CN101968414A - Method and system for analyzing deformation damage safety of ground well casing - Google Patents

Abstract

The invention belongs to the technical field of ground gas extraction, and in particular to a method and a system for analyzing deformation damage safety of a ground well casing for extracting ground gas. The method is used for effectively analyzing the deformation damage safety of the ground well casing by effectively integrating various influencing factors and comprises the following steps of: 1, obtaining the maximum settlement displacement of each rock stratum; 2, obtaining the maximum shearing slippage displacement and the maximum separation layer stretching displacement of the well casing at the position of an interface to be analyzed; 3, calculating to obtain the maximum shearing slippage displacement and the maximum separation stretching displacement of the well casing at the position of the interface to be analyzed; 4, calculating the shearing damage safety factor and/or stretching damage safety factor of the well casing at the interface to be analyzed; and 5, when the shearing damage safety factor and/or stretching damage safety factor of the well casing at the interface to be analyzed is less than 1h, judging that the well casing is going to be subjected to shearing damage or stretching damage. The invention can accurately obtain deformation damage safety analysis conclusion of the casing, and provides decision basis for the well design and the development of the protection engineering.

Description

Ground well casing deformation failure safety analysis method and analytic system

Technical field

The invention belongs to ground gas pumping technical field, be specifically related to safety analysis the ground well casing stress deformation destruction of ground gas pumping.

Background technology

In the ground drilling gas pumping engineering, well casing is subjected to effect recurring structure distortion such as rock stratum interlayer shear and absciss layer stretching.Because well casing is generally bullet fragility body materials such as carbon steel, when cannula scissors stress or tension reach and surmount the shear stress allowable of sleeve pipe or drawing stress, stress rupture will take place at the overstressing position in sleeve pipe, thereby cause overlapping tube leakage, gas leakage, also can cause silt to block pipeline when serious, cause drilling well to scrap.

The judgement of the hazard level of ground well casing deformation failure, the position of destruction etc. has crucial effect in drilling well distortion protection works.And, destruction reason complexity many owing to the influence factor of well casing deformation failure, it is passed judgment on and often takes engineering experience to judge, perhaps take to increase substantially the method for casing safety, so not only wasted construction material, improve engineering cost, also made the rationality of drilling well protection works reduce greatly.

Summary of the invention

In view of this, in order to address the above problem, the invention discloses a kind of can effectively comprehensive multiple influence factor, the method that security is effectively analyzed to the ground well casing deformation failure.

The object of the present invention is achieved like this: ground well casing deformation failure safety analysis method comprises the steps:

1) obtains and cover each rock stratum maximum settlement displacement on the stope;

2) the maximum shear sliding displacement and the maximum absciss layer stretching displacement of acquisition interface location well casing to be analyzed;

3) calculate the maximum shear stress and the maximum tensile stress that obtains interface location well casing to be analyzed;

4) calculate the shear failure safety coefficient and/or the fail in tension safety coefficient of well casing at the interface to be analyzed by following formula:

The shear failure safety coefficient:

In the formula: τ _LimThe ultimate shearing stress that can carry for well casing; A is the maximum shear sliding displacement that well casing takes place; E is the well casing elastic modulus; A is 2 times of share zone width; r ₁Be well casing external diameter and internal diameter; T is the wall thickness of well casing; Y be in the well casing share zone maximum shear point apart from the distance at edge, share zone.

The fail in tension safety coefficient:

In the formula: σ _T-limAllow the ultimate tensile stress of carrying for well casing; σ _T-inDrawing stress for the well casing actual bearer; E is the well casing elastic modulus; The well casing microcosmic stretcher strain of ε (y) for taking place because of the rock stratum shearing slip,

Δ w is the maximum absciss layer stretching displacement of the well casing of interface location to be analyzed;

$\mathrm{\Δw}\left(x\right)=(W_{\max }^n-W_{\max }^{n+1}){\∫}_0^{\∞}\frac{1}{r_Y}{e}^{-\mathrm{\π}\frac{{(x-r_Y-s)}^2}{r_Y^2}}\mathrm{ds};$

A is 2 times of share zone width.

5) when the shear failure safety coefficient of well casing at the interface to be analyzed or fail in tension safety coefficient during, judge that shear failure or fail in tension will take place well casing less than threshold value.

Further, in the described step 1), the subsidence P Y-factor method Y that passes through of the maximum settlement displacement of rock stratum is found the solution and is obtained.

Further, described step 2) in, calculate the maximum shear sliding displacement of interface location well casing to be analyzed by following formula:

$u_p={[u^2\left(x\right){\cos }^2\mathrm{\θ}+u^2\left(z\right)]}^{\frac{1}{2}};$

Wherein:

In the above-listed formula: u _pBe the maximum shear sliding displacement;

U (x), u (z) are respectively the stope tendency and move towards the maximum shear sliding displacement of direction;

h ₁Thickness for layer rock stratum on the interface;

w _iBe the maximum settlement displacement of plane, place, compound rock stratum;

Cos θ be the stope superincumbent stratum (x, z) the inclination angle cosine value of initial position relatively after the slippage between the compound rock beam genetic horizon of some place tendency direction,

W (x) ' by

Differentiate obtains;

Y is that the share zone inner sleeve is along self axial length;

r _YBe the mining influence radius at asking interface depth place, the buried depth of getting rock stratum upper surface on the interface is the benchmark buried depth,

H is a back production coal seam depth of burial;

Y for the surface level of asking apart from the degree of depth on the face of land;

R is mining influence half warp on the face of land;

N is an empirical index number.(please replenish span)

Calculate maximum absciss layer stretching displacement by following formula:

$\mathrm{\Δw}\left(x\right)=(W_{\max }^n-W_{\max }^{n+1}){\∫}_0^{\∞}\frac{1}{r_Y}{e}^{-\mathrm{\π}\frac{{(x-r_Y-s)}^2}{r_Y^2}}\mathrm{ds}$

In the formula, r _YMining influence radius for the interface location place;

S is the deviation of inflection point of rock stratum sedimentation;

With

In step 1), close the sedimentation deformation branch of key stratum by the two adjacent groups of P Y-factor method Y calculating.

Further, in the described step 3), calculate the maximum shear stress of interface location well casing to be analyzed by following formula:

In the formula,

A is the maximum shear sliding displacement that well casing takes place;

E is the sleeve pipe elastic modulus;

A is 2 times of share zone width;

r ₁, r ₀Be respectively cover external diameter of pipe and internal diameter;

T is the wall thickness of well casing;

Y is well casing length along its axis in the share zone;

Calculate the interface location maximum tensile stress by following formula:

σ _t＝E[ε(y)+Δw/a]

In the formula,

E is the well casing elastic modulus;

The sleeve pipe microcosmic stretcher strain of ε (y) for taking place because of the rock stratum shearing slip is determined by following formula,

${\mathrm{\ϵ}}_y=\mathrm{\η}(\frac{\frac{{\mathrm{\πu}}_p^2}{4a}\sin \left(\frac{4\mathrm{\πy}}{a}\right)+y}{\sqrt{0.125u_p^2[1-\cos \left(\frac{4\mathrm{\πy}}{a}\right)]+y^2}}-1);$

u _pWell casing maximum shear sliding displacement;

η is the mitigation coefficient to the well casing distortion that the plastic yield of well casing surrounding rock body produces, η=60%～70%;

Y is well casing length along its axis in the share zone;

Δ w is the maximum bed separation displacement of interface location well casing to be analyzed;

A is 2 times of share zone width.

Further, before the described step 1), also comprise the steps: to obtain the division rule of key stratum position and combination key stratum in the stope superincumbent stratum, will have under the key stratum of high risk the interface under the thick-layer rock stratum in the roch layer interface and combination key stratum as interface to be analyzed by following formula:

${\left(q_n\right)}_1=\frac{E_1{h}_1^3({\mathrm{\γ}}_1{h}_1+{\mathrm{\γ}}_2{h}_2+\·\·\·\·\·\·\·\·{\mathrm{\γ}}_n{h}_n)}{E_1{h}_1^3+E_2{h}_2^3+\·\·\·\·\·\·\·\·E_n{h}_n^3}$

In the formula, (q _n) ₁The 1st layer of equivalent load that bear the rock stratum during for consideration n layer rock stratum; E ₁E ₂... E _nBe the 1st layer of elastic modulus to n layer rock stratum; γ ₁γ ₂... γ _nBe the 1st layer of rock unit weight to n layer rock stratum; h ₁h ₂... h _nBe the 1st layer of thickness to n layer rock stratum.

As satisfied (q _N+1) ₁＜(q _n) ₁The time, the 1st～n layer rock stratum is a combination key stratum, the 1st layer of rock stratum is the high-risk roch layer interface down; Simultaneously, in any one combination key stratum, the thickest rock stratum is the high-risk interface down.

Further, described threshold value is 1.

The present invention also discloses a kind of ground well casing deformation failure safety analysis system, comprises

The sedimentation deformation acquisition module is in order to obtain the maximum settlement displacement of covering each rock stratum on the stope;

Shearing slip displacement and absciss layer stretching displacement acquisition module are in order to maximum shear sliding displacement and the maximum absciss layer stretching displacement that obtains interface location well casing to be analyzed;

Shear stress obtains and the drawing stress acquisition module, in order to the maximum shear stress and the maximum tensile stress that obtains interface location well casing to be analyzed;

Deformation failure safety coefficient acquisition module is in order to shear failure safety coefficient and the fail in tension safety coefficient of obtaining interface location well casing to be analyzed;

Ground well casing deformation failure security determination module, when the shear failure safety coefficient of well casing at the interface or fail in tension safety coefficient less than 1 the time, judge that shear failure or fail in tension will take place well casing, export result of determination.

The invention has the beneficial effects as follows: the shear failure safety coefficient and the fail in tension safety coefficient that have made up well casing in ground well casing deformation failure safety analysis method of the present invention and the analytic system, described safety coefficient has reflected the structure safe coefficient, considered that wherein the material of sleeve pipe and structure are to the influence of its mechanical property and the influence of rock layer mechanics environment, can accurately draw the casing deformation breach security and analyze conclusion, for carrying out of ground gas pumping drilling design and protection works provides decision-making foundation.

Description of drawings

In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention is described in further detail below in conjunction with accompanying drawing:

Fig. 1 shows stope superincumbent stratum rectangular beam cross section transversal force distribution schematic diagram;

Fig. 2 shows stope superincumbent stratum rectangular beam cross section shearing stress distribution synoptic diagram;

Fig. 3 shows annular girder cross section shear stress synoptic diagram

Fig. 4 shows ground well casing deformation failure safety analysis method flow synoptic diagram;

Fig. 5 shows ground well casing deformation failure safety analysis system architecture synoptic diagram.

Embodiment

The deformation failure of ground gas pumping drilling well is that the influence that well casing is subjected to the distortion of rock stratum and cement mantle, the changing of the relative positions is drawn, cut, crowded effect and the distortion of corresponding form takes place, and when casing deformation reached utmost carrying ability, destruction deformed.Therefore, similar with the interaction of petroleum casing pipe and rock mass, well cementing of cement material, the ability of ground gas pumping well casing load metamorphism and physics such as the aperture of drilling well, casing wall thickness, casing grade, guide-well cement mantle characteristic, rock soil mass material, geometric parameter are relevant, and this also is the main coupling influence factor of ground gas pumping well casing deformation failure.

But, be subjected to rock mass creep, heating power influence etc. with petroleum drilling engineering and push, the reason of shearing, stretching effect is different, gas pumping well casing distortion in ground has the characteristics of self: the influence of effect of falling because the large scale of seam mining and goaf collapse, generation sedimentation of stope superincumbent stratum and rock stratum slippage, the stratum is stretched as main form of distortion with the changing of the relative positions between the rock stratum and absciss layer, a little less than the influence relatively of extrusion effect.And, in the ground drilling gas pumping engineering practice that each Mining Group is carried out, at bed separation displacement bigger position takes place, the probability that the ground well casing generation destroys is much bigger.Therefore, the deformation failure of ground gas pumping well casing moves drawing of causing, cuts and be deformed into the master with the rock stratum, and its influence factor that is to say the main coupling deformation effect factor of ground gas pumping drilling well deformation failure.

Therefore, next mainly principal elements such as well casing wall thickness, internal diameter, shell material characteristic, cement mantle characteristic, rock soil mass material character are analyzed and verified the rule that influences of drawing, cutting deformation failure of ground gas pumping well casing, and its influence to extrusion effect can directly be used for reference with reference to both being fruitful in the petroleum drilling engineering.

Coupling factor is to the effect that influences of ground drilling deformation failure:

Sleeve pipe how much and material character influence effect

(1) detrusion

The deformation failure that ground well casing follows the stope superincumbent stratum to move is the performance to the comprehensive mechanical function of well casing of a rock stratum, cement mantle.The shearing slip distortion of well casing is " S " type and distributes; The casing deformation pattern can be similar to sine function to be represented, promptly

$u\left(y\right)=A\sin \left(\frac{2\mathrm{\&pi;y}}{a}\right)$ $(0<y<\frac{a}{2})---\left(1\right)$

In the formula:

Y is sleeve pipe length along its axis in the share zone;

U (y) is the perpendicular displacement of y point sleeve pipe;

A is the amplitude of displacement function;

A is relevant with rock stratum physico-mechanical properties and ambient stress, is the wavelength of displacement function, is 2 times of share zone width.

By mechanics of materials deflection of beam deformation principle as can be known, the line of deflection differential equation of beam is

$\frac{d^{2}w}{{\mathrm{dx}}^2}=-\frac{M}{\mathrm{EI}}---\left(2\right)$

In the formula,

W is a deflection of beam distortion amount of deflection;

X is the length coordinate along the beam neutral surface;

M is the moment of flexure of beam;

E is the elastic modulus of beam;

I is the moment of inertia of xsect to neutral axis.

Therefore, the Bending Moment Equations that (1) formula substitution (2) formula is got under the ground well casing shearing slip deformation state is

$M=\frac{4\mathrm{AEI}{\mathrm{\&pi;}}^2}{a^2}\sin \left(\frac{2\mathrm{\&pi;}}{a}y\right)$ $(0<y<\frac{a}{2})---\left(3\right)$

According to mechanics of materials deflection of beam principle, under the transversal force bending condition, existing moment of flexure has shearing again on the beam xsect.On the rectangular cross section beam arbitrary section, shearing Q all overlaps with cross section axis of symmetry x.About the regularity of distribution of shear stress on the xsect, do following hypothesis: 1. the direction of the shear stress of each point all is parallel to shearing Q on the xsect; 2. shear stress evenly distributes along cross-sectional width.According to this hypothesis, be that the shear stress of each point all equates on the horizontal line pq of x at the distance neutral axis, and all be parallel to Q.Again as can be known, on the pr plane that is parallel to neutral line that cuts out by pq, also the τ ' that equates with τ must be arranged, and along width b, τ ' also is equally distributed by shearing stress inter-equal theorem.

With cross section m-n and m ₁-n ₁From beam shown in Figure 1, take out long one period (as shown in Figure 2), carry out force analysis as can be known, at the y direction of principal axis, should satisfy balance equation ∑ Y=0, promptly for dy

N ₂-N ₁-dQ′＝0

After the simplification

${\mathrm{\&tau;}}^{\&prime;}=\frac{\mathrm{dM}}{\mathrm{dy}}\&CenterDot;\frac{S_Z^{*}}{I_{z}b}$

By

And principle such as shear stress is mutual,

$\mathrm{\&tau;}={\mathrm{\&tau;}}^{\&prime;}=\frac{Q{S}_Z^{*}}{I_{z}b}---\left(4\right)$

In the formula,

Q is the shearing on the beam xsect;

I _zBe the moment of inertia of xsect to neutral axis;

For on the cross section apart from neutral axis be beyond the horizontal line of x the part area to the quiet distance of neutral axis.

When beam section was annular, according to the proof of the mechanics of materials, the shear stress of each point and circumference were tangent on the section edges.Like this, on 4 end points of interior external diameter of horizontal string AB, intersect at certain some p on the x axle with the tangent shear stress active line of circumference.

Can suppose that thus the active line of each point shear stress is all by the p point on the AB string.If suppose the vertical component τ of each point shear stress on the AB string again _xEquate, so to τ _x, just identical with the hypothesis that the square-section is done, so can calculate with formula (4), just compare with the beam external diameter hour when the wall thickness of annular girder, can be similar to and think that the width of beam stress face is 2 times a beam wall thickness, therefore, the cross section Calculation Shear formula of annular girder is

$\mathrm{\&tau;}=\frac{Q{S}_Z^{*}}{I_{z}b}---\left(5\right)$

In the formula,

Q is the shearing on the beam xsect;

I _zBe the moment of inertia of xsect, here to neutral axis

For on the cross section apart from neutral axis be beyond the horizontal line of x the part area to the quiet distance of neutral axis, as shown in Figure 3, here

B is 2 times of beam wall thickness, here

r ₀, r ₁Be respectively external diameter in the annular girder.

Acquisition beam shearing Q expression formula and substitution (3.5) formula after (3) formula conversion are got

$\mathrm{\&tau;}=\frac{Q{S}_Z^{*}}{I_{z}b}=\frac{8\mathrm{AE}{\mathrm{\&pi;}}^3[{(r_1^2-x^2)}^{\frac{3}{2}}-{(r_0^2-x^2)}^{\frac{3}{2}}]}{3a^3[{(r_1^2-x^2)}^{\frac{1}{2}}-{(r_0^2-x^2)}^{\frac{1}{2}}]}\cos \left(\frac{2\mathrm{\&pi;}}{a}y\right)---\left(6\right)a$

This promptly is the shearing stress distribution function expression of ground gas pumping drilling well under the shearing slip state.

Therefore, maximum shear expression formula in well casing cross section is

${\mathrm{\&tau;}}_{\max }=\frac{8\mathrm{AE}{\mathrm{\&pi;}}^3(r_1^2+r_1{r}_0+r_0^2)}{3a^3}\cos \left(\frac{2\mathrm{\&pi;}}{a}y\right)=\frac{8\mathrm{AE}{\mathrm{\&pi;}}^3(3r_1^2-3r_{1}t+t^2)}{3a^3}\cos \left(\frac{2\mathrm{\&pi;}}{a}y\right)---\left(6\right)b$

In the formula,

A is the maximum deflection displacement that well casing takes place;

E is the sleeve pipe elastic modulus;

A is relevant with rock stratum physico-mechanical properties and ambient stress, is the wavelength of displacement function, is 2 times of share zone width;

r ₁, r ₀Be respectively cover external diameter of pipe and internal diameter;

T is the wall thickness of well casing.

By (6) a formula as can be known, on the xsect of ground well casing, the parabolic type symmetry that is of shear stress distributes, and on the casing deformation neutral surface, shear stress reaches maximal value; Because in the moving process of rock stratum, ground drilling maximum weighted direction promptly is in the diastrophic direction of well casing, therefore, the sleeve pipe boundary position on the maximum weighted direction, shear stress are zero.

By (6) b formula as can be known, well casing external diameter r1 is constant when ground, and when well casing wall thickness t increased gradually, the casing profile maximum shear was at first gradually and reduces, The time reach minimum value, the variation tendency that increases gradually then.Because the drilling well diameter is often much larger than well casing thickness, casing wall thickness seldom can reach

Minimum data point, therefore, it is big more generally to present the well casing wall thickness in the ground drilling engineering practice, the single Changing Pattern that the casing profile maximum shear is more little.

By (6) b formula as can be known, well casing wall thickness t is constant when ground, and the cover external diameter of pipe is when increasing gradually, and the casing profile maximum shear is at first gradually and reduces,

The time reach minimum value, the variation tendency that increases gradually then.Because ground well casing thickness is generally much smaller than the well casing diameter, the condition possibility that well casing reaches minimum value is less, therefore, it is big more generally to present the drilling well diameter in actual engineering, the single Changing Pattern that well casing xsect maximum shear is big more.

By (6) formula as can be known, the proportional example relation of the elastic modulus E of ground well casing interface shear stress and sleeve pipe.

By (2) formula as can be known, along with the increase of ground well casing wall thickness, internal diameter and tubing elastic modulus, the bendind rigidity of sleeve pipe increases, thereby makes the amplitude of deflection deformation of well casing to reduce, and promptly coefficient A reduces in (6) b formula.But, see that according to the universal law of well casing model its variation because of the sleeve pipe bendind rigidity that the variation of wall thickness, internal diameter and tubing elastic modulus causes is also little, therefore, can be similar to and think that coefficient A is constant here.The well casing stress that obtains under this disposal route can be bigger than normal, thereby can strengthen the safety coefficient of well casing design to a certain extent.

(2) stretcher strain

In ground drilling stretcher strain, the well casing stretcher strain that produces because of the rock stratum absciss layer is topmost stretching form.Under the situation that absciss layer stretches, be seam mining technology and stope overlying strata situation owing to influence the principal element of absciss layer effect, therefore, can be similar to and think that the stretching action power that well casing is subjected to is certain value.

Therefore, establishing the tensile force that well casing is subjected to is p, and external diameter and wall thickness are respectively r in the sleeve pipe ₁, r ₀, t, then the drawing stress on well casing xsect under the absciss layer stretching action is:

${\mathrm{\&sigma;}}_t=\frac{p}{\mathrm{\&pi;}(r_1^2-r_0^2)}=\frac{p}{\mathrm{\&pi;}(2r_1-t)t}=\frac{p}{\mathrm{\&pi;}(2r_0+t)t}---\left(7\right)a$

According to Hooke's law, well casing xsect drawing stress also can be expressed as under the absciss layer stretching condition:

σ _t＝Eε _s＝E[ε(y)+Δw/a] (7)b

In the formula,

E is the sleeve pipe elastic modulus;

The sleeve pipe microcosmic stretcher strain of ε (y) for taking place because of the rock stratum shearing slip;

Δ w is the maximum bed separation displacement of sleeve pipe cross-section rock stratum;

A is relevant with rock stratum physico-mechanical properties and ambient stress, is the wavelength of displacement function, is 2 times of share zone width.

By the transversal force mechanics of bending analysis of mechanics of materials axial tension and beam as can be known, the drawing stress that produces because of stope superincumbent stratum absciss layer stretching action can be thought approximate being evenly distributed on the well casing xsect, and this satisfies requirement of engineering precision.

By (7) formula as can be known, as ground well casing external diameter r ₁Constant, when well casing wall thickness t increased gradually, the casing profile drawing stress was at first gradually and reduces, at t=r ₁The time reach minimum value, the variation tendency that increases gradually then.Because well casing thickness often much smaller than the well casing external diameter, reaches minimum conditions t=r ₁Possibility very little, therefore, in the span that engineering practice allows, along with the increase of drilling well wall thickness, the drawing stress in ground well casing cross section often is single non-linear decline trend.

By (7) formula as can be known, when casing wall thickness t was constant, the casing profile drawing stress formed non-linear trend of successively decreasing with the increase of cover external diameter of pipe.

If the ultimate bearing shear stress of the material of well casing is τ _Lim, the actual shear stress of sleeve pipe in the moving process of rock stratum is τ _In, then ground well casing shear failure safety coefficient is:

$f_s=\frac{{\mathrm{\&tau;}}_{\lim }}{{\mathrm{\&tau;}}_{\mathrm{in}}}---\left(8\right)a$

(6) b formula substitution following formula is got

$f_s=\frac{{\mathrm{\&tau;}}_{\lim }}{{\mathrm{\&tau;}}_{\mathrm{in}}}=\frac{3a^3{\mathrm{\&tau;}}_{\lim }}{8\mathrm{AE}{\mathrm{\&pi;}}^3(3r_1^2-3r_{1}t+t^2)\cos \left(\frac{2\mathrm{\&pi;}}{a}y\right)}---\left(8\right)b$

If the ultimate bearing drawing stress of the material of well casing is σ _T-lim, the actual drawing stress of sleeve pipe in the moving process of rock stratum be σ _T-in, then ground well casing fail in tension safety coefficient is:

$f_t=\frac{{\mathrm{\&sigma;}}_{t-\lim }}{{\mathrm{\&sigma;}}_{t-\mathrm{in}}}---\left(9\right)a$

(7) formula substitution following formula is got

$f_t=\frac{{\mathrm{\&sigma;}}_{t-\lim }}{{\mathrm{\&sigma;}}_{t-\mathrm{in}}}=\frac{\mathrm{\&pi;t}(2r_1-t){\mathrm{\&sigma;}}_{t-\lim }}{p}=\frac{{\mathrm{\&sigma;}}_{t-\lim }}{E[\mathrm{\&epsiv;}\left(y\right)+\mathrm{\&Delta;w}/a]}---\left(9\right)b$

According to above-mentioned derivation, the ground well casing deformation failure safety analysis method referring to Fig. 4 present embodiment comprises the steps:

1) obtain the division rule of key stratum position and combination key stratum in the stope superincumbent stratum by following formula, will have under the key stratum of high risk the interface under the thick-layer rock stratum in the roch layer interface and combination key stratum as interface to be analyzed:

${\left(q_n\right)}_1=\frac{E_1{h}_1^3({\mathrm{\&gamma;}}_1{h}_1+{\mathrm{\&gamma;}}_2{h}_2+\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;{\mathrm{\&gamma;}}_n{h}_n)}{E_1{h}_1^3+E_2{h}_2^3+\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;E_n{h}_n^3}$

In the formula, (q _n) ₁The 1st layer of equivalent load that bear the rock stratum during for consideration n layer rock stratum; E ₁E ₂... E _nBe the 1st layer of elastic modulus to n layer rock stratum; γ ₁γ ₂... γ _nBe the 1st layer of rock unit weight to n layer rock stratum; h ₁h ₂... h _nBe the 1st layer of thickness to n layer rock stratum.

As satisfied (q _N+1) ₁＜(q _n) ₁The time, the 1st～n layer rock stratum is a combination key stratum, the 1st layer of the next high-risk roch layer interface in rock stratum; Simultaneously, in any one combination key stratum, under the thickest rock stratum high-risk interface, should carry out selective analysis.

2) obtain the maximum settlement displacement of each rock stratum

Under the subcritical extraction situation, the maximum sinking displacement in the face of land can be found the solution by the P Y-factor method Y that depression is estimated, this is a kind of computing method of classics, and concrete solution procedure is as follows,

1. calculate overlying strata comprehensive evaluation FACTOR P;

2. calculate the subsidence coefficient η fully adopt under the condition emotionally;

3. calculate and mainly influence angle tangent tg β and mining influence radius r;

4. calculating flex point moves apart from S;

5. calculate stope and fully exploit space length, the checking stope is inclined to and moves towards the exploitation sufficient degree of direction;

6. calculate the actual subsidence coefficient η in this exploiting field ⁰

7. calculate face of land maximum sinking value

The sedimentation deformation of arbitrary combination key stratum can use the P Y-factor method Y to find the solution equally in the stope superincumbent stratum, and just the parameters such as depth of burial in coal seam will only be considered the combination and the stressing conditions of combination key stratum and following rock stratum thereof.

3) the maximum shear sliding displacement and the maximum absciss layer stretching displacement of acquisition interface location well casing to be analyzed;

Calculate the maximum shear sliding displacement by following formula:

$u_p={[u^2\left(x\right){\cos }^2\mathrm{\&theta;}+u^2\left(z\right)]}^{\frac{1}{2}};$

Wherein:

In the above-listed formula: u _pBe the maximum shear sliding displacement;

U (x), u (z) are respectively the stope tendency and move towards the maximum shear sliding displacement of direction;

h ₁Thickness for layer rock stratum on the interface;

w _iBe the maximum settlement displacement of plane, place, compound rock stratum;

Cos θ be the stope superincumbent stratum (x, z) the inclination angle cosine value of initial position relatively after the slippage between the compound rock beam genetic horizon of some place tendency direction,

W (x) ' by

Differentiate obtains;

Y is that the share zone inner sleeve is along self axial length;

r _YBe the mining influence radius at asking interface depth place, the buried depth of getting rock stratum upper surface on the interface is the benchmark buried depth,

H is a back production coal seam depth of burial;

Y for the surface level of asking apart from the degree of depth on the face of land;

R is mining influence half warp on the face of land;

N is an empirical index number, generally gets 2 in China.

Calculate maximum absciss layer stretching displacement by following formula:

$\mathrm{\&Delta;w}\left(x\right)=(W_{\max }^n-W_{\max }^{n+1}){\&Integral;}_0^{\&infin;}\frac{1}{r_Y}{e}^{-\mathrm{\&pi;}\frac{{(x-r_Y-s)}^2}{r_Y^2}}\mathrm{ds}$

In the formula, r _YMining influence radius for the interface location place;

S is the deviation of inflection point of rock stratum sedimentation;

With

In step 1), close the sedimentation deformation of key stratum by the two adjacent groups of P Y-factor method Y calculating.

(4) by following formula, calculate the maximum shear stress and the maximum tensile stress that obtain interface location well casing to be analyzed, method is as follows:

Wherein, calculate the maximum shear stress of interface location well casing to be analyzed by following formula: ${\mathrm{\&tau;}}_{\max }=\frac{8\mathrm{AE}{\mathrm{\&pi;}}^3(r_1^2+r_1{r}_0+r_0^2)}{3a^3}\cos \left(\frac{2\mathrm{\&pi;}}{a}y\right)=\frac{8\mathrm{AE}{\mathrm{\&pi;}}^3(3r_1^2-3r_{1}t+t^2)}{3a^3}\cos \left(\frac{2\mathrm{\&pi;}}{a}y\right)$

In the formula,

A is the maximum shear sliding displacement that well casing takes place;

E is the sleeve pipe elastic modulus;

A is 2 times of share zone width;

r ₁, r ₀Be respectively cover external diameter of pipe and internal diameter;

T is the wall thickness of well casing;

Y is well casing length along its axis in the share zone;

Calculate the interface location maximum tensile stress by following formula:

σ _t＝Eε _s＝E[ε(y)+Δw/a]

In the formula,

E is the well casing elastic modulus;

The sleeve pipe microcosmic stretcher strain of ε (y) for taking place because of the rock stratum shearing slip is determined by following formula,

${\mathrm{\&epsiv;}}_y=\mathrm{\&eta;}(\frac{\frac{{\mathrm{\&pi;u}}_p^2}{4a}\sin \left(\frac{4\mathrm{\&pi;y}}{a}\right)+y}{\sqrt{0.125u_p^2[1-\cos \left(\frac{4\mathrm{\&pi;y}}{a}\right)]+y^2}}-1);$

u _pWell casing maximum shear sliding displacement;

η is the mitigation coefficient to the well casing distortion that the plastic yield of well casing surrounding rock body produces, η=60%～70%;

Y is well casing length along its axis in the share zone;

Δ w is the maximum absciss layer stretching displacement of interface location well casing to be analyzed;

A is 2 times of share zone width.

5) calculate the shear failure safety coefficient and/or the fail in tension safety coefficient of well casing at the interface to be analyzed by following formula:

The shear failure safety coefficient:

In the formula: τ _LimThe ultimate shearing stress that can carry for well casing; A is the maximum shear sliding displacement that well casing takes place; E is the well casing elastic modulus; A is 2 times of share zone width; r ₁Be well casing external diameter and internal diameter; T is the wall thickness of well casing; Y be in the well casing share zone maximum shear point apart from the distance at edge, share zone.

The fail in tension safety coefficient:

In the formula: σ _T-limAllow the ultimate tensile stress of carrying for well casing; σ _T-inDrawing stress for the well casing actual bearer; E is the well casing elastic modulus; The well casing microcosmic stretcher strain of ε (y) for taking place because of the rock stratum shearing slip,

Δ w is the maximum absciss layer stretching displacement of the well casing of interface location to be analyzed;

$\mathrm{\&Delta;w}\left(x\right)=(W_{\max }^n-W_{\max }^{n+1}){\&Integral;}_0^{\&infin;}\frac{1}{r_Y}{e}^{-\mathrm{\&pi;}\frac{{(x-r_Y-s)}^2}{r_Y^2}}\mathrm{ds};$

A is 2 times of share zone width.

6) when the shear failure safety coefficient of well casing at the interface or fail in tension safety coefficient less than 1 the time, judge that shear failure or fail in tension will take place well casing, give a warning, export result of determination.

Referring to Fig. 5, the ground well casing deformation failure safety analysis system of present embodiment comprises:

The sedimentation deformation acquisition module is in order to obtain the maximum deflection displacement of covering each rock stratum on the stope;

Shearing slip displacement and absciss layer stretching displacement acquisition module are in order to maximum shear sliding displacement and the maximum absciss layer stretching displacement that obtains interface location well casing to be analyzed;

Shear stress obtains and the drawing stress acquisition module, in order to the maximum shear stress and the maximum tensile stress that obtains interface location well casing to be analyzed;

Deformation failure safety coefficient acquisition module is in order to shear failure safety coefficient and the fail in tension safety coefficient of obtaining interface location well casing to be analyzed;

Ground well casing deformation failure security determination module, when the shear failure safety coefficient of well casing at the interface or fail in tension safety coefficient less than 1 the time, judge that shear failure or fail in tension will take place well casing, give a warning, export result of determination.

The above only preferably is not limited to the present invention for of the present invention, and obviously, those skilled in the art can carry out various changes and modification and not break away from the spirit and scope of the present invention the present invention.Like this, if of the present invention these are revised and modification belongs within the scope of claim of the present invention and equivalent technologies thereof, then the present invention also is intended to comprise these changes and modification interior.

Claims (7)

1. ground well casing deformation failure safety analysis method is characterized in that: comprise the steps:

1) obtains and cover each rock stratum maximum settlement displacement on the stope;

2) the maximum shear sliding displacement and the maximum absciss layer stretching displacement of acquisition interface location well casing to be analyzed;

3) calculate the maximum shear stress and the maximum tensile stress that obtains interface location well casing to be analyzed;

4) calculate the shear failure safety coefficient and/or the fail in tension safety coefficient of well casing at the interface to be analyzed by following formula:

The shear failure safety coefficient:

In the formula: τ _LimThe ultimate shearing stress that can carry for well casing; A is the maximum shear sliding displacement that well casing takes place; E is the well casing elastic modulus; A is 2 times of share zone width; r ₁Be the well casing external diameter; T is the wall thickness of well casing; Y be in the well casing share zone maximum shear point apart from the distance at edge, share zone.

The fail in tension safety coefficient:

In the formula: σ _T-limAllow the ultimate tensile stress of carrying for well casing; σ _T-inDrawing stress for the well casing actual bearer; E is the well casing elastic modulus; The well casing microcosmic stretcher strain of ε (y) for taking place because of the rock stratum shearing slip,

Δ w is the maximum absciss layer stretching displacement of interface location well casing to be analyzed;

A is 2 times of share zone width.

5) when the shear failure safety coefficient of well casing at the interface to be analyzed or fail in tension safety coefficient during, judge that shear failure or fail in tension will take place well casing less than threshold value.

2. ground well casing deformation failure safety analysis method as claimed in claim 1 is characterized in that: in the described step 1), the subsidence P Y-factor method Y that passes through of the maximum settlement displacement of rock stratum is found the solution and is obtained.

3. ground well casing deformation failure safety analysis method as claimed in claim 1 is characterized in that: described step 2), calculate the maximum shear sliding displacement of interface location well casing to be analyzed by following formula:

$u_p={[u^2\left(x\right){\cos }^2\mathrm{\&theta;}+u^2\left(z\right)]}^{\frac{1}{2}};$

Wherein:

In the above-listed formula: u _pBe the maximum shear sliding displacement;

U (x), u (z) are respectively the stope tendency and move towards the maximum shear sliding displacement of direction;

h ₁Thickness for rock stratum on the interface;

w _iBe the maximum settlement displacement of plane, place, compound rock stratum;

Cos θ be the stope superincumbent stratum (x, z) the inclination angle cosine value of initial position relatively after the slippage between the compound rock beam genetic horizon of some place tendency direction,

W (x) ' by

Differentiate obtains;

Y is that the share zone inner sleeve is along self axial length;

r _YBe the mining influence radius at asking interface depth place, the buried depth of getting rock stratum upper surface on the interface is the benchmark buried depth,

H is a back production coal seam depth of burial;

Y for the surface level of asking apart from the degree of depth on the face of land;

R is mining influence half warp on the face of land;

N is an empirical index number;

Calculate maximum absciss layer stretching displacement by following formula:

$\mathrm{\&Delta;w}\left(x\right)=(W_{\max }^n-W_{\max }^{n+1}){\&Integral;}_0^{\&infin;}\frac{1}{r_Y}{e}^{-\mathrm{\&pi;}\frac{{(x-r_Y-s)}^2}{r_Y^2}}\mathrm{ds};$

In the formula, r _YMining influence radius for the interface location place;

S is the deviation of inflection point of rock stratum sedimentation;

With

In step 1), close the sedimentation deformation of key stratum by the two adjacent groups of P Y-factor method Y calculating.

4. ground well casing deformation failure safety analysis method as claimed in claim 1 is characterized in that: in the described step 3), calculate the maximum shear stress of interface location well casing to be analyzed by following formula:

In the formula,

A is the maximum shear sliding displacement that well casing takes place;

E is the sleeve pipe elastic modulus;

A is 2 times of share zone width;

r ₁, r ₀Be respectively cover external diameter of pipe and internal diameter;

T is the wall thickness of well casing;

Y is well casing length along its axis in the share zone;

Calculate the interface location maximum tensile stress by following formula:

σ _t＝Eε _s＝E[ε(y)+Δw/a]

In the formula,

E is the well casing elastic modulus;

The sleeve pipe microcosmic stretcher strain of ε (y) for taking place because of the rock stratum shearing slip is determined by following formula,

${\mathrm{\&epsiv;}}_y=\mathrm{\&eta;}(\frac{\frac{{\mathrm{\&pi;u}}_p^2}{4a}\sin \left(\frac{4\mathrm{\&pi;y}}{a}\right)+y}{\sqrt{0.125u_p^2[1-\cos \left(\frac{4\mathrm{\&pi;y}}{a}\right)]+y^2}}-1);$

u _pWell casing maximum shear sliding displacement;

η is the mitigation coefficient to the well casing distortion that the plastic yield of well casing surrounding rock body produces, η=60%～70%;

Y is well casing length along its axis in the share zone;

Δ w is the maximum bed separation displacement of interface location well casing to be analyzed;

A is 2 times of share zone width.

5. ground well casing deformation failure safety analysis method as claimed in claim 1, it is characterized in that: before the described step 1), also comprise the steps: to obtain the division rule of key stratum position and combination key stratum in the stope superincumbent stratum, will have under the key stratum of high risk the interface under the thick-layer rock stratum in the roch layer interface and combination key stratum as interface to be analyzed by following formula:

${\left(q_n\right)}_1=\frac{E_1{h}_1^3({\mathrm{\&gamma;}}_1{h}_1+{\mathrm{\&gamma;}}_2{h}_2+\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;{\mathrm{\&gamma;}}_n{h}_n)}{E_1{h}_1^3+E_2{h}_2^3+\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;E_n{h}_n^3}$

In the formula, (q _n) ₁The 1st layer of equivalent load that bear the rock stratum during for consideration n layer rock stratum; E ₁E ₂... E _nBe the 1st layer of elastic modulus to n layer rock stratum; γ ₁γ ₂... γ _nBe the 1st layer of rock unit weight to n layer rock stratum; h ₁h ₂... h _nBe the 1st layer of thickness to n layer rock stratum.

As satisfied (q _N+1) ₁＜(q _n) ₁The time, the 1st～n layer rock stratum is a combination key stratum, the 1st layer of rock stratum is the high-risk roch layer interface down; Simultaneously, in any one combination key stratum, the thickest rock stratum is the high-risk interface down.

6. ground well casing deformation failure safety analysis method as claimed in claim 1, it is characterized in that: described threshold value is 1.

7. ground well casing deformation failure safety analysis system is characterized in that: comprise

The sedimentation deformation acquisition module is in order to obtain the maximum settlement displacement of covering each rock stratum on the stope;

Shearing slip displacement and absciss layer stretching displacement acquisition module are in order to maximum shear sliding displacement and the maximum absciss layer stretching displacement that obtains interface location well casing to be analyzed;

Shear stress obtains and the drawing stress acquisition module, in order to the maximum shear stress and the maximum tensile stress that obtains interface location well casing to be analyzed;

Deformation failure safety coefficient acquisition module is in order to shear failure safety coefficient and the fail in tension safety coefficient of obtaining interface location to be analyzed;

Ground well casing deformation failure security determination module, when the shear failure safety coefficient of well casing at the interface or fail in tension safety coefficient less than 1 the time, judge that shear failure or fail in tension will take place well casing, export result of determination.

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