CN105224758A - A kind of for design-calculated Ballast track high-speed railway modeling Analysis method - Google Patents

A kind of for design-calculated Ballast track high-speed railway modeling Analysis method Download PDF

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CN105224758A
CN105224758A CN201510669608.8A CN201510669608A CN105224758A CN 105224758 A CN105224758 A CN 105224758A CN 201510669608 A CN201510669608 A CN 201510669608A CN 105224758 A CN105224758 A CN 105224758A
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sleeper
rail
train
model
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CN105224758B (en
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庄妍
李劭邦
王康宇
王晓东
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Hohai University HHU
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Abstract

The invention discloses a kind of Ballast track high-speed railway modeling Analysis method, mainly comprise following step:? (1) being used as by rail is the Euler-Bernoulli beam acted on Winkler ground, calculates train to the equivalent load of substructure; (2) extract the geometric parameter of structure, set up the finite element model of each structural sheet with finite element software ABAQUS; (3) material properties and cell attribute is given and grid division to each structural sheet; (4) contact and boundary condition are set; (5) on sleeper, apply train equivalent load, utilize explicit solution device to carry out Cable Power Computation.The present invention is based on ABAQUS software, by simplifying structure, be used as by rail is act on Euler-Bernoulli beam on Winkler ground to calculate train equivalent load, model itself do not comprise rail but directly the train equivalent load of calculating is added to substructure to carry out the simplification of dynamic analysis, more close to the Three-dimensional finite element modeling method of truth, be applicable to the project navigator of Ballast track high-speed railway.

Description

A kind of for design-calculated Ballast track high-speed railway modeling Analysis method
Technical field
The present invention relates to computer-aided design for railway engineering technical field, be related specifically to a kind of for design-calculated Ballast track high-speed railway modeling Analysis method.
Background technology
In the carrying out that the construction of current China Express Railway trunk project is being advanced by leaps and bounds.Along with the oscillation intensity improving constantly the increase with trailing weight, train of train running speed, the interaction between wheel track, between track to roadbed also can correspondingly increase.Therefore high-speed railway requires more strict, especially very strict to the control of settlement after construction to the load-carrying properties of engineering under line and stability.Although achieved a lot of achievement for the research of railway dynamical problem, the research for high-speed railway power aspect problem also do not formed unified conclusion still need large quantifier elimination demonstration.Utilize finite element software to simulate high-speed railway to run and be reliable and achieve a large amount of achievements, but also come with some shortcomings in research before.
Current finite element model or be intercept the transversal section of vertical current of traffic and the two dimensional model set up, or be the large-scale three dimensional finite element model considering that all thin portions structure is set up.The former can not consider structure influencing each other and interacting in space, intuitively can not reflect the transmission characteristic of current of traffic stress wave.The latter considers the three-dimensional model of all thin portions structure, make model very complicated, relate to a large amount of contacts between rail and sleeper and border not easily processes, the grid that complex model is a large amount of simultaneously adds the difficulty and computing time and the storage space of wanting at substantial that calculate convergence.
Summary of the invention
Goal of the invention: the present invention is directed to the deficiency in existing research, proposes a kind of Ballast track high-speed railway Three-dimensional finite element modeling analytical approach of the simplification for Railway Design calculating.
Technical scheme: the Ballast track high-speed railway Three-dimensional finite element modeling analytical approach that the invention discloses a kind of simplification, mainly comprises following step:
(1) structure is regarded as by rail and its under structural sheet connected to form by discrete sleeper, Train induced load is delivered to substructure by sleeper discrete one by one.Rail is regarded as act on Euler-Bernoulli beam on Winkler ground with this to calculate train by time equivalent load to substructure;
(2) extract except rail is with the geometric parameter of external structure, application finite element software ABAQUS sets up the finite element model of sleeper, railway roadbed, embankment, bed course, stake and subsoil soil;
(3) material properties and cell attribute is given and grid division to each structure;
(4) arrange contact and the boundary condition of model, the stake soil contact of model adopts the plane-plane contact type in interaction, and model surrounding adopts infinite element to simulate absorbing boundary, and bottom surface adopts fixed boundary;
(5) on sleeper, applying to calculate the train equivalent load got utilizes ABAQUS explicit solution device to carry out Cable Power Computation.
Described step (1) is specially: to be regarded as by the high-speed railway of Ballast track and connected to form by sleeper discrete one by one by the railway roadbed under rail and its, and Train induced load is delivered in the railway roadbed of bottom, embankment and ground by sleeper and goes.Rail is regarded as act on Euler-Bernoulli beam on Winkler ground with this to calculate train by time each axle carry acting force to each sleeper, the acting force superposition then each axle being loaded in same sleeper try to achieve whole train by time equivalent action power to this sleeper;
Described step (2) is specially: extract except rail according to Ballast track high-speed railway typical section, the geometric parameter of sleeper, railway roadbed, embankment, bed course, foundation soil and stake, utilizes ABAQUS finite element software to set up the finite element model of each structure except rail;
Described step (3) is specially: sleeper and stake adopt elastic model simulation, and employing 3 dimension 8 nodes reduction integration solid element (C3D8R) simultaneously sleeper unit adopts enhancing hourglass control; Railway roadbed, embankment and bed course adopt mole of-coulomb of yield criteria and 3 dimensions 8 node reduction integration solid element (C3D8R), and wherein railway roadbed and embankment adopt and strengthen hourglass control; Foundation soil adopts modified Cam-clay and 3 dimensions 8 node reduction integration solid element (C3D8R).The grid of model adopts Meshing Method heterogeneous, and load action region adopts the tessellated mesh then uniform grid of the both sides employing to the left and right size along transversal section; Vertically by pile cover end face, progressively increase size of mesh opening downwards, pile cover end face upwards adopts uniform grid size;
Described step (4) is specially: according to the actual conditions of Ballast track high-speed railway typical section, and at the plane-plane contact of the stake of interaction module installation and foundation soil, model surrounding adopts infinite element simulation absorbing boundary; Model bottom surface adopts the degree of freedom in fixed boundary constraint x, y, z three directions;
Described step (5) is specially: step one is calculated the train that gets and be added on the surface of contact that each sleeper contacts with rail with the form of even distributed force the equivalent load of each sleeper, utilize ABAQUS explicit solution device to carry out Cable Power Computation.
Useful effect: the Ballast track high-speed railway Three-dimensional finite element modeling analytical approach of simplification provided by the invention, is reduced to the structure only considering sleeper, railway roadbed, embankment, bed course, stake and foundation soil in railway roadbed, embankment and ground by structure by the train load of sleeper transmission equivalence; Typical section according to actual Ballast track high-speed railway extracts the geometric parameter of each structural sheet and sets up finite element model with ABAQUS; The train load of equivalence is added to the enterprising action edge analysis in face that sleeper contacts with rail.Model can not only react transfer law and the deformation characteristic of power between each structural sheet of railway accurately, and required computing time and storage space all greatly reduce, easily widespread use in Railway Design calculates.
Accompanying drawing illustrates:
Fig. 1 is method flow diagram of the present invention;
Fig. 2 is Ballast track high-speed railway structure rough schematic view;
Fig. 3 is Ballast track high-speed railway typical section figure;
Fig. 4 be a joint compartment by time equivalent load figure to the sleeper at 54m place;
Fig. 5 is the geometric model and stress and strain model schematic diagram that modeling method of the present invention is concrete.
Fig. 6 is the distribution schematic diagram of vertical stress under quiet dynamic loading of the upwards embankment unit along weak soil center
Fig. 7 is the distribution schematic diagram of coefficient of earth pressure K value under quiet dynamic loading of the upwards embankment unit along weak soil center
Fig. 8 is along stake top and the weak soil center upwards distribution schematic diagram of embankment relative settlement under quiet dynamic loading
In figure, 1 is rail, and 2 is sleeper, and 3 is railway roadbed, and 4 carry for shifting axle, and 5 is that sleeper transmits load, and 6 be embankment, and 7 is bed course, and 8 is stake, and 9 is subsoil, and 10 is infinite element border, and 11 is fixed boundary.
Concrete embodiment
The specific embodiment of the present invention is described in detail below in conjunction with accompanying drawing.Protection scope of the present invention is not only confined to the description of present embodiment.
A kind of for design-calculated Ballast track high-speed railway modeling Analysis method, as shown in Figure 1, concrete step is as described below for the process flow diagram of enforcement:
(1) Ballast track high-speed railway is regarded as the structure be formed by connecting by sleeper 2 discrete one by one by the railway roadbed 3 of the rail 1 in Fig. 2 and bottom.The load 4 of movement is delivered in railway roadbed 3, embankment 6 and ground 9 by sleeper and goes.Rail is regarded as the Euler-Bernoulli beam be arranged on Winkler ground, during calculating train operation, each axle carries the acting force 5 to each sleeper, and the equivalent action power of whole train to this sleeper is tried to achieve in the acting force superposition then each axle being loaded in same sleeper.Fig. 4 be the 54m sleeper position one of trying to achieve save compartment by time equivalent load;
(2) according to the typical section of the Ballast track high-speed railway structure of Fig. 3, be the structure be made up of the sleeper 2 in figure, railway roadbed 3, embankment 6, bed course 7, subsoil 9 and stake 8 by model simplification, and draft the geometric parameters such as the position of these structural sheets, length, thickness and width according to case history;
(3) geometric parameter of each structural sheet drafted according to step 2, utilizes ABAQUS finite element software to set up the three-dimensional model comprising sleeper 2, railway roadbed 3, embankment 6, bed course 7, subsoil 9 and stake 8 shown in Fig. 5;
(4) finite element model of the sleeper 2 set up Fig. 5, railway roadbed 3, embankment 6, bed course 7, subsoil 9 and stake 8 gives material and cell attribute, arranges contacting and grid division of stake and foundation soil.Wherein sleeper and stake adopt elastic model simulation, and employing 3 dimension 8 nodes reduction integration solid element (C3D8R) simultaneously sleeper unit adopts enhancing hourglass control; Railway roadbed, embankment and bed course adopt mole of-coulomb of yield criteria and 3 dimensions 8 node reduction integration solid element (C3D8R), and wherein railway roadbed and embankment adopt and strengthen hourglass control; Foundation soil adopts modified Cam-clay and 3 dimensions 8 node reduction integration solid element (C3D8R).The grid of model adopts Meshing Method heterogeneous, and load action region adopts the tessellated mesh then uniform grid of the both sides employing to the left and right size along transversal section; Vertically by pile cover end face, progressively increase size of mesh opening downwards, pile cover end face upwards adopts uniform grid size;
(5) arrange the boundary condition of model, in Fig. 5 (a), model surrounding adopts infinite element 10 to simulate absorbing boundary; Model bottom adopts fixed boundary 11, the degree of freedom in constraint x, y, z three directions, bottom surface;
(6) equivalent load step one calculated, is not added on the surface of contact that each sleeper contacts with rail with the form of even distributed force with the similar M type wavelength-division of Fig. 4, shows the dynamic response of solver computation structure with ABAQUS;
(7) result of calculation of getting the model centre position shown in Fig. 5 a is analyzed.Fig. 6 show train by under front action of static load and under equivalent High-speed Train Loads along the distribution of vertical stress in weak soil center upwards embankment, in figure, dotted line is the distribution curve of gravity stress Υ h.Under action of static load, vertical stress starts consistent with the result starting to reduce finally to start again to increase this and Hewlett & Randolph soil arch theory after gravity stress curve co-insides to certain depth.Under equivalent High-speed Train Loads, vertical stress is consistent with variation tendency under action of static load after embankment surface is first reduced by a certain value.Fig. 7 to show under quiet Under Dynamic Load along weak soil center upwards embankment inner coefficient of earth pressure K value (K=σ h/ σ v, the ratio of horizontal stress and vertical stress) distribution situation.Can find out that K value increases above K gradually after K value remained on about 0.5 to certain depth before this under action of static load p for embankment fill material angle of internal friction) after reduce gradually, this is consistent with the numerical simulation result that Zhuan Yan etc. is published on " ArabianJournalofGeosciences " for 2014.Under Under Dynamic Load, K value variation tendency is consistent with static load but numerical value is all little than static load result, and under Under Dynamic Load is described, soil arching effect can weaken.Fig. 8 to show under quiet Under Dynamic Load the relative settlement of the upwards embankment along stake top and weak soil center, as can be seen from the figure within the scope of certain depth, relative settlement is 0, after being less than a certain degree of depth, pile head settlement starts to reduce, the sedimentation of weak soil central upper starts to increase, and bottom embankment, relative settlement reaches maximal value.Under Under Dynamic Load, sedimentation variation tendency but sedimentation value similar to static load is than large in static load situation.Can show that from result figure model of the present invention holds water.

Claims (1)

1., for a design-calculated Ballast track high-speed railway modeling Analysis method, it is characterized in that comprising the following steps:
(1) structure is regarded as by rail and its under each structural sheet connected to form by discrete sleeper, Train induced load is delivered to substructure by sleeper discrete one by one, rail is regarded as act on Euler-Bernoulli beam on Winkler ground with this to calculate train by time equivalent load to substructure;
(2) extract the geometric parameter of each structure except rail except, apply the finite element model that finite element software ABAQUS sets up sleeper, railway roadbed, embankment, bed course, stake and subsoil soil;
(3) material properties and cell attribute is given and grid division to each structure;
(4) arrange contact and the boundary condition of model, stake contacts with foundation soil the plane-plane contact adopted in interaction, and model surrounding adopts infinite element to simulate absorbing boundary, and bottom surface adopts fixed boundary;
(5) apply to calculate the train equivalent load got on sleeper, utilize ABAQUS explicit solution device to carry out Cable Power Computation.
Described step (1) is specially: to be regarded as by Ballast track high-speed railway and connected to form by sleeper by the railway roadbed under rail and its, and train load is delivered in the railway roadbed of bottom, embankment and ground by sleeper discrete one by one and goes.Rail is regarded as act on Euler-Bernoulli beam on Winkler ground with this to calculate train by time each axle carry acting force to each sleeper, the equivalent action power of whole train to this sleeper is tried to achieve in the acting force superposition then each axle being loaded in same sleeper;
Described step (2) is specially: extract except rail according to Ballast track high-speed railway typical section, the geometric parameter of sleeper, railway roadbed, embankment, bed course, foundation soil and stake, utilizes ABAQUS finite element software to set up the finite element model of each structure except rail;
Described step (3) is specially: sleeper and stake adopt elastic model simulation, and employing 3 dimension 8 nodes reduction integration solid element (C3D8R) simultaneously sleeper unit adopts enhancing hourglass control; Railway roadbed, embankment and bed course adopt mole of-coulomb of yield criteria and 3 dimensions 8 node reduction integration solid element (C3D8R), and wherein railway roadbed and embankment adopt and strengthen hourglass control; Foundation soil adopts modified Cam-clay and 3 dimensions 8 node reduction integration solid element (C3D8R), the grid of model adopts Meshing Method heterogeneous, and load action region adopts the tessellated mesh then uniform grid of the both sides employing to the left and right size along transversal section; Vertically by pile cover end face, progressively increase size of mesh opening downwards, pile cover end face upwards adopts uniform grid size;
Described step (4) is specially: according to the actual conditions of Ballast track high-speed railway typical section, and at the plane-plane contact of the stake of interaction module installation and foundation soil, model surrounding adopts infinite element simulation absorbing boundary; Model bottom surface adopts the degree of freedom in fixed boundary constraint x, y, z three directions;
Described step (5) is specially: step 1 is calculated the train that gets and be added on the surface of contact that each sleeper contacts with rail with the form of even distributed force the equivalent load of each sleeper, utilize ABAQUS explicit solution device to carry out Cable Power Computation.
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Cited By (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105354391A (en) * 2015-12-01 2016-02-24 中南大学 Bridge-tunnel transition section continuously welded rail track stability analysis method under extreme temperature condition
CN107092730A (en) * 2017-04-05 2017-08-25 中山大学 Suitable for the three-dimensional infinite element Artificial Boundaries method for building up of Explicit Analysis
CN107180131A (en) * 2017-05-15 2017-09-19 广东工业大学 Method for determining the laser impact intensified thin-wall part Deformation Curvature radius of multiple spot
CN107217133A (en) * 2017-05-27 2017-09-29 广东工业大学 Laser impact intensified Finite Element Method
CN108319753A (en) * 2017-12-25 2018-07-24 浙江大学城市学院 One kind 2.5 ties up triangular finite element metro operation dynamic response computational methods
CN108664707A (en) * 2018-04-17 2018-10-16 西南交通大学 A kind of wheel-rail contact cycle plus-unloading simulating analysis based on finite element modelling
CN110046393A (en) * 2019-03-18 2019-07-23 中铁二院工程集团有限责任公司 A kind of steep gradient ballast track bed method for estimating stability
CN110374145A (en) * 2019-06-27 2019-10-25 广东省水利水电科学研究院 The reduction of finite soil static horizontal loading test determines method, system and storage medium
CN111209701A (en) * 2020-01-02 2020-05-29 中车青岛四方机车车辆股份有限公司 Method and device for simulating strength of rail train body
CN112668087A (en) * 2021-01-11 2021-04-16 武汉理工大学 Ballasted track modeling analysis method and system based on finite element and discrete element coupling

Non-Patent Citations (6)

* Cited by examiner, † Cited by third party
Title
J.I.REAL等: "《Computational considerations of 3-D finite element method models of railway vibration prediction in ballasted tracks》", 《JOURNAL OF VIBROENGINEERING》 *
YAN ZHUANG等: "《Three-dimensional finite element analysis of arching in a piled embankment under traffic loading》", 《ARABIAN JOURNAL OF GEOSCIENCES》 *
刘玮: "《高速铁路桥上有砟轨道力学特性及结构选型研究》", 《中国优秀硕士学位论文全文数据库 工程科技II辑》 *
安杰: "《高速铁路有砟轨道结构状态分析》", 《中国优秀硕士学位论文全文数据库 工程科技II辑》 *
张斌等: "《基于车辆_轨道单元的无砟轨道动力特性有限元分析》", 《铁道学报》 *
王红军等: "高速滑车立环轨道的有限元建模和分析", 《北京机械工业学院学报》 *

Cited By (15)

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CN105354391B (en) * 2015-12-01 2018-06-12 中南大学 Bridge tunnel changeover portion CWR Track Stability analysis method under extreme temperature conditions
CN105354391A (en) * 2015-12-01 2016-02-24 中南大学 Bridge-tunnel transition section continuously welded rail track stability analysis method under extreme temperature condition
CN107092730A (en) * 2017-04-05 2017-08-25 中山大学 Suitable for the three-dimensional infinite element Artificial Boundaries method for building up of Explicit Analysis
CN107180131B (en) * 2017-05-15 2020-10-16 广东工业大学 Method for determining deformation curvature radius of multipoint laser shock peening thin-walled part
CN107180131A (en) * 2017-05-15 2017-09-19 广东工业大学 Method for determining the laser impact intensified thin-wall part Deformation Curvature radius of multiple spot
CN107217133A (en) * 2017-05-27 2017-09-29 广东工业大学 Laser impact intensified Finite Element Method
CN107217133B (en) * 2017-05-27 2018-10-19 广东工业大学 Laser impact intensified Finite Element Method
CN108319753A (en) * 2017-12-25 2018-07-24 浙江大学城市学院 One kind 2.5 ties up triangular finite element metro operation dynamic response computational methods
CN108664707A (en) * 2018-04-17 2018-10-16 西南交通大学 A kind of wheel-rail contact cycle plus-unloading simulating analysis based on finite element modelling
CN108664707B (en) * 2018-04-17 2021-04-09 西南交通大学 Finite element simulation-based wheel-rail contact circulation loading and unloading simulation analysis method
CN110046393A (en) * 2019-03-18 2019-07-23 中铁二院工程集团有限责任公司 A kind of steep gradient ballast track bed method for estimating stability
CN110374145A (en) * 2019-06-27 2019-10-25 广东省水利水电科学研究院 The reduction of finite soil static horizontal loading test determines method, system and storage medium
CN111209701A (en) * 2020-01-02 2020-05-29 中车青岛四方机车车辆股份有限公司 Method and device for simulating strength of rail train body
CN111209701B (en) * 2020-01-02 2023-09-12 中车青岛四方机车车辆股份有限公司 Rail train body strength simulation method and device
CN112668087A (en) * 2021-01-11 2021-04-16 武汉理工大学 Ballasted track modeling analysis method and system based on finite element and discrete element coupling

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