A vertical force applying device and method for base and underground structure shaking table test

Abstract

The application discloses a vertical force applying device and method for a shaking table test of a foundation and an underground structure, which comprises prestressed steel strands, prestressed anchorage devices, and a foundation or an underground structure or a pre-buried component thereof; the lower end of the prestressed steel strands is fixed on the bottom surface of a soil box; the upper end of the prestressed steel strands is fixed on the test foundation or the underground structure or the pre-buried component thereof through the prestressed anchorage devices; all the prestressed steel strands are the same and are arranged in a vertical direction; the applied prestress is equal to the yield tension of the steel strands; the projection center of all the prestressed steel strands on a horizontal plane is coincident with the projection of the gravity center of the model; the applied vertical force is ensured to be equal to the gravity of the counterweight that should be applied through the type and the number of the prestressed steel strands, that is, the yield tension of the steel strands is ensured to be equal to the product of the number of the steel strands and the gravity of the counterweight that should be applied. The application solves the problem of difficulty in applying the counterweight of the foundation and the underground structure and provides a reference for a counterweight application scheme of the shaking table test.

Description

Technical Field

[0001] This invention relates to the field of shaking table testing technology, and in particular to a vertical force application device and method for shaking table testing of foundations and underground structures. Background Technology

[0002] Shaking table testing is an important tool for seismic resistance research of engineering structures. Due to limitations in testing conditions and economic considerations, shaking table tests generally employ geometrically scaled models designed based on similarity theory. To meet mass similarity requirements, counterweights are usually added to the model. In practice, the mass of the counterweights is often quite large, even comparable to the model's mass. In such cases, adding counterweights presents difficulties due to insufficient space in the test model and excessive changes in the original structural damping and stiffness. Especially for underground structures, counterweights are not only difficult to attach to scaled models but also significantly occupy soil space, amplifying the adverse effects of the model's soil box boundary effects. Summary of the Invention

[0003] To overcome the shortcomings of the prior art, the present invention aims to provide a vertical force application device and method for shaking table tests of foundations and underground structures. The main function of the counterweight in the vertical direction is to provide a constant vertical force, i.e., the weight of the counterweight, to the test model. This solves the problem of difficult counterweight application for foundations and underground structures and provides a reference for counterweight application schemes in shaking table tests.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A vertical force application device for shaking table tests of foundations and underground structures includes prestressed steel strands, prestressed anchors, and the foundation or underground structure or its embedded components. The lower end of the prestressed steel strands is fixed to the bottom surface of the soil box, and the upper end is fixed to the test foundation or underground structure or its embedded components through the prestressed anchors. All prestressed steel strands are identical and arranged vertically. The applied prestress is equal to the yield strength of the steel strands. The centroid of the projection of all prestressed steel strands on the horizontal plane coincides with the projection of the model's center of gravity to ensure that the resultant force of the tension provided by the prestressed steel strands is always collinear with the gravity of the model. The type and number of prestressed steel strands ensure that the applied vertical force is equivalent to the weight of the counterweight that should be applied, that is, to ensure that the product of the yield strength of the steel strands and the number of steel strands is equal to the weight of the counterweight that should be applied.

[0006] A method for using a vertical force application device for shaking table tests of foundations and underground structures includes the following steps:

[0007] Step 1: Ensure that the force exerted on the structure by the prestressed steel strands is equivalent to the gravity of the theoretical counterweight;

[0008] Step 2: Determine the typical force-displacement curve of the steel strand under tension, assuming the length of the steel strand is l, F y d represents the yield strength of the steel strand, d0 represents the yield displacement of the steel strand, and d u This represents the ultimate displacement of the steel strand. After yielding, the increase in tensile force is very small as the displacement increases. The pre-tension strain of the steel strand is controlled within (d0+d). u ) / (2l) is used to ensure that the tension of the steel strand remains basically constant during the shaking table test;

[0009] Step 3: During installation, make sure to place rubber pads at the contact points between the prestressed anchor and the steel plate to prevent the prestressed anchor from loosening.

[0010] Step 1 includes the following two points:

[0011] (1) The prestressed steel strands are kept vertical, and the resultant vertical force exerted on the structure by all the prestressed steel strands is equal to the weight of the theoretical counterweight of the test model.

[0012] mg=n·f (1)

[0013] Where m represents the theoretical counterweight mass of the test model, n represents the number of steel strands, and f represents the preload of each steel strand. Each steel strand has the same cross-sectional area and equal preload.

[0014] (2) The resultant force of all prestressed steel strand tensions is collinear with the gravity of the model structure;

[0015] The first step is to determine the position of the model's center of gravity projected onto the horizontal plane. The second step is to ensure that the projection of the centroid of the figure formed by the lines connecting the pre-embedded components (i.e., the position of the prestressed steel strands) on the horizontal plane coincides with the projection of the model's center of gravity. Since the pretension of each steel strand is the same, this condition can be satisfied as long as the centroid of the projection of the action point of all steel strands on the horizontal plane coincides with the projection of the model's center of gravity on the horizontal plane. A symmetrically distributed arrangement of steel strands can satisfy the centroid coincidence condition.

[0016] In step 2, the average value of the yield displacement and ultimate displacement of the steel strand is (d0+d u ) / 2, the corresponding pre-tension strain of the steel strand is (d0+d u ) / (2l), the pre-tension strain of the steel strand is taken as this value, and the additional displacement range of the steel strand during the test is within [-(d u -d0) / 2,(d u When the strain varies within the range of [d0) / 2], the tensile force of the steel strand is approximately equal to its yield strength. This range represents the maximum displacement range that ensures the yield strength of the steel strand. Therefore, the strain of the steel strand is taken as (d0 + d2). u ) / (2l).

[0017] In step 2, the pre-tension strain and quantity of the steel strands are determined according to the following principles:

[0018] (1) The pre-tension strain of each steel strand is

[0019]

[0020] (2) To ensure that the tension of the steel strand remains at F during the shaking table test. y The strain of the steel strand during the test needs to be controlled within (d0 / l, d...). u The interval is / l), therefore the number and arrangement of steel strands n are determined by the following formula:

[0021]

[0022] Where, N max and M max E represents the upward vertical additional axial force and maximum bending moment experienced by the foundation or underground structure during the test; u γ represents the strengthening modulus of the steel after the steel strand enters the strengthening stage; γ represents the empirical safety factor, with a value of 0.8; W(n) represents the section modulus of the steel strand farthest from the center of gravity in the plane, determined by the following formula:

[0023]

[0024] Among them, D i D represents the distance between the i-th steel strand and the centroidal axis on the horizontal plane. max This represents the maximum distance between the steel strand and the centroidal axis on the horizontal plane, which is determined according to the direction of the bending moment.

[0025] (3) The cross-sectional area of ​​the steel strand can be determined by trial selection. First, based on the total tensile force F and the yield strength δ of the steel strand. s The total area A of the required steel strand is obtained. s ;

[0026] A s =Fδ s (5)

[0027] Then, determine the preload f (i.e., the cross-sectional area of ​​a single steel strand) and the quantity n and position of the steel strand according to formulas (2)-(4). If there are problems such as too many or too few steel strands which are not conducive to the arrangement, the cross-sectional area A of the steel strands is adjusted, and the preload, quantity and position of the steel strands are re-determined until it is appropriate. During the trial selection process, it is necessary to ensure that the total cross-sectional area of ​​the steel strands remains unchanged and is equal to the total area calculated.

[0028] A S = n×A(6).

[0029] The beneficial effects of this invention are:

[0030] 1. This invention is simple to manufacture: it only requires connecting the test model and the prestressed steel strands together through pre-embedded components and prestressed anchors, and ensuring that all steel strands are parallel to each other and in the same direction as the direction of gravity.

[0031] 2. This invention is easy to design: the sum of the tension of all steel strands is equal to the theoretically required counterweight, and the centroid of the projection of the point of action of the steel strands onto the horizontal plane coincides with the projection of the center of gravity of the model structure onto the horizontal plane.

[0032] 3. This invention has a wide range of applications: it is applicable to the foundations or underground structures of most concrete or steel structures.

[0033] 4. This method can provide a stable vertical force equivalent to the weight of the counterweight for the test model, and has important reference value for solving the problem of applying counterweight in shaking table tests, especially the problem of applying counterweight to foundations and underground structures. Attached Figure Description

[0034] Figure 1 Elevation view of the device for applying vertical force.

[0035] Figure 2 Plan view of the device for applying vertical force.

[0036] Figure 3 This is a schematic diagram of the planar layout of the steel strands.

[0037] Figure 4 This is a schematic diagram of the force-displacement curve of a steel strand under tension. Detailed Implementation

[0038] The present invention will now be described in further detail with reference to the accompanying drawings.

[0039] like Figure 1 and Figure 2 As shown, the vertical force application device for shaking table testing of foundations or underground structures proposed in this invention mainly comprises three parts: the foundation or underground structure or its embedded components, prestressed anchors, and prestressed steel strands. During the fabrication of the foundation or underground structure, the embedded components are buried in the pre-designed corresponding positions. One end of the prestressed steel strand is fixed to the embedded component of the structure via a prestressed anchor, and the other end is fixed to the bottom of the soil box by welding.

[0040] The quantity and location of the prestressed steel strands and corresponding accessories shown in the figure are for illustrative purposes only. Their quantity and location should be determined according to the following basic principles.

[0041] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0042] 1. The key to this vertical force application device is to ensure that the force exerted on the structure by the steel strand is equivalent to the weight of the theoretical counterweight. Therefore, the following two points must be met:

[0043] (1) The steel strands remain vertical, and the resultant vertical force exerted on the structure by all the steel strands is equal to the weight of the theoretical counterweight of the test model.

[0044] mg=n·f (1)

[0045] Where m represents the theoretical counterweight mass of the test model, n represents the number of steel strands, and f represents the preload of each steel strand. For simplicity, each steel strand has the same cross-sectional area and equal preload.

[0046] (2) The resultant force of all steel strand tensions is collinear with the gravity of the model structure. The first step is to determine the position of the model's center of gravity projected onto the horizontal plane. The second step is to ensure that the projection of the centroid of the figure formed by the lines connecting the embedded components (i.e., the positions of the steel strands) onto the horizontal plane coincides with the projection of the model's center of gravity. Since the pre-tension of each steel strand is the same, this condition can be satisfied as long as the centroid of the projection of the point of action of all steel strands onto the horizontal plane coincides with the projection of the model structure's center of gravity onto the horizontal plane. Figure 3 As shown. Generally speaking, a symmetrically distributed arrangement of steel strands can satisfy the condition of centroid coincidence.

[0047] 2. Typical force-displacement curves of steel strands under tension are shown below. Figure 4 As shown. Assuming the length of the steel strand is l, F y d represents the yield strength of the steel strand, d0 represents the yield displacement of the steel strand, and d u This represents the ultimate displacement of the steel strand. As can be seen from the figure, after yielding, the increase in tensile force is very small as the displacement increases. Therefore, in this invention, the pre-tension strain of the steel strand is controlled within (d0+d...). u With approximately ) / (2l), the tension of the steel strand can be kept basically constant during the vibration table test.

[0048] like Figure 4 As shown, the average values ​​of the yield displacement and ultimate displacement of the steel strand are (d0+d u ) / 2, the corresponding pre-tension strain of the steel strand is (d0+d u ) / (2l). The pre-tension strain of the steel strand is taken as this value. During the test, the additional displacement of the steel strand is within the range of [-(d u -d0) / 2,(d u When the strain varies within the range of [d0) / 2], the tensile force of the steel strand is approximately equal to its yield strength. This range represents the maximum displacement range that ensures the yield strength of the steel strand; therefore, in this invention, the strain value of the steel strand is taken as (d0 + d2). u ) / (2l).

[0049] Based on the above analysis, the pretension strain and quantity of the steel strands are determined according to the following principles:

[0050] (1) The pre-tension strain of each steel strand is

[0051]

[0052] (2) To ensure that the tension of the steel strand remains at F during the shaking table test. y The strain of the steel strand during the test needs to be controlled within (d0 / l, d...). u / l) interval. Therefore, the number n and arrangement of steel strands are determined by the following formula.

[0053]

[0054] Where, N max and M max E represents the upward vertical additional axial force and maximum bending moment experienced by the foundation or underground structure during the test; u γ represents the strengthening modulus of the steel after the steel strand enters the strengthening stage; γ represents the empirical safety factor, which is taken as 0.8 in this invention; the calculation of W(n) is based on Figure 3 The schematic diagram of the steel strand layout shown represents the modulus of the steel strand furthest from the center of gravity in the plane, which is determined by the following formula.

[0055]

[0056] Among them, D i D represents the distance between the i-th steel strand and the centroidal axis on the horizontal plane. max This represents the maximum distance between the steel strand and the centroidal axis on the horizontal plane. The centroidal axis is determined based on the direction of the bending moment. It should be noted that the influence of the downward vertical additional axial force and compressive stress caused by the bending moment on the foundation or underground structure during the shaking table test is not considered, because the downward vertical force is mainly borne by the soil and its influence on the steel strand is negligible.

[0057] (3) The cross-sectional area of ​​the steel strand can be determined through trial and error. First, based on the total tensile force F and the yield strength δ of the steel strand... s The total area A of the required steel strand is obtained. s .

[0058] A s =Fδ s (5)

[0059] Then, determine the preload f (i.e., the cross-sectional area of ​​a single steel strand), quantity n, and location of the steel strands according to equations (2)-(4). If problems arise such as too many or too few steel strands making the arrangement difficult, adjust the cross-sectional area A of the steel strands and re-determine the preload, quantity, and location until a suitable arrangement is reached. During the trial selection process, it is necessary to ensure that the total cross-sectional area of ​​the steel strands remains unchanged and equal to the calculated total area. This is to keep the total tension constant.

[0060] A S =n×A(6)

[0061] 3. During installation, it is important to place rubber pads at the contact points between the prestressed anchor and the steel plate to prevent the prestressed anchor from loosening.

Claims

1. A method for using a vertical force application device for shaking table tests of foundations and underground structures, characterized in that, Includes the following steps; Step 1: Ensure that the force exerted on the structure by the prestressed steel strands is equivalent to the gravity of the theoretical counterweight; Step 2: Determine the typical force-displacement curve of the steel strand under tension, assuming the length of the steel strand is... , Indicates the yield strength of the steel strand. This represents the yield displacement of the steel strand. This represents the ultimate displacement of the steel strand. After yielding, the increase in tensile force is very small as the displacement increases. The pre-tension strain of the steel strand is controlled within... This is used to ensure that the tension of the steel strand remains basically constant during the shaking table test; Step 3: During installation, make sure to place rubber pads at the contact points between the prestressed anchor and the steel plate to prevent the prestressed anchor from loosening; In step 2, the pre-tension strain and quantity of the steel strands are determined according to the following principles: (1) The pre-tension strain of each steel strand is （2） (2) To ensure that the tension of the steel strand remains constant during the shaking table test Around [a certain value], the strain of the steel strand during the test needs to be controlled. The interval, therefore the number of steel strands The layout is determined by the following formula: （3） in, and These represent the upward vertical additional axial force and maximum bending moment experienced by the foundation or underground structure during the test, respectively. This indicates the strengthening modulus of the steel after the steel strand enters the strengthening stage; This represents the empirical safety factor, with a value of 0.

8. The modulus of the strand furthest from the center of gravity in the plane is determined by the following formula: （4） in, Indicates the first on the horizontal plane The distance between the steel strand and the centroidal axis. This represents the maximum distance between the steel strand and the centroidal axis on the horizontal plane, which is determined according to the direction of the bending moment. (3) The cross-sectional area of ​​the steel strand is determined by trial selection. First, it is based on the total tensile force. Yield strength of steel strand Determine the total area of ​​the required steel strand. ; （5） Then, the preload of the steel strand is determined according to equations (2) to (4). and quantity Regarding the location, if there are too many or too few steel strands, which would be detrimental to the layout, the cross-sectional area of ​​the steel strands should be adjusted. Adjustments should be made to redetermine the preload, quantity, and location of the steel strands until they are suitable. During the trial selection process, it is necessary to ensure that the total cross-sectional area of ​​the steel strands remains unchanged and is equal to the calculated total area. （6）； The method is achieved through a vertical force application device for shaking table tests of foundations and underground structures, including prestressed steel strands, prestressed anchors, and the foundation or underground structure or its embedded components. The lower end of the prestressed steel strands is fixed to the bottom surface of the soil box, and the upper end is fixed to the test foundation or underground structure or its embedded components through the prestressed anchors. All prestressed steel strands are identical and arranged vertically. The applied prestress is equal to the yield strength of the steel strands. The centroid of the projection of all prestressed steel strands on the horizontal plane coincides with the projection of the model's center of gravity, ensuring that the resultant force of the tension provided by the prestressed steel strands is always collinear with the model's gravity. The type and number of prestressed steel strands ensure that the applied vertical force is equivalent to the weight of the counterweight that should be applied, that is, ensuring that the product of the yield strength of the steel strands and the number of steel strands is equal to the weight of the counterweight that should be applied.

2. The method of using the vertical force application device for shaking table tests of foundations and underground structures according to claim 1, characterized in that, Step 1 includes the following two points: (1) The prestressed steel strands are kept vertical, and the resultant vertical force exerted on the structure by all the prestressed steel strands is equal to the weight of the theoretical counterweight of the test model. （1） in, This represents the theoretical counterweight mass of the experimental model. Indicates the number of steel strands. This indicates the preload of each steel strand. Since each steel strand has the same cross-sectional area, the preload is equal. (2) The resultant force of all prestressed steel strand tensions is collinear with the gravity of the model structure; The first step is to determine the position of the model's center of gravity projected onto the horizontal plane. The second step is to ensure that the projection of the centroid of the figure formed by the lines connecting the embedded components on the horizontal plane coincides with the projection of the model's center of gravity. Since the preload of each steel strand is the same, this condition can be satisfied as long as the centroid of the projection of the action point of all steel strands on the horizontal plane coincides with the projection of the model's center of gravity on the horizontal plane. A symmetrically distributed arrangement of steel strands can satisfy the centroid coincidence condition.

3. The method of using the vertical force application device for shaking table tests of foundations and underground structures according to claim 1, characterized in that, In step 2, the average values ​​of the yield displacement and ultimate displacement of the steel strand are The corresponding pre-tension strain of the steel strand is The pre-tension strain of the steel strand is taken as this value, and the additional displacement range of the steel strand during the test is within... When the strain varies within a certain range, the tensile force of the steel strand is approximately equal to its yield strength. This range represents the maximum displacement range that ensures the yield strength of the steel strand; therefore, the strain of the steel strand is taken as... .

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