

5. The composite lining joint surface calculation model according to claim 3 is characterized in that: When simulating the bonding mode, the reinforcing spring K s Failure, normal spring K n Can transmit compressive stress and certain tensile stress, tangential spring K τ Transfer shear stress.

6. A composite lining joint surface calculation model according to claim 5, characterized in that: When the normal spring K n When in compression, the stiffness calculation method is consistent with the cushion mode; when the normal spring K n In the tensile state, if the force is less than or equal to the product of the normal bond strength and the effective area, the stiffness calculation method is still consistent with the cushion mode. If the force is greater than the product of the normal bond strength and the effective area, the normal spring K n Invalid.

7. The composite lining joint surface calculation model according to claim 1 is characterized in that: When the shear stress of the composite lining joint surface is less than the tangential bond strength, the tangential spring K τ The stiffness is calculated based on the series relationship of the two tangential springs; when the shear stress on the composite lining interface is greater than the tangential bond strength, the tangential spring K τ The applied force is always the product of the tangential bond strength and the applied area.

8. The composite lining joint surface calculation model according to claim 1 is characterized in that: When simulating the inserted reinforcement mode, the normal spring K is also activated. n , Tangential spring K τ And the reinforcing spring K s , and the normal spring K n and tangential spring K τ The stiffness calculation method is the same as the bonding mode, the reinforcing bar spring K s The stiffness of the spring is obtained from the bond stress-slip curve between concrete and steel bars; s The force F s -Deformation D s The relationship is expressed as: F s =τ(s)·A s Where: τ(s) is the bond stress between concrete and steel bar when the slip is s; A s K is the spring s The area of ​​effect.

9. A composite lining joint surface calculation model according to claim 8, characterized in that: It also includes working condition simulation and solution steps, which include assembly conditions, tensioning conditions and water filling conditions. By solving the model, some calculation results of different interlayer treatment methods under different working conditions are extracted.

10. A composite lining joint surface calculation model according to claim 9, characterized in that: Under water-filled conditions, the effects of different interlayer treatment methods on the lining stress increment were simulated by adjusting the cushion compression stiffness, bonding strength and reinforcement dosage parameters.

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