CN104268373A - Method for calculating active earth pressure of inter-pile retaining plates of support piles - Google Patents

Abstract

The invention discloses a method for calculating the active earth pressure of inter-pile retaining plates of support piles. According to the main operation procedures, a three-dimensional sliding wedge-shaped body model for earth body collapse damage behind the inter-pile retaining plates is established, the internal energy loss coefficient and the external load power of a three-dimensional earth body instability mechanism are worked out, and the relationship between the earth pressure P of the inter-pile retaining plates and the feature angle beta of the three-dimensional sliding wedge-shaped body model is obtained according to the limit analysis principle that the internal energy loss coefficient is equal to the external load power, wherein the maximum value of P relative to beta is the active earth pressure of the inter-pile retaining plates. The method can be used for calculating the active earth pressure of the inter-pile retaining plates and inter-pile retaining walls of the support piles.

Description

A kind of breast boards earth pressure computation method between stake of support pile

Technical field

The present invention relates to Geotechnical Engineering field.

Background technology

Support pile is a kind of soil body retaining structure conventional in slope project and base pit engineering.Because support pile is the discontinuous soil-baffling structure of a kind of horizontal direction, when the soil body between two exists free face, under the effect of outer load and soil body self gravitation, local slump may occur inter-pile soil destroys.For guaranteeing the stability of the soil body between two, enable that gear system is permanently effective runs, general needs arranges breast boards between two.

Between support pile stake, breast boards earth pressure gauge typical three-dimensional problem at last, cannot adopt plane strain to suppose.At present, between stake, breast boards soil pressure distribution mainly adopts " planization silo method ", this method is based on the Janssen formula in mechanics of granular media, think when breast boards be located to face sky side before stake time, the calculating of breast boards load keeps off a sidewall of the silo formed to calculate the earth pressure at rest suffered by it by planization one by stake, between soil arch and stake.The method supposition is encircleed by stake, soil and between stake, a silo sidewall that gear forms is not subjected to displacement and is out of shape.

But, between support pile-stake in breast boards system, for giving full play to soil arching effect, soil pressure is delivered on support pile more, between stake, breast boards generally to be selected between the less thin plate of rigidity or support pile-stake and to be adopted flexibly connecting of allowing to deform between breast boards, also between stake, can backfill sand on rear side of breast boards thus form cushion.Under the external load effects such as gravity, on rear side of breast boards, the soil body can form a slide wedge body, and moves to baffle plate direction.The soil pressure now acted on breast boards is not the earth pressure at rest that " planization silo method " obtains, but closer to active earth pressure." planization silo method ", owing to have employed the supposed premise different from actual conditions, can not obtain data exactly.

Summary of the invention

The object of the invention is to solve when the soil body forms a slide wedge body on rear side of breast boards, more adequately can not calculate the problem of breast boards soil pressure between support pile stake.

The technical scheme adopted for realizing the object of the invention is such, and a kind of breast boards earth pressure computation method between stake of support pile, is characterized in that, comprise the following steps:

1) three-dimensional coordinate system is set up:

Soil body free face arranges some support piles perpendicular to surface level, arranges the breast boards perpendicular to surface level between two adjacent support pile A and support pile B; After setting up three-dimensional system of coordinate, the end face of the described soil body is the x0y face of three-dimensional coordinate, and soil body free face is the x0z face of three-dimensional coordinate;

If after described breast boards soil body generation slump below, by formation slump face, described slump face is regarded as a regular three-dimension curved surface approx; The soil body that above described slump face, slump falls is slide mass; Described slide mass is regarded as a regular three-dimensional graph approx;

The intersection of described slump face and soil body end face is para-curve AE ₀b, wherein, E ₀for para-curve summit, A point and B point are the summit of support pile A and support pile B respectively; The initial point O of three-dimensional system of coordinate is the mid point of A point and B point line, OE ₀perpendicular to AB; Bottom, described slump face is G _opoint, OG _operpendicular to AB;

2) get parms:

OE ₀equaling breast boards height between stake is that h, AB equal clear distance w between stake, and soil body severe is γ, and soil body cohesive strength is c, and soil body angle of internal friction is oG _owith E ₀g _oangle β;

3) breast boards active earth pressure P between stake _afor:

According to this formula, try to achieve the maximal value P of P for β _a; Namely the active earth pressure P acted between stake on breast boards is obtained _avalue.

What deserves to be explained is, between support pile-stake in breast boards system, because each component (or coupling part of component) has elasticity, make the soil body on rear side of breast boards can form a slide wedge body, and move to baffle plate direction.The present invention by Modling model, and takes into full account above-mentioned dynamic process, is namely obtained the active earth pressure acted between support pile stake on breast boards by above-mentioned steps.The method is also applicable to the situation of retaining wall between stake.

Accompanying drawing explanation

Fig. 1 is inter-pile soil body three-dimensional slump surface model schematic diagram;

Fig. 2 is three-dimensional slip unstability mechanism's vertical view and side view;

Fig. 3 is that three-dimensional slipping plane simplifies process.

Embodiment

Below in conjunction with drawings and Examples, the invention will be further described, but should not be construed the above-mentioned subject area of the present invention and be only limitted to following embodiment.Without departing from the idea case in the present invention described above, according to ordinary skill knowledge and customary means, make various replacement and change, all should be included in protection scope of the present invention.

Embodiment 1:

Breast boards earth pressure computation method between the stake that the present embodiment discloses a kind of support pile, and its derivation is disclosed.

1) set up three-dimensional coordinate system, namely first set up the support pile inter-pile soil body slump unstability mechanism meeting speed consistency condition.：

Soil body free face arranges some support piles perpendicular to surface level, arranges the breast boards perpendicular to surface level between two adjacent support pile A and support pile B; After setting up three-dimensional system of coordinate, the end face of the described soil body is the x0y face of three-dimensional coordinate, and soil body free face is the x0z face of three-dimensional coordinate;

If after described breast boards soil body generation slump below, by formation slump face, described slump face is regarded as a regular three-dimension curved surface approx; The soil body that above described slump face, slump falls is slide mass; Described slide mass is regarded as a regular three-dimensional graph approx;

The intersection of described slump face and soil body end face is para-curve AE ₀b, wherein, E ₀for para-curve summit, A point and B point are the summit of support pile A and support pile B respectively; The initial point O of three-dimensional system of coordinate is the mid point of A point and B point line, OE ₀perpendicular to AB; Bottom, described slump face is G _opoint, OG _operpendicular to AB;

What deserves to be explained is, the foundation setting up above-mentioned model can obtain from the engineering site of reality.In the present embodiment, between stake, on rear side of breast boards, the three-dimensional slump surface model of soil body local buckling is as shown in Figure 1.As shown in Figure 2, the slump face in this model adopts bus to generate along the method for directrix translation, and wherein directrix is defined as the intersection of slump face and soil body end face, uses para-curve AE ₀b represents; Bus is defined as slump face and the intersection of vertical plane being parallel to coordinate plane yoz, and adopting with vertical plane xoz angle is the straight line E of β _ig _irepresent, such straight line has made altogether n+1 bar, wherein i=0,1,2 ... n, n are natural number, the intersection point (E of soil body end face after each root bus and stake _i) all at directrix AE ₀on B.Symmetrical section Up Highway UHW E between stake ₀g ₀end points G ₀be positioned at the lower limb at inter-pile soil body free face (i.e. the interface of breast boards and the soil body).The geometry entity that the interface of breast boards and the soil body, soil body end face and three-dimensional slump face surround to be between stake slide wedge body model (described slide mass) on rear side of baffle plate.

2) get parms:

In accompanying drawing 2 representation models, OE ₀equaling breast boards height between stake is that h, AB equal clear distance w between stake, and soil body severe is γ, and soil body cohesive strength is c, and soil body angle of internal friction is oG _owith E ₀g _oangle β;

3) breast boards soil pressure P between stake is obtained:

Under the external load effects such as gravity, the trend of the oriented breast boards direction movement of slide wedge body.According to associated flow rule, the speed V of slide wedge body and the angle of bus are ignore the friction between breast boards and the soil body, then breast boards to the reacting force P horizontal force of slide wedge body on sphenoid.

According to Theory of Limit Analysis, when slide mechanism internal energy coefficient of losses is equal with external load power, mechanism is in critical stable state.

The internal energy coefficient of losses of slide mechanism is made up of the energy dissipation on the energy dissipation on three-dimensional slump face and breast boards-slide wedge body interface.When ignore rub between breast boards and the soil body, only need to calculate the energy dissipation rate on three-dimensional slump face.

Energy dissipation rate on direct calculating three-dimensional slump face is comparatively difficult, processes further slide wedge body based on differential thought.Using the plane of symmetry between stake for getting the half of slide wedge body as research object in interface, make one group of equidistant vertical plane being parallel to coordinate surface yoz and be divided into n thin slice, the width of each thin slice is (w/2n).Each vertical plane and directrix AE ₀b intersects at E ₀, E ₁..., E _n.Cross E ₀, E ₁..., E _ndoing with xoz vertical plane angle is the inclined-plane of β, thus forms dimensional slip folding face (Fig. 3) carrying out approximate directrix with right angle folding.

After carrying out above-mentioned approximate processing, the energy dissipation rate D on slump face changes the energy dissipation rate D calculating cascaded surface and be parallel to the part of bus into _iwith the energy dissipation rate of cascaded surface vertical portion.

By reference to the accompanying drawings 2 with accompanying drawing 3 representation models, if directrix equation is

y＝ax ²+b (1)

In formula, a and b is constant.Because A, B two point coordinate are known, OE ₀length be htan β,

Therefore a and b can be tried to achieve by the method for undetermined coefficients: b=htan β.

Obtain following geometric relationship further:

$O{E}_i=-\frac{4h\tan \mathrm{\β}}{w^2}{(i\·\frac{w}{2n})}^2+h\tan \mathrm{\β}---\left(2\right)$

$E_0{G}_0=\sqrt{h^2+{\left(h\tan \mathrm{\β}\right)}^2}---\left(3\right)$

OE ₀＝htanβ (4)

$E_i{G}_i=h(1-\frac{i^2}{n^2})\sqrt{1+\mathrm{ta}{n}^{2\mathrm{\β}}}---\left(5\right)$

$O{G}_i=h(1-\frac{i^2}{n^2})---\left(6\right)$

When the energy dissipation rate of face tilt part is rolled in computer memory slip, velocity reversal and the slipping plane angular separation at each point place are meet associated flow rule.Therefore, its energy dissipation rate can by the area in this face with cohesion c and and tangential velocity continued product calculate.The energy dissipation rate in each tilt slide bar face is

During the energy dissipation rate of computer memory slip folding face vertical portion, because rigid body speed V is parallel to coordinate plane yoz, the angle of speed V and sliding surface is 0, does not meet the requirement of Coulomb materials to narrow transition bed, is therefore regarded as the narrow transition bed of Tresca material.The energy absorbing device sum calculating vertical fillet slipping plane according to the narrow transition bed of Tresca material is

$D_{\mathrm{OEG}}=\frac{1}{2}O{E}_0\·O{G}_0\·V\·c---\left(8\right)$

Can be obtained by above derivation, for the translation unstability mechanism shown in Fig. 2, the gross energy coefficient of losses D along slipping plane is

Can be obtained by aforementioned computation model, the power W of each thin slice gravity acting of slide wedge body _giequal the vertical component of speed and the product of thin slice soil body weight,

The power W of slide wedge body gravity acting _gfor

Between stake, breast boards to the power that the reacting force of sphenoid does work is

Make internal energy coefficient of losses equal with external load power, then

Geometric relationship formula (2) ~ (6) Suo Shi is substituted into (13) Shi Ke get:

When n trends towards infinity

$\mathrm{li}{m}_{n\→\∞}\underset{i=0}{\overset{n-1}{\mathrm{\Σ}}}\left[(1-\frac{i^2}{n^2})\frac{1}{n}\right]=\frac{2}{3}---\left(15\right)$

$\mathrm{li}{m}_{n\→\∞}\underset{i=0}{\overset{n-1}{\mathrm{\Σ}}}\left[(1-\frac{i^2}{n^2})\frac{1}{n}\right]=\frac{8}{15}---\left(16\right)$

Formula (15), (16) are substituted into formula (14) and obtain

When geometric parameter and physical parameter known, formula (17) reflects the relation of breast boards soil pressure P between β angle and stake.The β angle that the maximal value of P is corresponding is least stable slide wedge body.Now the maximal value of P is breast boards active earth pressure between stake and with joint efforts, is designated as P _a.

Claims (1)

1. a breast boards earth pressure computation method between the stake of support pile, is characterized in that, comprise the following steps:

1) three-dimensional coordinate system is set up:

Soil body free face arranges some support piles perpendicular to surface level, arranges the breast boards perpendicular to surface level between two adjacent support pile A and support pile B; After setting up three-dimensional system of coordinate, the end face of the described soil body is the x0y face of three-dimensional coordinate, and soil body free face is the x0z face of three-dimensional coordinate;

If after described breast boards soil body generation slump below, by formation slump face, described slump face is regarded as a regular three-dimension curved surface approx; The soil body that above described slump face, slump falls is slide mass; Described slide mass is regarded as a regular three-dimensional graph approx;

The intersection of described slump face and soil body end face is para-curve AE ₀b, wherein, E ₀for para-curve summit, A point and B point are the summit of support pile A and support pile B respectively; The initial point O of three-dimensional system of coordinate is the mid point of A point and B point line, OE ₀perpendicular to AB; Bottom, described slump face is G _opoint, OG _operpendicular to AB;

2) get parms:

OE ₀equaling breast boards height between stake is that h, AB equal clear distance w between stake, and soil body severe is γ, and soil body cohesive strength is c, and soil body angle of internal friction is oG _owith E ₀g _oangle β;

3) breast boards active earth pressure P between stake _afor:

Obtain P according to this formula and the active earth pressure P acted between stake on breast boards is for the maximal value of β _asize.