CN102930148B - Method for determining piping penetration coefficient based on random start - Google Patents

Abstract

The invention discloses a method for determining a piping penetration coefficient based on random start. The method for determining the penetration coefficient in the piping generation and development process is based on distribution densities or probability functions of a mean speed, a mean particles size of particles and a mean positional relation, based on parameters of mathematical expectation and the like, and based on combination of mechanical analysis. The method has significance for reasonably evaluating the dam safety, predicting an area where penetration damage possibly occurs and the form and reducing the losses caused by the penetration damage.

Description

A kind of piping infiltration coefficient defining method based on random start

Technical field

The invention belongs to seepage action of ground water computing technique field, be specifically related to a kind of piping infiltration coefficient defining method based on random start.

Background technology

In piping research in the past, often visual cognitive ability in the research of mean characteristics (namely in certainty rule), and the randomness that non-pay abundant attention piping occurs, considerable part theoreticians still adopts simple mechanics method to study by inevitable phenomenon, and do not analyze its randomness, so usually cannot explain some actual phenomenons.The randomness of piping is familiar with, can be familiar with from following two aspects: the 1) randomness of movable particle starting; 2) randomness of soil mass property in spatial distribution.

The essence of piping is the process that movable particle moves, constantly runs off under the pulling of current in hole, and the starting of particle in the soil body has contingency.In the ordinary course of things, size and its position of particle and the situation that contacts of other particle and water velocity are all the stochastic variables being difficult to determine in time.Therefore start phenomenon and there is very large contingency.Even if know by the waterpower critical condition of judgement piping in the past and be now in starting state, but due to there is no telling at that time instantaneous velocity, start particle diameter and its position and contact relation, it is the quantitative law being difficult to determine to start particle, that is, if only know average permeate flow velocity, the average grain diameter of particle and mean place relation, its quantitative law is difficult to determine.

Summary of the invention

Goal of the invention: calculate Problems existing for infiltration coefficient in above-mentioned piping generation evolution, the object of the invention is to consider that particle starts on the basis of randomness, proposes the defining method of infiltration coefficient in a kind of piping generation evolution.

Technical scheme: the present invention mainly calculates from thin sight aspect the randomness that movable particle starts, according to average permeate flow velocity, the average grain diameter of particle and the distribution density of mean place relation three or probability function, according to parameters such as mathematic expectaions, in conjunction with the analysis of mechanics, propose the defining method of infiltration coefficient in piping generation evolution.

Piping infiltration coefficient defining method based on random start of the present invention, is characterized in that comprising the steps:

(1) particle of inviscid piping-typed soils is divided into two classes, skeleton particle and movable particle, its cut-off size formula (1) calculates:

$x_a=\frac{{2c}_1}{{2c}_1+1+{2c}_2}\·\frac{A_a}{B_a^2}---\left(1\right)$

In formula: x _afor cut-off size, being greater than this particle diameter is skeleton particle, and being less than is then movable particle; Coefficient c ₁for the form factor of particle; Coefficient c ₂for the coefficient relevant with the packing of soil (for natural rounded sand and gravel, c ₁=0.73, to rock debris, c ₁=1.0; Coefficient c ₂characterize the packing of soil, time the closeest, c ₂=0, c time slightly close ₂=0.05, time the most loose, c ₂=0.18); A _aand B _aformula (2) and formula (3) is used to determine respectively:

$A_a={\∫}_{y_a}^1\frac{y}{x\left(y\right)}\mathrm{dy}-y_a{\∫}_{y_a}^1\frac{\mathrm{dy}}{x\left(y\right)}---\left(2\right)$

$B_a={\∫}_{y_a}^1\frac{\mathrm{dy}}{x\left(y\right)}---\left(3\right)$

In formula: y _afor with cut-off size x _acorresponding movable granule content; Y is the content being less than certain particle diameter x, and x (y) is the particle diameter of corresponding y;

X _asolve and can adopt trial and error procedure or iterative method: first suppose x _ainitial value x _a0, calculate A by formula (2), formula (3) _aand B _a, by A _aand B _abring formula (1) into, obtain an x _a, be designated as x _a1if, x _a0with x _a1differ less, then get the two mean value as x _a, otherwise use x _a1repeat above step;

(2) according to the cut-off size x that formula (1) calculates _a, be less than x _athe average grain diameter of each particle diameter group of movable particle be:

${\stackrel{\‾}{D}}_i=\frac{D_{(i-1)}+D_{\left(i\right)}}{2}---\left(4\right)$

In formula: be i-th can kinetochore group average grain diameter; D _(i-1)and D _(i)be respectively the representative diameter of (i-1) and the i-th particle diameter group;

I-th can the granule number of kinetochore group be:

$N_i=\frac{{6M}_i}{\mathrm{\π}{\stackrel{\‾}{D}}_i^3{\mathrm{\ρ}}_s}---\left(5\right)$

In formula: N _ibe i-th can the granule number of kinetochore group; be i-th can kinetochore group average grain diameter, determined by formula (4); M _ibe i-th can kinetochore group quality, can be determined by grading curve; ρ _sfor movable grain density;

(3) consider the randomness of hole flow rate of water flow, assuming that Normal Distribution, after movable particle runs off, the porosity of the soil body is:

$n^{\′}=\frac{n+\underset{i=1}{\overset{k}{\mathrm{\Σ}}}E{\left(N\right)}_i{V}_i}{1-\underset{i=1}{\overset{k}{\mathrm{\Σ}}}E{\left(N\right)}_i{V}_i}---\left(6\right)$

In formula: the porosity of n ' rear soil body for movable particle runs off; N is original porosity; K is movable particle grouping number; E (N) _ibe i-th desired value can starting numbers of particles in kinetochore group, determined by formula (7); V _ibe i-th can kinetochore group start pore velocity, determined by formula (8);

The desired value of i-th numbers of particles that can start in kinetochore group is:

In formula: E (N) _ibe i-th desired value can starting numbers of particles in kinetochore group; N _ibe i-th can the movable numbers of particles of kinetochore group, determined by formula (5); V _ibe i-th can kinetochore group start pore velocity, determined by formula (8); V ' is average pore flow rate of water flow; σ is standard deviation.

I-th can kinetochore group starting pore velocity be:

In formula: V _ibe i-th can kinetochore group start pore velocity; be i-th can the average grain diameter of kinetochore group, determined by formula (4); ρ _s, ρ _wbe respectively the density of movable particle and fluid; μ be fluid the coefficient of viscosity; θ is the angle of two granular center lines and vertical direction; for the angle of current drag direction and horizontal direction, g is acceleration of gravity;

(4) by movable particle from being carefully k grain group to rough segmentation, then organize remainder particulate quality for i-th by i from 1 value to k, calculate each group residual mass, according to result of calculation, obtain the soil body grading curve upgraded after movable particle runs off.By formula (6) result of calculation and the determined d of grading curve after upgrading _ωbring the coefficient of permeability K that formula (9) obtains the rear soil body of movable particle loss into:

$K=780\frac{{\left(n^{\′}\right)}^3}{{\{1-\left(n^{\′}\right)\}}^3}{d}_{\mathrm{\ω}}---\left(9\right)$

In formula: K is soil body osmotic coefficient after movable particle runs off; d _ωfor equivalent grain size, determine by formula (10):

$\frac{1}{d_{\mathrm{\ω}}}=\underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{M_{d_i}}{d_i}+\frac{3}{2}\frac{M_{d_1}}{d_1}---\left(10\right)$

In formula: d _ibe the average grain diameter of i-th grade of particle diameter, for corresponding to d _ithe particle weight of grain-size grade, d ₁be the 1st group of movable grain diameter.

The present invention compared with prior art, its beneficial effect is: the infiltration coefficient distribution that the inventive method is calculated by said process, owing to considering the randomness that Rock And Soil particle starts, its result more accurately and reliably, and calculates the change procedure that finally can obtain piping and occur to develop by subregion.To rational evaluation embankment safety, the prediction contingent region of seepage failure and form, the loss etc. that minimizing seepage failure causes all has great importance.

Accompanying drawing explanation

Fig. 1 is the layer of sand grading curve that the embodiment of the present invention 1 calculates;

Fig. 2 is dyke model division and the dividing elements figure of the embodiment of the present invention 1 calculating;

The head isogram of piping mouth is there is in Fig. 3 when being the distance levee toe 30m place of the embodiment of the present invention 1 calculating;

Fig. 4 is the piping mouth near zone hydraulic gradient isogram that the embodiment of the present invention 1 calculates;

Fig. 5 is after infiltration coefficient calculating is carried out in region that the embodiment of the present invention 1 pair of gradient is greater than 0.2, the hydraulic gradient isogram of dyke.

Detailed description of the invention

Below technical solution of the present invention is described in detail, but protection scope of the present invention is not limited to described embodiment.

Embodiment 1: the present embodiment has carried out seepage calculation for an embankment.

Embankment adopts homogeneous dike structure, and piled up by homogeneous clay and form, infiltration coefficient is 1 × 10 ^-8m/s, levee foundation upper strata is clay cover layer, and infiltration coefficient is 1 × 10 ^-6m/s, lower floor is layer of sand, and infiltration coefficient is 1.5 × 10 ^-4m/s.Layer of sand physical index in table 1, wherein C _cand C _ube respectively coefficient of curvature and the nonuniformity coefficient of grading curve, G _sfor specific density of solid particles, n is initial porosity, d ₁₀, d ₃₀and d ₆₀be respectively the soil particle diameter corresponding to mass accumulation percentage composition 10%, 30% and 60% being less than certain particle diameter.Grain composition and calculating subregion are shown in Fig. 1 and Fig. 2, and after there is piping mouth, hydraulic gradient distribution results is shown in Fig. 3 and Fig. 4.Get hydraulic gradient and be greater than the scope of 0.2 as computer capacity, its result of calculation is Fig. 5.

Layer of sand physical index in table 1 embodiment of the present invention 1

C c	C u	G s	n	d 10(mm)	d 30(mm)	d 60(mm)
							1.29	7.60	2.68	0.38	0.113	0.355	0.62

According to the inventive method, each step result of calculation is as follows:

(1) c is got ₁=0.73, c ₂=0.05, calculate x through step (1) _a=0.5mm,

(2) movable particle is divided into 3 groups, is respectively 0-0.075mm, 0.075mm-0.25mm, 0.25mm-0.5mm.Particle diameter grouping, average grain diameter, mass content and often organize the result of calculation such as numbers of particles in table 2.

Movable particle grouping situation in table 2 embodiment of the present invention 1.

Particle size range mm	0-0.075	0.075-0.25	0.25-0.5
				Average grain diameter	0.038mm	0.163mm	0.375mm
Shared mass percent	6.2	11	25.2
				1cm 3Middle numbers of particles	1338610	30091	5661

(3) n '=0.5 is calculated through step (3).

(4) through step (4) d _ω=0.449mm, obtains K=0.35.

(5) adopt coefficient of permeability K=0.35, the hydraulic gradient isogram got hydraulic gradient and be greater than the scope of 0.2 can be calculated.

As mentioned above, although represented with reference to specific preferred embodiment and described the present invention, it shall not be construed as the restriction to the present invention self.Under the spirit and scope of the present invention prerequisite not departing from claims definition, various change can be made in the form and details to it.

Claims (2)

1., based on a piping infiltration coefficient defining method for random start, it is characterized in that comprising the steps:

(1) particle of inviscid piping-typed soils is divided into two classes, skeleton particle and movable particle, its cut-off size formula (1) calculates:

$x_a=\frac{{2c}_1}{2c_1+1+2c_2}\·\frac{A_a}{B_a^2}---\left(1\right)$

In formula: x _afor cut-off size, being greater than this particle diameter is skeleton particle, and being less than is then movable particle; Coefficient c ₁for the form factor of particle; Coefficient c ₂for the coefficient relevant with the packing of soil; A _aand B _aformula (2) and formula (3) is used to determine respectively:

$A_a={\∫}_{y_a}^1\frac{y}{x\left(y\right)}\mathrm{dy}-y_a{\∫}_{y_a}^1\frac{\mathrm{dy}}{x\left(y\right)}---\left(2\right)$

$B_a={\∫}_{y_a}^1\frac{\mathrm{dy}}{x\left(y\right)}---\left(3\right)$

In formula: y _afor with cut-off size x _acorresponding movable granule content; Y is the content being less than certain particle diameter x, and x (y) is the particle diameter of corresponding y;

(2) according to the cut-off size x that formula (1) calculates _a, be less than x _athe average grain diameter of each particle diameter group of movable particle be:

${\stackrel{\‾}{D}}_i=\frac{D_{(i-1)}+D_{\left(i\right)}}{2}---\left(4\right)$

In formula: be i-th can kinetochore group average grain diameter; D _(i-1)and D _(i)be respectively the representative diameter of (i-1) and the i-th particle diameter group;

I-th can the granule number of kinetochore group be:

$N_i=\frac{6M_i}{\mathrm{\π}{{\stackrel{\‾}{D}}_i}^3{\mathrm{\ρ}}_s}---\left(5\right)$

In formula: N _ibe i-th can the granule number of kinetochore group; be i-th can kinetochore group average grain diameter, determined by formula (4); M _ibe i-th can kinetochore group quality, can be determined by grading curve; ρ _sfor movable grain density;

(3) consider the randomness of hole flow rate of water flow, assuming that Normal Distribution, after movable particle runs off, the porosity of the soil body is:

$n^{\′}=\frac{n+\underset{i=1}{\overset{k}{\mathrm{\Σ}}}E{\left(N\right)}_i{V}_i}{1-\underset{i=1}{\overset{k}{\mathrm{\Σ}}}E{\left(N\right)}_i{V}_i}---\left(6\right)$

In formula: the porosity of n ' rear soil body for movable particle runs off; N is original porosity; K is movable particle grouping number; E (N) _ibe i-th desired value can starting numbers of particles in kinetochore group, determined by formula (7); V _ibe i-th can kinetochore group start pore velocity, determined by formula (8);

The desired value of i-th numbers of particles that can start in kinetochore group is:

In formula: E (N) _ibe i-th desired value can starting numbers of particles in kinetochore group; N _ibe i-th can the movable numbers of particles of kinetochore group, determined by formula (5); V _ibe i-th can kinetochore group start pore velocity, determined by formula (8); V ' is average pore flow rate of water flow; σ is standard deviation;

I-th can kinetochore group starting pore velocity be:

In formula: V _ibe i-th can kinetochore group start pore velocity; be i-th can the average grain diameter of kinetochore group, determined by formula (4); ρ _s, ρ _wbe respectively the density of movable particle and fluid; μ be fluid the coefficient of viscosity; θ is the angle of two granular center lines and vertical direction; for current drag direction and horizontal direction angle, g is acceleration of gravity;

(4) by movable particle from being carefully k grain group to rough segmentation, then organize remainder particulate quality for i-th by i from 1 value to k, calculate each group residual mass, according to result of calculation, obtain the soil body grading curve upgraded after movable particle runs off;

By formula (6) result of calculation and the determined d of grading curve after upgrading _ωbring the coefficient of permeability K that formula (9) obtains the rear soil body of movable particle loss into:

$K=780\frac{{\left(n^{\′}\right)}^3}{{\{1-\left(n^{\′}\right)\}}^3}{d}_{\mathrm{\ω}}---\left(9\right)$

In formula: K is soil body osmotic coefficient after movable particle runs off; d _ωfor equivalent grain size, determine by formula (10):

$\frac{1}{d_{\mathrm{\ω}}}=\underset{i=2}{\overset{n}{\mathrm{\Σ}}}\frac{M_{d_i}}{d_i}+\frac{3}{2}\frac{M_{d_1}}{d_1}---\left(10\right)$

In formula: d _ibe the average grain diameter of i-th grade of particle diameter, for corresponding to d _ithe particle weight of grain-size grade, d ₁be the 1st group of movable grain diameter.

2. the piping infiltration coefficient defining method based on random start according to claim 1, is characterized in that: in step (1), cut-off size x _asolve and can adopt trial and error procedure or iterative method: first suppose x _ainitial value x _a0, calculate A by formula (2), formula (3) _aand B _a, by A _aand B _abring formula (1) into, obtain an x _a, be designated as x _a1if, x _a0with x _a1differ less, then get the two mean value as x _a, otherwise use x _a1repeat above step.