An experimental device capable of continuously measuring the four-dimensional motion state inside the soil mass
By designing an experimental device including model boxes, transparent soil, imaging system, light source system and signal excitation and acquisition analysis system, the problem that the existing technology cannot continuously measure the four-dimensional motion state inside the soil is solved, and the multi-dimensional motion state measurement of soil under multiple terrain is realized, providing more accurate structural-soil interaction research data.
Patent Information
- Application Number
- CN202111614053.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Priority Date
- 2021-12-07
- Filing Date
- 2021-12-27
- Publication Date
- 2025-06-10
- Estimated Expiration
- 2041-12-27
AI Technical Summary
The prior art cannot continuously measure the four-dimensional motion state inside the soil in laboratory model tests, and cannot adapt to the soil motion characteristics under multiple terrain.
An experimental device was designed, including a model box, transparent soil, camera system, light source system and signal excitation and acquisition analysis system. The three-dimensional motion state inside the soil is captured through a laser emitter and camera, and continuous measurement and data analysis are achieved through a signal excitation and acquisition analysis system.
The continuous four-dimensional motion state measurement inside the soil is realized, and the multi-dimensional motion state data of the soil can be obtained under multi-terrain conditions, providing more accurate structure-soil interaction research data.
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Figure CN114264793B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of geotechnical engineering, and particularly to geotechnical engineering model experiments based on transparent soil. Background Art
[0002] In geotechnical engineering, the internal displacement of soil is an important research index and also an important bridge to reveal the interaction between soil and structure. In the on-site tests of the prior art, inclinometers, settlement layers, etc. are usually used to measure the deep horizontal displacement and deep vertical displacement of soil. However, the existing on-site test methods are not applicable to the model tests in the laboratory, mainly for the following reasons:
[0003] Firstly, the measuring equipment used in on-site tests is too large in volume. The method of inserting inclinometers and layered monitoring points into the soil during measurement is not applicable to laboratory devices because this will interfere with the deformation of the soil with a limited volume in the laboratory, resulting in a large deviation in test results. Therefore, it is not feasible.
[0004] Secondly, although the monitoring speed of the existing methods or devices is more convenient after being transformed into automatic monitoring, the measuring points can only be arranged discontinuously during actual operation, resulting in scattered data points and unable to realize the three-dimensional reconstruction of the dynamic displacement of the soil.
[0005] Thirdly, the interior of the soil is opaque, making it impossible to monitor the internal situation of the soil.
[0006] Therefore, the current on-site test methods and devices are not applicable to indoor model tests.
[0007] In response to the above problems, some researchers recently used transparent soil, particle image velocimetry and corresponding devices to achieve the internal soil deformation test. Using transparent soil to equivalently replace the soil solves the problem of soil opacity; adopting particle image velocimetry and cooperating with a laser emitter realizes the capture and test of the displacement of internal particles in transparent soil. This method is convenient for researchers to observe the internal displacement of the soil. However, the existing transparent soil observation technology can only test the internal displacement of the soil under static conditions. Because it is necessary to stop the test after the soil deforms, ingest the laser on different surfaces, and gradually take pictures for measurement, it cannot record the displacement under the continuous motion state of the soil.
[0008] When studying the interaction between structure and soil (such as in static cone penetration tests or jacked pile penetration tests, etc.), it is very important to observe the internal and dynamic continuous deformation of the soil because the change of pore water pressure often occurs during the soil deformation process. If the structure is stopped to observe the internal deformation of the soil, it will cause the dissipation of pore water pressure, change the soil stress, and seriously affect the result of the interaction between structure and soil.
[0009] In addition, existing observation means and devices can often only observe the displacement in the vertical plane and cannot simultaneously observe the settlement of the soil mass on the plane or in other directions, resulting in the lack of settlement of the soil mass on the plane.
[0010] In addition, in the existing technology, the model box is limited to its fixed shape and has a single function, and it cannot conveniently simulate complex topographies and landforms, so the characteristics of soil mass movement under various topographies and landforms cannot be obtained.
[0011] To sum up, there is currently no experimental device that can simultaneously measure the internal, four-dimensional (three-dimensional space + time dimension), continuous motion state of the soil mass, and there is currently no experimental device that can obtain data on the four-dimensional motion state of the soil mass under multiple topographies. Therefore, there is an urgent need to develop a device that can continuously observe the multi-dimensional motion state inside the soil mass and the multi-dimensional motion state inside the soil mass under multiple topographies. Summary of the Invention
[0012] The present invention aims to provide an experimental device that can continuously measure the four-dimensional motion state inside the soil mass, greatly expanding the application of transparent soil in geotechnical engineering and providing a new research method for studying the structure-soil interaction relationship. The technical solution adopted by the present invention is as follows:
[0013] The present invention provides an experimental device that can continuously measure the four-dimensional motion state inside the soil mass. The device includes a model box, transparent soil, a camera system, a light source system, and a signal excitation and acquisition analysis system. The model box contains transparent soil inside, and the transparent soil is used to equivalently replace conventional opaque soil masses so that the internal situation of the soil mass can be observed. The camera system includes a camera arranged on the side of the model box and a camera arranged above the model box. Among them, the camera arranged above the model box can simultaneously collect the horizontal displacement data and the vertical displacement data of the soil mass and transmit the data to the signal excitation and acquisition analysis system. The light source system provides at least two non-coplanar laser planes that illuminate the model box. The signal excitation and acquisition analysis system controls the laser emission of the light source system and / or collects data from the camera.
[0014] Preferably, a substance that shows color under laser is added to the transparent soil to help capture soil particles during shooting.
[0015] Preferably, it further includes a gasket. The gasket is adjustably installed in the model box and can support the soil mass above the gasket. At least one lifting device that can be individually adjusted for lifting is installed below the gasket.
[0016] Preferably, the surface of the gasket is flat or curved; the surface of the gasket is either without leakage holes or with leakage holes; the gasket is placed horizontally or non - horizontally; thus enabling the device of the present application to simulate the soil movement state under different terrain conditions.
[0017] Preferably, the device includes a light - absorbing plate, which is removably placed inside the bottom surface of the model box and / or inside the remaining side surfaces of the non - laser incident surface of the model box. The light - absorbing plate is adjustably placed. For the convenience of adjusting the position of the light - absorbing plate, the lengths of the sides of the bottom surface of the model box are equal and the side areas of the model box are the same; in addition, the light - absorbing plate can be replaced by paint, such as black paint, to avoid the influence of light pollution.
[0018] Preferably, the three - way motion brackets support both the microparticle - capturing camera and the binocular camera. The three - way motion brackets have six degrees of freedom of motion, realizing the front - back, left - right, and up - down three - direction planar adjustment and three - direction orthogonal torsion adjustment of the camera system, and can fix the camera system at any angle or position.
[0019] Preferably, the camera set above the model box body is a binocular camera, and the camera set on the side of the model box body is a microparticle - capturing camera.
[0020] Preferably, the at least two non - coplanar laser planes are emitted by a plurality of detachably assembled laser emitters; the two non - coplanar laser planes include a horizontal plane and a vertical plane.
[0021] Preferably, the signal excitation and acquisition analysis system controls each laser emitter to emit laser separately, and simultaneously collects and analyzes the image data of the camera. For example, the laser emitters at different positions are triggered continuously and without intervals to emit laser. The signal excitation and acquisition analysis system synchronously controls the camera system to collect the transparent soil body movement pictures and analyze them, realizing the capture of the displacement of soil particles on the horizontal plane and vertical plane inside the transparent soil body. Then, the three - dimensional motion state inside the soil body is calculated and inverted by equations (1) - (4), and then multiple three - dimensional motion states are integrated in chronological order to obtain the four - dimensional motion state of the soil body.
[0022]
[0023] Δv ii =u ii / ΔT (2)
[0024] Δa ii =u ii / ΔT 2 (3)
[0025]
[0026] where: Δε ij is the strain increment vector; Δv ii is the increment velocity vector; Δa ii is the increment acceleration vector; the subscripts i and j are taken in the x, y, and z directions; u i,j is the displacement partial derivative matrix in each direction.
[0027] Preferably, the model box includes two side panels, two transparent plates and a bottom plate. The components are assembled by bolts. The top is empty for the upper camera to take pictures. Preferably, the side panels and the bottom plate are made of metal plates, and the metal plates are selected from one or more of steel, aluminum, and copper; the transparent plates are made of plexiglass.
[0028] Preferably, the micro-particle capture camera can be used to take high-definition and high-speed pictures and identify soil micro-particles to measure the vertical displacement of the soil mass, while the binocular camera is used to quickly take pictures of the particle displacement on the horizontal plane of the soil mass, including settlement; among them, the three-way motion bracket can fix the camera system at different angles and positions, making it have a stable and good test angle.
[0029] Preferably, the light source system includes a cross-shaped laser bracket, and the laser emitters are modularly assembled on the cross-shaped laser bracket. Multiple laser emitters can be installed on the cross-shaped laser bracket, and any number can be arranged according to the experimental requirements. The laser emitters on the cross-shaped laser bracket are arranged horizontally and vertically, and are respectively used to emit surface light perpendicular to the bottom surface of the model box and parallel to the bottom surface of the model box. The laser emitter at the intersection of the horizontal and vertical directions can emit two kinds of surface light, perpendicular and parallel, and its excitation situation is controlled by the signal excitation and acquisition analysis system.
[0030] Preferably, the signal excitation and acquisition analysis system The signal excitation and acquisition analysis system includes a signal generator, a signal collector, a cable, and analysis software.
[0031] The present invention also provides a method for measuring the four-dimensional motion state inside the soil mass using the above device, including,
[0032] Step 1, fill the model box with transparent soil and add fluorescent agent to the transparent soil;
[0033] Step 2: Set the value of the time interval ΔT such that the signal excitation and acquisition analysis system emits 2N laser excitation signals within the time interval ΔT, where N is the number of laser emitters used in the device plus 1, and simultaneously emits 2N camera acquisition signals; the first N laser excitation signals are used to excite the horizontal laser emitters, and each laser excitation signal excites one horizontal laser emitter; the synchronized first N camera acquisition signals are used to trigger the micro-particle capture camera to take records; the last N laser excitation signals are used to excite the vertical laser emitters, and each laser excitation signal excites one vertical laser emitter; the synchronized last N camera acquisition signals are used to trigger the binocular camera to take records;
[0034] Step 3: By reducing the time interval ΔT and increasing the acquisition frequency, make the acquisition adapt to the penetration speed; record the time using the signal excitation and acquisition analysis system while collecting the signals;
[0035] Step 4: Change the positions of the light source system, signal excitation and acquisition analysis system, and repeat Steps 1 to 4 to achieve multi-directional recording in the soil mass;
[0036] Step 5: Analyze the data in Steps 1 to 4 to obtain the displacement data of the transparent soil mass at different times and different surface positions, and use the displacement data to establish the three-dimensional displacement deformation process of the transparent soil mass; take the derivative in the spatial dimension of the result to obtain the soil strain field, and take the derivative in the time dimension to obtain the results of the velocity field and acceleration field of the soil particles in space; calculate and invert the three-dimensional motion state inside the soil mass from Equations (1)-(4); use u = u(x, y, z), v = v(x, y, z), w = w(x, y, z) to represent that within the time interval ΔT, the displacements of any point inside the soil mass in the x, y, and z directions are:
[0037]
[0038] Δv ii =u ii / ΔT (2)
[0039] Δa ii =u ii / ΔT 2 (3)
[0040]
[0041] where: Δε ij is the strain increment vector; Δv ii is the incremental velocity vector; Δa ii is the incremental acceleration vector; the subscripts i and j take the x, y, and z directions; u i,j is the displacement partial derivative matrix in each direction;
[0042] Step 6: Integrate multiple three-dimensional motion states in chronological order to obtain the four-dimensional motion state of the soil mass.
[0043] The beneficial effects of the present invention are as follows:
[0044] 1) In the device of the present invention, the model box includes gaskets, and the lifting device for supporting the gaskets can be independently controlled for lifting, enabling the simulation design of the space inside the model box according to the actual terrain. Without changing the shape of the box, the influence of the soil layer thickness of different terrains on the soil motion state can be simulated by adjusting the position and height of the gaskets. For example, changing the inclination angle of the gaskets and changing the surface shape of the gaskets to a curved surface can simulate the influence of mountain terrain on the soil motion. At the same time, fine holes can be drilled in the gaskets to simulate the soil motion state under seepage conditions or water gushing conditions.
[0045] 2) The device of the present invention uses a cross laser bracket to mount the laser emitter, which can conveniently realize laser irradiation on multiple horizontal and vertical planes, helping to quickly excite the light source and providing a basis for obtaining the internal motion of the soil mass.
[0046] 3) The device of the present invention smears light-absorbing materials inside the side plates and the bottom plate, avoiding the reflection of laser light within the boundaries of the model box, eliminating the influence of light pollution on the test results, and improving the accuracy of the binocular camera and the micro-particle capture camera in capturing the displacement of soil particles.
[0047] 4) The device of the present invention uses a signal excitation and acquisition analysis system to sequentially excite the laser and control the camera system to capture photos, quickly obtaining the three-dimensional particle motion conditions of different parts of the soil mass, obtaining the change process of the three-dimensional motion inside the transparent soil mass over time, and realizing the continuous measurement of the four-dimensional motion state inside the soil mass.
[0048] 5) The device of the present invention can further analyze and obtain the internal strain, soil particle velocity, acceleration, etc. of the soil mass through the captured internal displacement field of the soil mass. Further combined with the modulus of the transparent soil in the experiment, the change process of the internal stress of the soil mass during the experiment can be calculated.
[0049] Through the above technical solutions, this application greatly helps researchers to reveal the mechanism of the interaction between the moving structure and the soil mass. Description of the Drawings
[0050] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.
[0051] Figure 1 Overall device diagram of the present invention without a gasket;
[0052] Figure 2 Overall device diagram of the present invention with a gasket.
[0053] In the figure: 1 - Micro - particle capture camera; 2 - Binocular camera; 3 - Laser emitter; 4 - Cross - shaped laser bracket; 5 - Side panel; 6 - Three - way movement bracket; 7 - Transparent plate; 8 - Bottom plate; 9 - Signal excitation and acquisition analysis system; 10 - Cable; 11 - Gasket; 12 - Lifting device. Detailed implementation mode
[0054] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be described in detail below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other implementation manners obtained by those of ordinary skill in the art without creative efforts belong to the scope protected by the present invention.
[0055] Embodiment 1
[0056] As Figure 1 shown, the device of the present invention is composed of a model box, transparent soil, fluorescent agent, a camera system, a light source system, and a signal excitation and acquisition analysis system;
[0057] The model box includes two steel side panels 5, two high - strength transparent plates 7, and a bottom plate 8, and the components are assembled by bolts; an anti - reflective coating is applied to the inner surfaces of the steel side panels 5 and the bottom plate 8 to avoid the influence of light reflection on the shooting of the camera system;
[0058] The transparent soil is used to equivalently replace the conventional opaque soil body so as to observe the internal situation of the soil body;
[0059] The fluorescent agent is used to be incorporated into the transparent soil to help the transparent soil particles be clearer under laser irradiation, facilitating the shooting and capturing of soil particles;
[0060] The camera system includes a micro - particle capture camera 1 and a binocular camera 2, which are respectively arranged on the side and top of the model box through a three - way movement bracket 6;
[0061] The light source system includes a laser emitter 3 and a cross - shaped laser bracket 4, and multiple laser emitters are modularly assembled on the cross - shaped laser bracket 4; the arrangement of the laser emitters 3 is divided into a horizontal direction and a vertical direction, which are respectively used to emit a light surface perpendicular to the bottom surface of the model box, i.e., a vertical light surface, and a light surface parallel to the bottom surface of the model box, i.e., a parallel light surface. Among them, the laser emitter at the intersection of the horizontal direction and the vertical direction can participate in emitting the vertical light surface and the parallel light surface;
[0062] The signal excitation and acquisition analysis system includes the signal excitation and acquisition analysis system 9 and the cable 10;
[0063] Taking the static cone penetration test (CPT) as an example, the experimental steps using the device of the present invention are as follows:
[0064] Before the experiment, assemble the experimental device as required, and fill the transparent soil in the model box according to the experimental plan requirements. One or more fluorescent agents can be selectively added to the transparent soil to enhance the recognition ability of the soil body when being photographed.
[0065] During the test, while the CPT penetrates into the soil, within the time interval ΔT, the signal excitation and acquisition analysis system 9 emits 2N laser excitation signals (N is the number of laser emitters plus 1), and simultaneously emits 2N camera acquisition signals. The first N laser excitation signals are used to excite the horizontal laser emitters. Each laser excitation signal excites a single horizontal laser emitter, and the order is from front to back; the synchronized first N camera acquisition signals are used to excite the microparticle capture camera 1 for shooting and recording. The last N laser excitation signals are used to excite the vertical laser emitters. Each laser excitation signal excites a single vertical laser emitter, and the order is from top to bottom; the synchronized last N camera acquisition signals are used to excite the binocular camera 2 for shooting and recording. Among them, by reducing the time interval ΔT and increasing the acquisition frequency, the acquisition can be adapted to the penetration speed. While collecting the signals, the signal excitation and acquisition analysis system 9 records the time in real time. By repeatedly emitting signals like this, the capture of the displacement of soil particles on the internal horizontal and vertical planes of the soil and the time recording are realized, achieving the four-dimensional recording of the soil body. The obtained motion states include but are not limited to: velocity, position, acceleration, etc. Then, by changing the positions of the light source system and the signal excitation and acquisition analysis system, the multi-directional recording in the soil body is realized.
[0066] Then, use software analysis to obtain the displacement data of the transparent soil body at different times and different surface positions. Then use programming to process these displacement data to establish the three-dimensional displacement deformation process of the transparent soil body. Take the derivative of the result in the spatial dimension to obtain the soil strain field, and take the derivative in the time dimension to obtain results such as the velocity field and acceleration field of the soil particles in space. The signal excitation and acquisition analysis system calculates and inversely analyzes the three-dimensional motion state inside the soil body according to formulas (1)-(4). Let u = u(x, y, z), v = v(x, y, z), w = w(x, y, z) respectively represent the displacements of any point inside the soil body in the x, y, and z directions within the time interval ΔT:
[0067]
[0068] Δv ii = u ii / ΔT (2)
[0069] Δa ii = u ii / ΔT 2 (3)
[0070]
[0071] where: Δε ij is the strain increment vector; Δv ii is the incremental velocity vector; Δa ii is the incremental acceleration vector; the subscripts i, j take the x, y, z directions; u i,j is the displacement partial derivative matrix in each direction.
[0072] Embodiment 2
[0073] This embodiment includes the content of Embodiment 1. On the basis of Embodiment 1, as Figure 2 shown, a gasket 11 is arranged inside the device of the present invention, so that the gasket is adjustably installed in the model box through the support of the lifting device 12 for partitioning the internal space of the model box. The gasket 11 is composed of a hard material to support the soil above the gasket, and the periphery of the gasket is sealed by a sealing strip. Figure 2 Among them, the four lifting devices can be adjusted independently for lifting, and the types of the lifting devices are common lifting instruments on the market, such as hydraulic cylinders. The height and position of the gasket in the box are adjusted by the lifting of the hydraulic cylinders.
[0074] Two large groups of experiments, namely a flat gasket group and a curved gasket group, are respectively selected. Each large group respectively includes a gasket without leakage holes placed horizontally, a gasket with leakage holes placed horizontally, a gasket without leakage holes placed obliquely, and a gasket with leakage holes placed obliquely as four small parallel experiments. The experimental steps in Embodiment 1 are repeated to obtain the numerical values of soil movement for analysis. In this embodiment, the surface shape of the gasket is flat or curved to study the influence of different geological shapes on the soil movement state; the gasket is without leakage holes or has leakage holes to study the influence of different geological conditions on the soil movement state.
[0075] The above specific embodiments are used to explain the present invention, rather than limiting the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims of the present invention fall within the protection scope of the present invention.
Claims
1. A device capable of continuously measuring the four-dimensional motion state inside the soil mass, characterized in that, the device includes a model box, transparent soil, a camera system, a light source system, and a signal excitation and acquisition analysis system; the inside of the model box contains transparent soil; the camera system includes a camera arranged on the side of the model box and a camera arranged above the model box; among them, the camera arranged above the model box can simultaneously collect the horizontal displacement data and vertical displacement data of the soil mass and transmit the data to the signal excitation and acquisition analysis system; the light source system provides at least two non-coplanar laser planes directed at the model box; the signal excitation and acquisition analysis system controls the laser emission of the light source system and / or collects data from the camera; the camera arranged above the model box body is a binocular camera, and the camera arranged on the side of the model box is a micro-particle capture camera; the signal excitation and acquisition analysis system separately controls each laser emitter to emit laser, simultaneously collects and analyzes the image data of the camera, then calculates and inverses the three-dimensional motion state inside the soil mass by formulas (1)-(4), and then integrates multiple three-dimensional motion states in chronological order to obtain the four-dimensional motion state of the soil mass; Δv ii = u ii / ΔT (2) Δa ii = u ii / ΔT 2 (3) where: Δε ij is the strain increment vector; Δv ii is the increment velocity vector; Δa ii is the increment acceleration vector; the subscripts i, j take the x, y, z directions; u i,j is the displacement partial derivative matrix in each direction.
2. The device according to claim 1, characterized in that, a substance that shows color under laser is added to the transparent soil.
3. The device according to claim 1, characterized in that, it further includes a gasket, which is adjustably installed in the model box and can support the soil mass above the gasket; at least one lifting device that can be individually adjusted for lifting is installed below the gasket.
4. The device according to claim 3, characterized in that, the surface shape of the gasket is a plane or a curved surface; the surface of the gasket is without leakage holes or has leakage holes; the gasket is placed horizontally or non-horizontally.
5. The device according to claim 1, characterized in that, the device includes a light-absorbing plate, which is removably placed on the inner side of the bottom surface of the model box and / or on the inner sides of the remaining sides of the non-laser incident surface of the model box.
6. The device according to claim 1, characterized in that, both the micro-particle capture camera and the binocular camera have six degrees of freedom of movement.
7. The device according to claim 1, characterized in that, the at least two non-coplanar laser planes are emitted by a plurality of detachably assembled laser emitters; the two non-coplanar laser planes include a horizontal plane and a vertical plane.
8. A method for measuring the four-dimensional motion state inside the soil mass using the device according to any one of claims 1-7, including, Step 1, fill the transparent soil mass in the model box and incorporate a fluorescent agent into the transparent soil; Step 2: Set the value of the time interval ΔT such that the signal excitation and acquisition analysis system emits 2N laser excitation signals within the time interval ΔT, where N is the number of laser emitters used in the device plus 1, and simultaneously emits 2N camera acquisition signals; the first N laser excitation signals are used to excite the horizontally oriented laser emitters, and each laser excitation signal excites one horizontally oriented laser emitter; the synchronized first N camera acquisition signals are used to trigger the micro-particle capture camera to take records; the last N laser excitation signals are used to excite the vertically oriented laser emitters, and each laser excitation signal excites one vertically oriented laser emitter; the synchronized last N camera acquisition signals are used to trigger the binocular camera to take records. Step 3: By reducing the time interval ΔT and increasing the acquisition frequency, make the acquisition adapt to the penetration speed; record the time using the signal excitation and acquisition analysis system while collecting the signals. Step 4: Change the positions of the light source system, signal excitation and acquisition analysis system, and repeat Steps 1 to 4 to achieve multi-directional recording in the soil mass. Step 5: Analyze the data in Steps 1 to 4 to obtain the displacement data of the transparent soil mass at different times and different surface positions, and use the displacement data to establish the three-dimensional displacement deformation process of the transparent soil mass; take the derivative in the spatial dimension of the result to obtain the soil strain field, and take the derivative in the time dimension to obtain the results of the velocity field and acceleration field of the soil particles in space; calculate and invert the three-dimensional motion state inside the soil mass from Equations (1)-(4); let u = u(x, y, z), v = v(x, y, z), and w = w(x, y, z) represent the displacements of any point inside the soil mass in the x, y, and z directions within the time interval ΔT as follows: Δv ii = u ii / ΔT (2) Δa ii = u ii / ΔT 2 (3) where: Δε ij is the strain increment vector; Δv ii is the increment velocity vector; Δa ii is the increment acceleration vector; the subscripts i, j take the x, y, z directions; u i,j is the displacement partial derivative matrix in each direction; Step 6: Integrate multiple three-dimensional motion states in chronological order to obtain the four-dimensional motion state of the soil mass.
Citation Information
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