CN114510770B - Railway pre-stressed embankment slope stability analysis method - Google Patents
Railway pre-stressed embankment slope stability analysis method Download PDFInfo
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Abstract
The invention discloses a railway pre-stressed road embankment slope stability analysis method, which comprises the following steps: determining geometric shape parameters of the embankment side slope to be calculated, filler strength parameters of each structural layer and reinforcement parameters; calculating the self weight of the track structure and the train load according to the converted soil-column method according to the standard; establishing a prestressed embankment mechanical model; dividing soil strips of the sliding body according to the potential slide surface of the embankment; obtaining additional normal load and additional tangential load of the bottom surface of each soil strip caused by prestress according to an additional stress diffusion method; calculating equivalent strip force between adjacent soil strips by a simple method; calculating normal counter force at the bottom of the soil strips and downward sliding force of the soil strips according to the stress of the soil strips; and calculating the safety coefficient of the prestressed embankment. The analysis method takes a limit balance strip division method as a frame, and comprehensively considers the prestress diffusion effect, the equivalent strip force action, the track self-weight and the train axle weight, so that the safety coefficient of the prestressed embankment can be quickly and efficiently evaluated, and a relevant reinforcement efficiency reference is provided for relevant designs.
Description
Technical Field
The invention relates to the technical field of railway roadbed engineering, in particular to a method for analyzing the stability of a railway pre-stressed embankment slope.
Background
Stability analysis is a key link in embankment and side slope design, but due to the diversity of slope media and anchoring bodies, how prestress is treated as anchoring load in stability analysis is not unified. At present, the common treatment mode in the engineering industry is to consider the influence of the anchoring load on the stress and balance of the directly acting bar block, and ignore the diffusion effect of the anchoring load on other bar blocks. However, in practice the anchoring load is not applied to a single bar or is distributed uniformly, but rather can be spread over a wide range. Therefore, this treatment method does not conform to the actual mechanism of action and has certain drawbacks. For the prestressed embankment, the change of the prestressed reinforcement scheme inevitably has certain influence on the overall stability of the embankment, so that the problem of being worthy of deep exploration is to fully consider the diffusion effect of the prestressed stress and simultaneously quickly and accurately evaluate the prestressed embankment reinforcement effect and obtain the quantified safety coefficient.
Disclosure of Invention
The invention mainly aims to provide a railway pre-stressed embankment slope stability analysis method, which takes a limit balance strip division method as a frame, simultaneously comprehensively considers a pre-stress diffusion effect, an equivalent strip force effect, a track self-weight and a train axle weight, can quickly and efficiently evaluate the pre-stressed embankment safety coefficient and provides a reinforcement efficiency reference for related designs.
Therefore, the method for analyzing the stability of the railway pre-stressed embankment slope comprises the following steps:
s1, determining geometric shape parameters of a embankment slope to be calculated, filler strength parameters of each structural layer and reinforcement parameters;
s2, calculating the self weight of the track structure and the train load according to the standard by a converted soil column method;
s3, establishing a prestressed embankment mechanical model;
simplifying the action effect of the prestress reinforcing device into a horizontally-distributed surface load q acting on the slope surface of the embankment, and further decomposing the action effect into a distributed load q along the normal direction of the slope surface n And load q distributed along the slope tangential direction t The following formula:
f is the steel bar pretensioning force of the prestress reinforcing device, A is the bottom surface area of a side pressure plate of the prestress reinforcing device, L and W are the lengths of the side pressure plate along the longitudinal direction of a line and a slope respectively, and alpha is a slope angle of the embankment;
s4, dividing soil strips of the sliding body according to the potential slide surface of the embankment;
s5, establishing a coordinate system xoz by taking the slope foot of the embankment as an original point o, the normal direction of the embankment slope as a z-axis direction and the slope direction of the embankment as an x-axis direction, and obtaining an additional normal load and an additional tangential load of the bottom surface of each soil bar caused by prestress according to an additional stress diffusion method, wherein the additional normal load and the additional tangential load are as follows:
wherein, Δ F Ni And Δ F Ti Respectively an additional normal load and a tangential load, x, acting on the bottom of the ith soil strip i And x i+1 Respectively is the x-direction coordinate of the top surface start and end points of the ith soil strip, phi i The included angle between the tangential direction and the horizontal direction at the midpoint of the bottom surface of the ith soil strip is formed;
s6, calculating the equivalent inter-strip force acting on the sliding arc curvature center at the bottom of the soil strip by a simple method, wherein the expression is as follows:
wherein, P i And Q i The volume force of the ith soil strip in the vertical direction and the horizontal direction is respectively; x i 、X i+1 、E i And E i+1 For vertical and horizontal forces acting on the ith soil strip, h i Is the height of the ith soil strip gravity center G from the point A, phi i The included angle between the tangent line passing through the point A and the horizontal line, the point A is the intersection point of the vertical line of the gravity center G of the ith soil strip and the sliding arc at the bottom of the ith soil strip, and R is i The curvature radius of the sliding arc at the bottom of the ith soil strip;
s7, calculating normal counter force at the bottom of the soil strips and gliding force of the soil strips according to the stress of the soil strips:
wherein N is i Is the normal counter force at the bottom of the ith soil strip, T i Is the downward slip force of the ith soil strip, T i Equal to the tangential counter force at the bottom of the soil strips;
s8, calculating the safety coefficient of the prestressed embankment
Based on the limit balance principle, the definition of stability and the molar coulomb intensity criterion, and according to the normal reaction force N at the bottom of the obtained soil strips i Glide force T of kneading soil i Obtaining the safety factor F of the prestressed embankment s Expression (c):
wherein j is the total number of the divided soil strips, l i Is the length of the bottom edge of the ith soil strip, c i And
respectively the cohesive force and the internal friction angle of the embankment soil.
Specifically, step S5 specifically includes:
deducing and obtaining the normal stress sigma along the embankment slope direction under the action of the horizontal plane load q at any point M in the prestressed embankment according to the elasticity theory x Normal positive stress sigma of embankment slope along road z And shear stress tau in plane x-z xz Expression:
wherein σ xn 、σ zn And τ xzn Respectively is the normal component load q of any point M in the prestressed embankment with the width d eta n Normal stress along the slope and normal of the embankment and shear stress in the plane x-z under the action of d eta, sigma xt 、σ zt And τ xzt Respectively is a tangential element load q of any point M in the prestressed embankment with the width d eta t d is the net distance from the side pressure plate to the origin of coordinates;
the additional stress caused by the slope surface preloading load at the bottom surface of each soil strip can be obtained by calculation according to the unit stress state, and the following formula is as follows:
wherein σ N And τ N Normal stress of the sliding surface and tangential stress along the tangential direction of the sliding surface are respectively; beta is the included angle between the tangential direction of the sliding surface and the direction of the slope surface.
And then integrating the length of the sliding surface at the bottom of the soil strip to obtain the additional load caused by the preloading on the bottom surface of the soil strip.
Specifically, the geometric parameters include the top width of the embankment, the slope rate, the height of the embankment and the depth of the foundation.
Specifically, the filler strength parameters include an internal friction angle and a cohesive force of the soil body.
Specifically, the reinforcement parameters comprise reinforcement positions, row numbers, steel bar pretensioning force and the bottom surface size of the side pressure plate.
Compared with the prior art, the invention has the following beneficial effects: the method takes a limit balance bar division method as a frame, simultaneously considers the stress diffusion effect of the pre-pressed load in the embankment, and overcomes the defect that the anchoring force is directly acted on a sliding surface as a concentrated force in the conventional anchoring slope stability analysis; and finally, according to the load bearing characteristics of the railway roadbed, when the stability of the embankment is analyzed, the track on the upper part of the roadbed and the train load are considered according to a converted soil-column method, the safety coefficient of the prestressed embankment can be accurately evaluated, and a related reinforcing efficiency reference is provided for related design.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method for analyzing the stability of a railway pre-stressed road embankment slope according to an embodiment of the invention;
FIG. 2 is a diagram illustrating a mechanical model of a pre-stressed embankment constructed according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of the calculation of the additional stress at any point in the prestressed embankment according to the embodiment of the present invention;
FIG. 4 is a schematic view of additional stress on the sliding surface in an embodiment of the present invention;
FIG. 5 is a schematic illustration of the calculation of the additional load on the soil strip in an embodiment of the present invention;
FIG. 6 is a schematic diagram of equivalent strip forces in an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it is to be understood that the terms "central," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," "circumferential," and the like are used in the orientations and positional relationships indicated in the drawings for convenience in describing the invention and to simplify the description, but are not intended to indicate or imply that the device or element so referred to must have a particular orientation, be constructed in a particular orientation, and be operated in a particular manner, and are not to be construed as limiting the invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
As shown in fig. 1, the method for analyzing stability of a railway pre-stressed road bank slope according to an embodiment of the present invention includes:
s1, determining geometric shape parameters of a embankment side slope to be calculated, and filler strength parameters and reinforcement parameters of each structural layer; wherein, the first and the second end of the pipe are connected with each other,
the geometric shape parameters comprise the top width of the embankment, the slope rate, the height of the embankment and the depth of the foundation; the filler strength parameters comprise the internal friction angle and the cohesive force of the soil body; the reinforcement parameters mainly determine the reinforcement position, the row number, the pretension force of the reinforcing steel bars and the bottom surface size of the side pressure plate.
S2, determining the operation axle weight of the line, and calculating the self weight of the track structure and the train load according to the design specification of the heavy haul railway and a converted soil column method; and the self weight of the track structure and the train load can be calculated according to the converted soil column method according to the design specifications of the railway subgrade and the high-speed railway.
S3, establishing a prestressed embankment mechanical model;
as shown in fig. 2, taking a single-row reinforcement scheme as an example, a plane strain mechanics model of a prestressed embankment is established, where F is a steel bar pretension force, a is a bottom surface area of a side pressure plate, L and W are lengths of the side pressure plate along a line longitudinal direction and a slope surface respectively, d is a net distance from the side pressure plate to a slope toe, and α is an embankment slope angle. The action effect of the prestress reinforcing device can be simplified into uniform distribution surface load q acting on the slope surface of the embankment and can be further decomposed into distribution load q along the normal direction of the slope surface n And load q distributed along the slope tangential direction t The following formula:
wherein F is the pretension force of the steel bar; a is the bottom surface area of the side pressure plate, and L and W are the lengths of the side pressure plate along the longitudinal direction of the line and the slope surface respectively; alpha is the embankment slope angle.
S4, taking a limit balance strip division method as a frame, and dividing soil strips of the sliding body according to the potential sliding surface of the embankment;
s5, estimating additional tangential and normal loads of the bottom surfaces of the blocks, which are caused by prestress, according to an additional stress diffusion method; establishing a coordinate system xoz as shown in fig. 3; wherein the origin o is located the embankment toe, and the net distance of prestressing force reinforcing apparatus apart from origin o is d. Distributed load q n And q is t The additional stress induced in the embankment can be pushed according to the elastic theoryAnd (4) calculating, and obtaining the total additional stress at any point M in the prestressed embankment according to the superposition principle.
The normal element load (q) of any point M in the prestressed embankment with the width d eta (see figure 2 (b)) is n d η), i.e. normal and normal stresses along the embankment slope at point M and shear stress (σ) in plane x-z xn 、σ zn And τ xzn ) And the integral can be obtained by Boussinesq formula integration. Similarly, tangential element load (q) t d eta) normal and normal stress of M point along embankment slope and shear stress (sigma) in plane x-z xt 、σ zt And τ xzt ) Can be obtained by integrating Cerrtui formula. Then 6 components are in the range of the load q (namely the interval [ d, d + W ]]) The internal integral is integrated, and the loads in the same direction are superposed, so that the normal stress sigma along the embankment slope direction under the action of the horizontal plane load q at any point M in the prestressed embankment x And the normal positive stress sigma of the slope surface of the embankment along the road z And shear stress tau in plane x-z xz The specific expressions are shown in formulas (4) to (6).
Wherein σ xn 、σ zn And τ xzn Respectively is the normal component load q of any point M in the prestressed embankment with the width of d eta n Normal stress along the slope and normal of the embankment and shear stress in the plane x-z under the action of d eta, sigma xt 、σ zt And τ xzt Respectively is a tangential element load q of any point M in the prestressed embankment with the width of d eta t d eta normal stress and shear stress in plane x-z along embankment slope direction, with origin at embankment slope toe, and prestressThe net distance of the fastening device from the origin is d, and x, z are the coordinates of point M in coordinate system xoz.
When analyzing the stability of the prestressed embankment, the additional normal stress and the additional shear stress on the potential sliding surface of the prestressed embankment need to be further calculated, as shown in FIG. 4; wherein, beta is an included angle between the tangential direction of the sliding surface and the slope surface direction (namely the x direction). The additional normal stress sigma at any point on the sliding surface can be obtained according to the stress state analysis N And additional shear stress tau tangential to the sliding surface N Can be obtained from the respective formulae (7) and (8). The sign of stress in soil mechanics is different from that of material mechanics; the compressive stress is positive and the tensile stress is negative, and the shear stress that has an anti-slip effect is defined as positive.
The geometric relation shows that theta = beta +90 degrees; therefore, the additional normal stress and the shear stress at any point on the sliding surface can also be calculated from the expressions (9) and (10), respectively.
Therefore, the additional normal load (delta F) of the bottom of the ith earth bar on the inner sliding surface of the prestressed embankment Ni ) And tangential load (Δ F) Ti ) Can be calculated from equations (11) and (12) by integration; the ith soil strip is schematically shown in FIG. 5.
Wherein x is i And x i+1 Respectively is the x-direction coordinate of the top surface start and end points of the ith soil strip, phi i Is the included angle between the tangential direction of the midpoint of the bottom surface of the ith soil strip and the horizontal direction.
S6, calculating the equivalent strip force acting on the sliding arc curvature center at the bottom of the soil strip by a simple method;
as shown in FIG. 6, according to the concept of equivalent inter-strip force, the center of curvature O of the sliding arc acting on the bottom of the soil strip can be calculated i The equivalent inter-strip force of (a) is as follows:
wherein, P i And Q i The volume force of the ith soil strip in the vertical direction and the horizontal direction is respectively; x i 、X i+1 、E i And E i+1 For the vertical and horizontal forces acting on the i-th soil strip, h i Is the height of the ith soil strip gravity center G from the point A, phi i An included angle between a tangent line passing through the point A and a horizontal line, wherein the point A is an intersection point of a vertical line of the gravity center G of the ith soil strip and a sliding arc at the bottom of the ith soil strip, and R i The curvature radius of the sliding arc at the bottom of the ith soil strip.
S7, calculating normal reaction force N at the bottom of the ith soil strip i Glide force T of kneading soil i ：
And S8, calculating the safety coefficient of the prestressed embankment.
For potential sliding surface with any shape, according to the limit balance principle, the definition of stability and the molar coulomb intensity criterion, and according to the normal counter force N at the bottom of the obtained soil strip i Glide force T of kneading soil i Obtaining the safety coefficient F of the prestressed embankment s The expression of (a) is as follows:
wherein j is the total number of the divided soil strips, l i Is the length of the bottom edge of the ith soil strip, c i And
respectively the cohesive force and the internal friction angle of the embankment soil.
In order to verify the accuracy and reliability of the method, the stability of the prestressed embankment is analyzed by respectively adopting an FLAC 3D numerical model and the method aiming at the same fixed sliding surface, so that the calculation results of the two are compared. Through comparison, sliding surfaces in the numerical model are all arranged on a preset sliding belt, the obtained safety coefficients are 1.31,1.42 and 1.71 respectively, the difference between the obtained safety coefficients and the obtained safety coefficients obtained by the method is only 1.36%, 1.73% and 1.84%, the two safety coefficients are in good agreement, and therefore the stability analysis method for the railway prestressed embankment slope provided by the application is proved to have sufficient reliability.
Compared with the prior art, the embodiment of the application has the following beneficial effects:
(1) An analytic calculation method for calculating additional normal stress and shear stress on the potential sliding surface of the embankment under any slope rate, different reinforcing loads, different reinforcing positions, different reinforcing device row numbers and different side pressure plate widths is provided based on an elasticity theory.
(2) And establishing a limit balance method for analyzing the stability of the prestressed embankment by simultaneously considering the additional stress diffusion effect and the strip force effect by combining the additional stress meter algorithm, the equivalent strip force meter algorithm and the load bearing characteristic of the railway embankment.
(3) The safety coefficient of the prestressed embankment obtained by analyzing the numerical calculation method is well consistent with the method, and the method has enough reliability when being used for analyzing the stability of the prestressed embankment.
In conclusion, the analysis method takes the ultimate balance strip division method as a framework, and comprehensively considers the prestress diffusion effect, the equivalent strip force action, the track self-weight and the train axle weight, so that the safety coefficient of the prestressed embankment can be quickly and efficiently evaluated, and a relevant reinforcement efficiency reference is provided for relevant designs.
Any embodiment disclosed herein above is meant to disclose, unless otherwise indicated, all numerical ranges disclosed as being preferred, and any person skilled in the art would understand that: the preferred ranges are merely those values which are obvious or representative of the technical effect which can be achieved. Since the number is large and cannot be exhaustive, some of the numbers are disclosed to exemplify the technical solutions of the present invention, and the above-mentioned numbers should not be construed as limiting the scope of the present invention.
Meanwhile, if the invention as described above discloses or relates to parts or structural members fixedly connected to each other, the fixedly connected parts can be understood as follows, unless otherwise stated: a detachable fixed connection (for example using a bolt or screw connection) can also be understood as: non-detachable fixed connections (e.g. riveting, welding), but of course, fixed connections to each other may also be replaced by one-piece structures (e.g. manufactured integrally using a casting process) (unless it is obviously impossible to use an integral forming process).
In addition, terms used in any technical solutions disclosed in the present invention to indicate positional relationships or shapes include approximate, similar or approximate states or shapes unless otherwise stated. Any part provided by the invention can be assembled by a plurality of independent components, or can be manufactured by an integral forming process.
The above examples are merely illustrative for clearly illustrating the present invention and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. Nor is it intended to be exhaustive of all embodiments. And obvious variations or modifications of the invention may be made without departing from the scope of the invention.
Claims (6)
1. A railway prestressed embankment slope stability analysis method is characterized by comprising the following steps:
s1, determining geometric shape parameters of a embankment side slope to be calculated, filler strength parameters of each structural layer and reinforcement parameters;
s2, calculating the self weight of the track structure and the train load according to the standard by a converted soil column method;
s3, establishing a prestressed embankment mechanical model;
simplifying the action effect of the prestress reinforcing device into a load q of a horizontally uniform plane acting on the slope surface of the embankment, and further decomposing the load q into a distributed load q along the normal direction of the slope surface n And load q distributed along the slope tangential direction t ：
F is the steel bar pretensioning force of the prestress reinforcing device, A is the bottom surface area of a side pressure plate of the prestress reinforcing device, L and W are the lengths of the side pressure plate along the longitudinal direction of a line and a slope respectively, and alpha is a slope angle of the embankment;
s4, dividing soil strips of the sliding body according to the potential slide surface of the embankment;
s5, establishing a coordinate system xoz by taking the slope foot of the embankment as an original point o, the normal direction of the embankment slope as a z-axis direction and the slope direction of the embankment as an x-axis direction, and obtaining additional normal load and additional tangential load of the bottom surface of each soil bar, which are caused by prestress, according to an additional stress diffusion method:
wherein, Δ F Ni And Δ F Ti Respectively an additional normal load and a tangential load, x, acting on the bottom of the ith soil strip i And x i+1 Respectively are x-direction coordinates phi of the top surface start and end points of the ith soil strip i Is the included angle between the tangential direction and the horizontal direction at the midpoint of the bottom surface of the ith soil strip, sigma N And τ N Normal stress of the sliding surface and tangential stress along the tangential direction of the sliding surface are respectively;
s6, calculating the equivalent strip force acting on the sliding arc curvature center at the bottom of the soil strip by a simple method, wherein the expression is as follows:
wherein, P i And Q i The volume force of the ith soil strip in the vertical direction and the horizontal direction is respectively; x i 、X i+1 、E i And E i+1 For vertical and horizontal forces acting on the ith soil strip, h i Is the height of the gravity center G of the ith soil strip from the point A, phi i Is the included angle between the tangent line passing through the point A and the horizontal line, and the point A is the vertical line of the gravity center G of the ith soil stripPoint of intersection with sliding arc at bottom of ith soil strip, R i The curvature radius of the sliding arc at the bottom of the ith soil strip;
s7, calculating normal counter force at the bottom of the soil strips and gliding force of the soil strips according to the stress of the soil strips:
wherein N is i Is the normal counter force at the bottom of the ith soil strip, T i The downward sliding force of the ith soil strip;
s8, calculating the safety coefficient of the prestressed embankment
Based on the limit balance principle, the definition of stability and the molar coulomb strength criterion, and according to the obtained normal reaction force N at the bottom of the soil strip i Glide force T of kneading soil i Obtaining the safety factor F of the prestressed embankment s The expression of (c):
wherein j is the total number of the divided soil strips, l i Is the length of the bottom edge of the ith soil strip, c i And
respectively the cohesive force and the internal friction angle of the embankment soil.
2. The method for analyzing the stability of the railway pre-stressed road embankment slope according to claim 1, wherein the step S5 specifically comprises: deducing and obtaining the normal stress sigma along the embankment slope direction under the action of the horizontal plane load q at any point in the prestressed embankment according to the elastic theory x Normal positive stress sigma of embankment slope along road z And in plane x-zShear stress tau xz Expression:
wherein, d σ xn 、dσ zn And d τ xzn Respectively normal element load q of any point in the prestressed embankment with the width d eta n Normal stress along the slope and normal of the embankment under the action of d eta, and shear stress in the plane x-z, d sigma xt 、dσ zt And d τ xzt Respectively is a tangential element load q of any point in the prestressed embankment with the width of d eta t d eta normal stress and tangential stress in plane x-z along the slope of the embankment, d is the net distance from the side pressure plate to the origin of coordinates, x, z are the coordinates of any point in the prestressed embankment in the coordinate system xoz, and sigma is x Positive stress along the embankment slope direction under the action of horizontal plane load q at any point in the prestressed embankment z Is normal stress along the slope surface of the prestressed embankment under the action of horizontal plane load q at any point in the prestressed embankment xz The shear stress of any point in the prestressed embankment in the plane x-z under the action of the horizontal plane load q;
the additional stress caused by the slope surface preloading load at the bottom surface of each soil strip can be calculated according to the unit stress state as follows:
wherein σ N And τ N Normal stress of the sliding surface and tangential stress along the sliding surface are respectively; beta is an included angle between the tangential direction of the sliding surface and the direction of the slope surface;
and then integrating the length of the slip surface at the bottom of the soil strip to obtain the additional load caused by the preloading on the bottom surface of the soil strip.
3. The method for analyzing the stability of the railway pre-stressed road embankment slope according to claim 1 or 2, wherein: the geometric parameters comprise the top width of the embankment, the slope rate, the height of the embankment and the depth of the foundation.
4. The method for analyzing the stability of the railway pre-stressed road embankment slope according to claim 1 or 2, wherein: the filler strength parameters comprise the internal friction angle and the cohesive force of the soil body.
5. The method for analyzing stability of a railway pre-stressed embankment slope according to claim 1 or 2, wherein: the reinforcement parameters comprise reinforcement position, row number, steel bar pretensioning force and side pressure plate bottom surface size.
6. The method for analyzing the stability of the railway pre-stressed road embankment slope according to claim 1 or 2, wherein: the standard is 'design standard of heavy haul railways', 'design standard of railway subgrades' or 'design standard of high speed railways'.
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| CN104120677A (en) * | 2014-07-04 | 2014-10-29 | 河海大学 | Method for dike side slope two-dimensional safety and stability analysis taking shield pass-through influences into consideration |
| CN109543326A (en) * | 2018-11-30 | 2019-03-29 | 浙江大学 | Open mine side slope rock mass discontinuity normal stress is classified the method for determination |
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| CN111814369B (en) * | 2020-06-18 | 2023-04-18 | 中国地质大学（武汉） | Strip division method capable of accurately calculating force inclination angle between strips and stability safety coefficient of side slope |
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| CN104120677A (en) * | 2014-07-04 | 2014-10-29 | 河海大学 | Method for dike side slope two-dimensional safety and stability analysis taking shield pass-through influences into consideration |
| CN109543326A (en) * | 2018-11-30 | 2019-03-29 | 浙江大学 | Open mine side slope rock mass discontinuity normal stress is classified the method for determination |
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| 马学宁 ; 吴培元 ; 王旭 ; 王博林 ; .加筋土边坡稳定性分析水平条分简化计算方法.铁道学报.2017,(第09期),全文. * |
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