CN110457728A - A kind of scanning search Calculating method of earth pressure - Google Patents
A kind of scanning search Calculating method of earth pressure Download PDFInfo
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Abstract
A kind of scanning search Calculating method of earth pressure, so that soil pressure distribution not by the constraint of slope surface boundary condition and ground load form, largely saves the time and improves working efficiency.Include the following steps: 1. to establish coordinate system, slope surface after wall and road bed are segmented by fixed spacing, calculates scanning search boundary, successively obtain several coordinate point sets；It is assumed that wall heel O point and road bed are met at a little, OA is connectediTwo o'clock obtains assuming plane of fracture OAi；2. seeking the self weight and center of gravity of rupture rib body, coordinate method calculation assumption plane of fracture OA is utilizediWith wall antiform at rupture rib body self weight and focus point coordinate；3. seeking load self weight and its position on the road bed of ground；4. calculating soil pressure and position of action point, soil pressure and its position that rupture rib body and load generate are calculated；5. repeat step 2.~step 4., successively calculate all plane of fracture OA0,OA1,......OAnGenerated Coulomb's earth pressure, from all plane of fracture OA0,OA1,......OAnIn generated soil pressure or tilting moment, maximum value is selected.
Description
Technical field
The present invention relates to civil engineering, in particular under the various Complex Sloping forms of a kind of rapid solving and load situation
Scanning search Calculating method of earth pressure.
Background technique
In railway, highway subgrade construction, need to build a large amount of supporting constructions come bracing reinforcement banket or hillside soil
Body, prevention and treatment collapse to ensure road structure safety, and soil pressure refers to the main external force of guide structure design.
Currently, most common soil pressure distribution theory is coulomb and Rankine's earth pressure theory in design.Soil body after wall
The variation of slope surface form is limited, and when load form is few, and the soil pressure distribution that can be directly derived according to existing Coulomb block effect is public
Formula calculates soil pressure, and reckoner corresponding to the relevant industries specification such as railway, highway gives part calculation formula, with
For " railway engineering designing technique handbook ", the linear type wall under different operating conditions is carried on the back, wall under segmental back and type of discounting
Back provides that 110 groups of calculation formula are selective altogether, but these formula are with the difference on landing ground stratum and the variations of overcharge on ground
Form is different, uses and inconvenient.When slope surface is complicated or load form multiplicity, calculation of boundary conditions has exceeded existing public affairs
When the range of formula, need to derive new calculation formula again.Currently, existing formula boundary condition has certain simplification,
The reason is that the derivation of equation of soil pressure is extremely difficult due under complicated boundary condition, it is under specific, changeable boundary condition
Derivation formula is lost more than gain and different is surely derived by.
To sum up, there is an urgent need to propose that one kind can consider each arbitrary boundary conditions and can guarantee that calculated result is accurate
Calculating method of earth pressure.
Summary of the invention
Technical problem to be solved by the invention is to provide a kind of scanning search Calculating method of earth pressure, so that soil pressure
It calculates not by the constraint of slope surface boundary condition and ground load form, calculated result is accurate, and convenience of calculation, when largely saving
Between and improve working efficiency.
It is as follows that the present invention solves technical solution used by the above technical problem:
A kind of scanning search Calculating method of earth pressure of the invention, includes the following steps:
1. establishing coordinate system, slope surface after wall and road bed are segmented by fixed spacing, including slope surface knick point, lotus
Carry edge, in load, the outer key point of load, be that coordinate origin establishes coordinate system using wall heel O point, calculating scanning search boundary, according to
It is secondary to obtain several coordinate point set { A0,A1,......,An, i.e. { (x0,y0),(x1,y1)......(xn,yn)}；It is assumed that wall is called in person
O point and road bed meet at point Ai(xi,yi), connect OAiTwo o'clock obtains assuming plane of fracture OAi；
2. seeking the self weight and center of gravity of rupture rib body, coordinate method calculation assumption plane of fracture OA is utilizediWith wall antiform at it is broken
Split self weight and the focus point coordinate of rib body；
3. seek load self weight and its position on the road bed of ground, when it is assumed that the plane of fracture and wall back between roadbed
There are when load, seek the self weight of its load and topocentric coordinates on face；When no-load on the road bed between the plane of fracture and wall back
When, self weight is taken as 0；
4. calculating soil pressure and position of action point, according to Coulomb's earth pressure general formula, calculates rupture rib body and load produces
Raw soil pressure and its position；
5. repeat step 2.~step 4., successively calculate all plane of fracture OA0,OA1,......OAnGenerated coulomb
Soil pressure, from all plane of fracture OA0,OA1,......OAnIn generated soil pressure or tilting moment, maximum value is selected.
The invention has the advantages that soil pressure distribution is by the constraint of slope surface boundary condition and ground load form, it can
To calculate different operating conditions (general, immersion, earthquake operating condition), different wall antiform formula (straight lines according to the universal calculation equation derived
Wall under wall, broken line type on type wall back, broken line type) under, the soil pressure under nearly all slope surface form and load situation；Compared to
Traditional Coulomb's earth pressure equation, calculated result is accurate, and convenience of calculation, largely saves the time and improves working efficiency.
Detailed description of the invention
This specification includes following 4 width attached drawing:
Fig. 1 is road bed stepwise schematic views in scanning search limit；
Fig. 2 linear type Wall back pressure and position calculate schematic diagram；
Fig. 3 segmental back soil pressure and position calculate schematic diagram；
Wall back pressure and position calculate schematic diagram under Fig. 4 broken line type.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples.
Referring to Fig.1, a kind of scanning search Calculating method of earth pressure of the invention, includes the following steps:
1. establishing coordinate system, slope surface after wall and road bed are segmented by fixed spacing, including slope surface knick point, lotus
Carry edge, in load, the key points such as load is outer, be that coordinate origin establishes coordinate system using wall heel O point, calculating scanning search boundary,
Successively obtain several coordinate point set { A0,A1,......,An, i.e. { (x0,y0),(x1,y1)......(xn,yn)}；It is assumed that wall
Heel O point and road bed meet at point Ai(xi,yi), connect OAiTwo o'clock obtains assuming plane of fracture OAi；
2. seeking the self weight and center of gravity of rupture rib body, coordinate method calculation assumption plane of fracture OA is utilizediWith wall antiform at it is broken
Split self weight and the focus point coordinate of rib body；
3. seek load self weight and its position on the road bed of ground, when it is assumed that the plane of fracture and wall back between roadbed
There are when load, seek the self weight of its load and topocentric coordinates on face；When no-load on the road bed between the plane of fracture and wall back
When, self weight is taken as 0；
4. calculating soil pressure and position of action point, according to Coulomb's earth pressure general formula, calculates rupture rib body and load produces
Raw soil pressure and its position；
5. repeat step 2.~step 4., successively calculate all plane of fracture OA0,OA1,......OAnGenerated coulomb
Soil pressure, from all plane of fracture OA0,OA1,......OAnIn generated soil pressure or tilting moment, maximum value is selected.
2. the step carries out as follows:
(2.1) counterclockwise, each micro- section of triangle area OA is successively calculatednAn-1,......,OA2A1,OA1A0And
Summation obtains rupture rib body self weight Wsoil, it is calculated as follows:
In formula: WsoilFor the self weight for rupturing rib body, S is the area for rupturing rib body, and γ is ground severe after wall, and n is coordinate
Point number；
(2.2) the rupture rib weight heart (C is calculatedx,Cy), it is calculated as follows:
In formula: CxTo rupture rib weight heart abscissa, CyTo rupture rib weight heart ordinate.
4. the step carries out as follows:
(4.1) the sum of self weight that the load on the self weight of rupture rib body and rupture rib body generates and total centre of gravity coordinate are calculated；
(4.2) form calculus Wall back pressure and position are carried on the back according to wall.
Referring to Fig. 2 and Fig. 3, in the step (4.2), linear type and segmental back soil pressure and position are by as follows
Formula calculates:
Ey=Ex tan(δ-α)
Zy=Zx·tanα
In formula: ExThe horizontal earth pressure born is carried on the back by wall, W is the gravity for rupturing rib body and the roadbed within the plane of fracture
The gravity that load generates on face, θiThe angle of the plane of fracture and vertical plane that generate in ground is carried on the back for wall,It is comprehensive that ground is carried on the back for wall
Internal friction angle, δ are that wall carries on the back angle of friction, and α is grading angle, EyThe vertical earth pressure born is carried on the back by wall,For total centroid point with
The horizontal intersection point abscissa of the plane of fracture, xcFor total centroid point abscissa；
Referring to Fig. 4, in the step (4.2), Wall back pressure position is by the rupture rib bodily form heart under under broken line type
The projection of wall is found out, and Wall back pressure is calculated as follows under broken line type:
E2y=E2x tan(δ-α)
In formula: E2xThe horizontal earth pressure born, E are carried on the back by wall under broken line type2yIt is vertical to be born by wall back under broken line type
To soil pressure, W2The gravity that load generates on the road bed within gravity and the plane of fracture to rupture rib body, R1For on fold-line-shaped
Wall carries on the back counter-force, βiFor upper first plane of fracture of wall, θ is the angle that lower wall carries on the back the plane of fracture and vertical plane that generate in ground, δ2For under
Wall carries on the back angle of friction, α2For lower grading angle.
Soil pressure distribution of the present invention, can be according to being derived not by the constraint of slope surface boundary condition and ground load form
Universal calculation equation calculate under different operating conditions, different wall antiform formulas, the soil pressure under nearly all slope surface form and load situation
Power.Compared to traditional Coulomb's earth pressure equation, convenience of calculation largely saves the time and improves working efficiency.Wall antiform formula
It can be carried on the back for wall under linear type wall back, segmental back, broken line type, slope surface and load can be arbitrary form after wall, calculate work
Condition is general operating condition, immersion operating condition or earthquake operating condition.The Earth Pressure derived is committed step of the invention, is broken
The position for splitting the Gravity calculation of rib body and the calculating of center of gravity and overcharge on ground calculates, and the key of calculation method of the present invention
Content.
Embodiment 1: linear type wall back
Calculating parameter: linear type wall back, if the high 4m of wall, wall back slope rate is 1:0.25, rolling earth behind retaining wall bulk density γ=19kN/
m3, internal friction angleRetaining walls carry on the back angle of friction δ=17.5 ° with soil, width of the subgrade surface 5.5m after wall, road bed
On have even overloading q=60.8kN/m2, Load Distribution Width l0=3.7m, K=0.9m.
1, coordinate system is established using wall heel O point as coordinate origin, it is wide to calculate the road bed in boundary by the spacing of 0.001m
Degree is segmented, and coordinate point set { A is successively obtained0,A1......A4716, i.e., (1.000,4), (1.001,4) ...,
(4.716,4)}。
2, assume that the plane of fracture and road bed intersection point are located at Ai(xi, 4), connection wall heel point O point and AiAs the hypothesis plane of fracture
OAi；This example introduces scanning search Calculating method of earth pressure process by taking i=2308 as an example, at this time assume angle of rupture θ=
39.591°。
3, coordinate method calculation assumption plane of fracture OA is utilizediThe gravity and focus point of the rupture rib body formed with the soil body after wall
Coordinate.The rupture rib body of this example is triangle, and three angular coordinates are respectively as follows: O (0,0), A2(3.308,4)、A1(Isosorbide-5-Nitrae), meter
Calculate the self weight of rupture rib body and the rupture rib weight heart (Cx,Cy):
4, there are loads on the road bed between the plane of fracture and wall back, calculate load gravity and centroid projection coordinate:
Load width l=2.308-0.9=1.408 (m)；
Q=lq=1.408 × 60.8=85.6064 (kN)
Load graph centroid is in road bed subpoint coordinate (2.604,4).
5, according to Coulomb's earth pressure general formula, calculate level that rupture rib body and load generate retaining walls back and
Vertically to soil pressure and its position.
Calculate the sum of gravity of broken rib body and load and barycentric coodinates:
W=Wsoil+ Q=173.3114 (kN)；
According to Coulomb's earth pressure general formula, rupture rib body and load are calculated to the level of retaining walls back generation and is erected
Directly to soil pressure and its position:
Ey=ExTan (δ-α)=2.844 (kN)
Zy=ZxTan α=0.319 (m)
6, repeat step 3~step 5, successively to i=0,1,2 ..., 4716 totally 4718 planes of fracture be scanned
It calculates, this algorithm implementation procedure need to be realized by computer programming.Finally search out in 4718 planes of fracture Coulomb's earth pressure and
Tilting moment.
7, from Coulomb's earth pressure caused by 4718 planes of fracture that scanning obtains or tilting moment, maximum value is selected,
Ex=46.984 (kN).
2 fold-line-shaped wall back wall of embodiment
Calculating parameter: the high 4m of balance weight retaining wall, it is 0.4 that upper wall, which accounts for full wall ratio, and upper wall back slope rate is 1:0.55, lower wall
Back slope rate is 1:0.25, and wall chest ratio of slope is 1:0.05, the wide 1.12m of weight platform, rolling earth behind retaining wall bulk density γ=19kN/m3, interior friction
AngleRetaining walls are carried on the back and angle of friction δ=17.5 ° of soil, width of the subgrade surface 8m after wall, have on road bed and uniformly surpass
Carry 60.8kN/m2, Load Distribution Width l0=3.7m, K=0.9m.
1, it is that coordinate origin establishes coordinate system with wall heel O ' point, the road bed in boundary will be calculated by the spacing of 0.001m
Width is segmented, and coordinate point set { A is successively obtained0,A1......A4285, i.e., (- 2.000,1.6), (- 1.999,
1.6),......,(2.285,1.6)}.Wherein, the second angle of rupture αiCalculating point set is { A0,A1......A1999,A2000, the
One angle of rupture βiCalculating point set is { A2000,A2002......A4284,A4285}。
2, assume that second plane of fracture and first plane of fracture meet at point A with road bed respectivelyi(xi, 1.6) and Aj(xj,1.6)
(wherein i=0,1,2 ..., 2000；J=2000,2002 ..., 4285).This example is with i=1167, j=2833
Example introduces the scanning search Calculating method of earth pressure process of two broken faces, assumes the second angle of rupture α=27.503 ° at this time, and first is broken
Split angle beta=27.503 °.
3, first plane of fracture of coordinate method calculation assumption O'A is utilizedjWith the second plane of fracture O'AiThe weight of the rupture rib body of formation
Power and focus point coordinate.The rupture rib body of this example is triangle, and three angular coordinates are respectively as follows: O'(0,0), A2(0.833,
1.6)、A1(- 0.833,1.6) calculate the self weight of rupture rib body and the rupture rib weight heart (Cx,Cy):
4, there are loads on the road bed between the plane of fracture and wall back, calculate load gravity and centroid projection coordinate:
Load width l=0.833 × 2=1.666 (m)；
Q=lq=1.666 × 60.8=101.2928 (kN)；
Load graph centroid is in road bed subpoint coordinate (0,1.6).
5, according to Coulomb's earth pressure general formula, calculate level that rupture rib body and load generate retaining walls back and
Vertically to soil pressure and its position.
Calculate the sum of gravity of broken rib body and load and barycentric coodinates:
W1=Wsoil+ Q=126.616 (kN)；
According to Coulomb's earth pressure general formula, rupture rib body and load are calculated to the level of retaining walls back generation and is erected
Directly to soil pressure and its position:
Ey=ExTan (δ+α)=63.308 (kN)；
Zy=ZxTan α=- 0.389 (m)；
6, step 3~step 5 is repeated, is successively calculated under all first and second plane of fracture combinations, corresponding coulomb soil pressure
Power and tilting moment.
7, it is combined in generated Coulomb's earth pressure or tilting moment from all planes of fracture that scanning obtains, selects broken line
Wall soil pressure or tilting moment maximum value, E in shapex=32.952 (kN).
3 fold-line-shaped wall of embodiment carries on the back lower wall
The Coulomb's earth pressure of wall under load retaining wall is calculated using the balance weight retaining wall parameter in embodiment 2.By calculating,
The corresponding angle of rupture group of upper wall maximum Coulomb's earth pressure is combined into α=27.503 °, β=27.503 °, and plane of fracture position is i=
1167, j=2833, calculating counter-force is
1, the coordinate system of example 2 is continued to use, i.e., the above wall wall heel point O ' is origin, will calculate boundary by the spacing of 0.001m
Interior width of the subgrade surface is segmented, and coordinate point set { A is successively obtained0,A1......A6913, i.e., (- 2.000,1.6), (-
1.999,1.6),......,(4.913,1.6)}。
2, assume that the plane of fracture and road bed intersection point are located at Am(xm, 4), connection wall heel point O and AiAs the hypothesis plane of fracture
OAi；This example introduces wall scanning search Calculating method of earth pressure process under fold-line-shaped by taking m=4073 as an example, assumes the plane of fracture at this time
θ=33.753 °.
3, coordinate method calculation assumption plane of fracture OA is utilizedmThe weight of the rupture rib body formed with lower wall back and first plane of fracture
Power and focus point coordinate.The quadrangle that the rupture rib body of this example surrounds, four angular coordinates be respectively as follows: O ' (0,0), O (-
0.6, -2.4), C (2.073,1.6), B (0.833,1.6) calculate the self weight of rupture rib body and the rupture rib weight heart (Cx,Cy):
At this point, the lower wall plane of fracture and road bed intersection point A4073With the upper wall plane of fracture and road bed intersection point A2833Distance dZ=
4.073-2.833=1.24 (m).
Referring to Fig. 4, rupture rib body is divided into two triangle O ' CB, OCO ', by rupturing the rib bodily form heart in the throwing of lower wall
Shadow seeks lower wall soil pressure point of force application:
Zx1=1.0646 (m)；
4, there are loads on the road bed between the plane of fracture and wall back, calculate load gravity and centroid projection coordinate:
Load width l=dz=1.24 (m)；
Q=lq=1.24 × 60.8=63.232 (kN)；
Load graph centroid is in road bed subpoint coordinate (1.453,1.6).
5, according to Coulomb's earth pressure general formula, calculate level that rupture rib body and load generate retaining walls back and
Vertically to soil pressure and its position.
Calculate the sum of gravity of broken rib body and load and barycentric coodinates:
W2=Wsoil+ Q=132.3844 (kN)；
Referring to Fig. 4, load is projected into lower wall and is carried on the back, the acting force arm of load is obtained.
By solving, load action arm of force Zxq=1.2 (m)；
According to Coulomb's earth pressure general formula, rupture rib body and load are calculated to the level of retaining walls back generation and is erected
Directly to soil pressure and its position:
E2y=E2x·tan(δ2-α2)=2.551 (kN)
Zy=Zxtanα2=0.2579 (m)；
6, step 3~step 5 is repeated, calculating successively is scanned to the plane of fracture, finally calculates all Coulomb's earth pressures
And tilting moment.
7, it from Coulomb's earth pressure caused by all planes of fracture that scanning obtains or tilting moment, selects under fold-line-shaped
Wall soil pressure or tilting moment maximum value.
Claims (5)
1. a kind of scanning search Calculating method of earth pressure, includes the following steps:
1. establishing coordinate system, slope surface after wall and road bed are segmented by fixed spacing, including slope surface knick point, load side
In edge, load, the outer key point of load, be that coordinate origin establishes coordinate system using wall heel O point, calculate scanning search boundary, successively must
To several coordinate point set { A0,A1,......,An, i.e. { (x0,y0),(x1,y1)......(xn,yn)}；It is assumed that wall heel O point with
Road bed meets at point Ai(xi,yi), connect OAiTwo o'clock obtains assuming plane of fracture OAi；
2. seeking the self weight and center of gravity of rupture rib body, coordinate method calculation assumption plane of fracture OA is utilizediWith wall antiform at rupture rib body
Self weight and focus point coordinate；
3. seek load self weight and its position on the road bed of ground, when it is assumed that the plane of fracture and wall back between road bed on deposit
In load, the self weight of its load and topocentric coordinates are sought；When no-load on the road bed between the plane of fracture and wall back, will be self-possessed
It is taken as 0；
4. calculating soil pressure and position of action point, according to Coulomb's earth pressure general formula, calculates rupture rib body and load generates
Soil pressure and its position；
5. repeat step 2.~step 4., successively calculate all plane of fracture OA0,OA1,......OAnGenerated coulomb soil pressure
Power, from all plane of fracture OA0,OA1,......OAnIn generated soil pressure or tilting moment, maximum value is selected.
2. preferred a kind of scanning search Calculating method of earth pressure as described in claim 1, it is characterized in that: 2. the step is pressed
Following steps carry out:
(2.1) counterclockwise, each micro- section of triangle area OA is successively calculatednAn-1,......,OA2A1,OA1A0And sum,
Obtain rupture rib body self weight Wsoil, it is calculated as follows:
In formula: WsoilFor the self weight for rupturing rib body, S is the area for rupturing rib body, and γ is ground severe after wall, and n is coordinate points
Number；
(2.2) the rupture rib weight heart (C is calculatedx,Cy), it is calculated as follows:
In formula: CxTo rupture rib weight heart abscissa, CyTo rupture rib weight heart ordinate.
3. preferred a kind of scanning search Calculating method of earth pressure as described in claim 1, it is characterized in that: 4. the step is pressed
Following steps carry out:
(4.1) the sum of self weight that the load on the self weight of rupture rib body and rupture rib body generates and total centre of gravity coordinate are calculated；
(4.2) form calculus Wall back pressure and position are carried on the back according to wall.
4. preferred a kind of scanning search Calculating method of earth pressure as claimed in claim 3, it is characterized in that: the step
(4.2) in, linear type and segmental back soil pressure and position are calculated as follows:
Ey=Ex tan(δ-α)
Zy=Zx·tanα
In formula: ExThe horizontal earth pressure born is carried on the back by wall, W is to rupture lotus on the gravity of rib body and the road bed within the plane of fracture
Carry the gravity generated, θiThe angle of the plane of fracture and vertical plane that generate in ground is carried on the back for wall,The comprehensive interior friction of ground is carried on the back for wall
Angle, δ are that wall carries on the back angle of friction, and α is grading angle, EyThe vertical earth pressure born is carried on the back by wall,For total centroid point and the plane of fracture
Horizontal intersection point abscissa, xcFor total centroid point abscissa.
5. preferred a kind of scanning search Calculating method of earth pressure as claimed in claim 3, it is characterized in that: the step
(4.2) in, Wall back pressure position is found out by the rupture rib bodily form heart in the projection of lower wall under broken line type, and wall is carried on the back under broken line type
Soil pressure is calculated as follows:
E2y=E2xtan(δ-α)
In formula: E2xThe horizontal earth pressure born, E are carried on the back by wall under broken line type2yIt is born by wall back under broken line type vertically to soil pressure
Power, W2The gravity that load generates on the road bed within gravity and the plane of fracture to rupture rib body, R1It is anti-for wall back on fold-line-shaped
Power, βiFor upper first plane of fracture of wall, θ is the angle that lower wall carries on the back the plane of fracture and vertical plane that generate in ground, δ2It carries on the back and rubs for lower wall
Angle, α2For lower grading angle.
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| CN114818070A (en) * | 2022-04-29 | 2022-07-29 | 西南交通大学 | Active soil pressure determination method for balance weight type retaining wall |
| CN114912177A (en) * | 2022-05-13 | 2022-08-16 | 中铁二院工程集团有限责任公司 | Coulomb soil pressure simplified calculation method considering load effect |
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