CN111814369B - Strip division method capable of accurately calculating force inclination angle between strips and stability safety coefficient of side slope - Google Patents
Strip division method capable of accurately calculating force inclination angle between strips and stability safety coefficient of side slope Download PDFInfo
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Abstract
The invention relates to the field of slope stability calculation methods, in particular to a strip division method capable of accurately calculating a force inclination angle between strips and a slope stability safety coefficient. The strip division method for calculating the force inclination angle between strips and the stability safety coefficient of the side slope comprises the following steps: s1, determining calculation parameters according to slope survey data, S2, dividing a slide body of a slope into a plurality of vertical strips, S3, calculating an inclination angle of acting force between the strips, and S4, calculating a slope stability safety coefficient by adopting a semi-accurate strip method or an accurate strip method. The strip division method capable of accurately calculating the dip angle of the force between the strips and the stability safety coefficient of the side slope breaks through the bottleneck that the existing strip division method solves the problem of statically indeterminate by assuming the direction or position of the force between the strips, and theoretically deduces the functional relation between the ratio of the shearing force and the normal force between the strips and the dip angle and the shearing strength parameter of the sliding surface, and between the physical property parameter of the strips and the load based on the Mohr-Coulomb criterion, so that the problem of statically indeterminate strip division method is solved.
Description
Technical Field
The invention relates to the field of slope stability calculation methods, in particular to a strip division method capable of accurately calculating a force inclination angle between strips and a slope stability safety coefficient.
Background
The strip method is developed based on the limit balance theory, is a stability simple and convenient calculation method aiming at slopes (including natural slopes and artificial slopes) which are possibly damaged in a landslide mode, and is widely used for slope stability analysis and slope protection engineering design. Over the last hundred years, tens of fractionation methods have emerged, and the differences of the fractionation methods are summarized as follows: (1) The statics equations used to derive the stability coefficients are different; (2) the assumptions used to determine the problem are different. Based on the difference in the statics equation used to derive the stability factor, the striping method can be divided into two broad categories: one is a semi-precise segmentation method, such as a swedish arc method, a simplified Janbu method, a simplified Bishop method and the like, namely a segmentation method which meets static balance conditions or meets moment balance and partial static balance conditions; another category is the exact method of the bars, such as Janbu, spencer, and M-P, which satisfy both static and moment equilibrium conditions. Because the unknown variables exceed the number of statics equilibrium equations, the existing semi-precision strip method and precision strip method both belong to the problem of statics uncertainty, and when the strip method is used for solving the slope stability coefficient, different hypothesis conditions (basically, the hypothesis conditions can be concluded to the hypothesis strip force inclination angle or the action point position) must be introduced.
(1) The semi-precise strip method for solving the stability coefficient which meets the static balance condition has 4n-1 unknown variables, but only 3n equations can be established, and the difference is n-1 conditions (figure 2):
(1) the overall stability factor fos along the shear plane, counted as 1;
(2) counting the normal reaction force and the tangential reaction force at the bottom of the strip to be 2n;
(3) horizontal force and vertical force between strips, count as 2n-2.
The load and the counter force of the strip satisfy the balance condition (Sigma F) x ＝0,∑F y = 0) and ultimate equilibrium conditions on shear plane
3n equations can be established. The difference of n-1 conditions compared to 4n-1 unknown variables is essentially a static problem. Traditionally, by assuming n-1 unknown conditions to solve:
(1) assuming that n-1 vertical force values between the strips are 0, namely only horizontal force exists between the strips, such as a simplified simple distribution method, a simplified common method and the like;
(2) the ratio of n-1 vertical force values to horizontal force values between strips is assumed, such as an improved transfer coefficient method, a U.S. army and army law and the like;
(3) supposing that n-1 vertical force values and horizontal force values among the strips reach critical states, the method is called a blocking limit balancing method, namely an upper limit solution meeting static balance conditions.
(2) The solution stability coefficient of the precise strip method which simultaneously satisfies the static force and moment balance conditions has 6n-1 unknown variables, but only 4n equations can be established, and the difference is n-1 conditions (figure 2):
(1) the overall stability coefficient k along the shear plane is counted as 1;
(2) counting the normal reaction force and the tangential reaction force of the bottom of the strip and the moment of the midpoint of the bottom of the strip as 3n;
(3) the moments of horizontal acting force, vertical acting force and gravity acting on the central point of the bottom of the stripe among the stripes are counted as n +2 (n-1).
The load and the counter force of the strip satisfy the balance condition (Sigma F) x ＝0,∑F y = 0), limit equilibrium condition on shear plane
And moment balance at the midpoint of the bottom of the stripe, 4n equations can be established. When the slivers are sufficiently thin (Δ x) i 0) the moment induced at the bottom of the bar can be ignored and the undetermined variable is reduced by n. And 6n-1 unknownsThe variable is inherently a static and uncertain problem, compared with n-1 unknown conditions, and traditionally, the solution is also carried out by assuming n-1 unknown conditions:
(1) assuming the location of the force action between the bars, such as the method of Janbu;
(2) the ratio of n-1 vertical force values to horizontal force values between the bars is assumed, and the ratio is adjusted by equal proportion or through a certain linear relation, so that the static balance condition and the moment balance condition are simultaneously satisfied, and the solution of the problem is obtained, such as a Spencer method, an M-P method and the like.
The above-mentioned assumptions about the ratio of the shearing force between strips to the normal force or the position of the point of action are not theoretical, and the assumed values are not practical regardless of the magnitude of the load, the geometry of the sliding belt, the strength parameters, etc. Both numerical simulation and actual monitoring results show that the ratio of the shear force between strips and the normal force is related to the geometric shape and the strength parameter of the sliding belt. Duncan (1996) and Duncan and Wright (1980) have indicated that: the result of using only the static balancing method (semi-exact banding) is extremely sensitive to the assumed direction of the inter-band forces, which would cause the calculated stability factor to deviate significantly from the correct value. Although the precision binning method is conditioned on satisfying both static and moment balances, the computational accuracy is improved to some extent by adjusting the above assumptions proportionally or via some linear relationship. However, such adjustment is limited, and the distribution trend of the force direction between the strips or the acting position along the sliding direction and the implicit precondition that the value of the distribution trend is not related to the load size, the geometric shape of the sliding belt, the strength parameter and the like are not changed from the original point, so that the situation that the balance equation is not converged or the calculated stability coefficient deviates from the correct value cannot be avoided. It can be seen that the reasonableness of the assumptions of the inter-bar force application directions (inter-bar force ratios) or the positions of the force points determine the accuracy of the various semi-accurate and accurate bar divisions.
The rationality of the solutions introduced into the postulated striping methods has been of general interest. On the basis of comparing and analyzing different bar method calculation results, morgenstrin & Price originally provides a generally accepted rationality limiting condition of a bar method solution, and the reasonable solution obtained by obtaining the bar method is considered to meet two limiting conditions: (1) no tension is generated between the strips; (2) The shear force acting on the soil strip interface does not exceed the shear strength provided by the mole-coulomb method rule. Meanwhile, morgenstrin & Price also proposed the following reasoning: regarding the different assumptions of the forces acting between the bars, the respective stability factors do not differ much from each other as long as the above-mentioned two rationality constraints are met. Generally, the inference proposed by Morgenstrin & Price is in line with reality, but in the case that the two rationality limiting conditions are met, the difference of the calculation results of different strip methods on the same slope is more than 20%. It should be particularly noted that under the condition of setting the safety coefficient of the working condition, the difference of the design residual slip force calculated by different strip division methods can reach 100%, which cannot be tolerated in the slope stability evaluation and protection engineering design practice. On the other hand, the problem that the equilibrium equation is not converged and has no solution due to the fact that the stripe method, especially the precise stripe method, assumes that the force direction or the action point position between the stripes is not appropriate is common. Therefore, the accurate determination of the force direction or the action point position between the strips is the key for ensuring that the strip division method obtains an accurate and reasonable solution and the designed slope management project is safe, feasible in technology, economical and reasonable.
Disclosure of Invention
In view of the above, the invention provides a semi-precise strip method which can accurately calculate the inter-strip acting force inclination angle and further solve the slope stability safety coefficient based on the static equilibrium equation, and a slope stability analysis precise strip method which enables static and moment balance conditions to be satisfied simultaneously, and the problem of non-convergence of the moment balance equation can be completely solved based on the calculated inter-strip force inclination angle.
The invention provides a striping method capable of accurately calculating an inter-strip force inclination angle and a side slope stability safety coefficient, which comprises the following steps of:
s1, determining calculation parameters according to slope survey data;
s2, dividing a slide body of the side slope into a plurality of vertical strips;
s3, calculating by using the calculation parameters in the step S1 to obtain the inclination angle of the acting force between the strips;
s4, calculating the side slope by adopting a semi-precise strip method or a precise strip methodAnd if a semi-precise segmentation method is adopted, calculating and stopping after the slope stability safety coefficient is obtained, and if the precise segmentation method is adopted, setting an adjustment coefficient v after the slope stability safety coefficient is obtained 1 Simultaneously acquiring horizontal force components among the n-1 strips, and continuing to perform the step S5;
s5, respectively obtaining force arms corresponding to the n-1 inter-strip force horizontal components according to the n-1 inter-strip force horizontal components in the S4, and simultaneously obtaining an adjustment coefficient v 2 ；
S6, setting a calculation precision delta, when | v |) 1 -v 2 When | is ≦ Δ, the calculation is stopped, and when | v ≦ Δ 1 -v 2 If the value is greater than delta, continuing to perform the step S7;
s7, comparing v 1 V and v 2 The value of (a) is recorded as v 1 Let v stand for 1 ＝v 1 +0.618|v 1 -v 2 And then returns to S4, and repeatedly executes the commands of S4-S6 until | v is satisfied 1 -v 2 |≤Δ。
Further, formula (1) -formula (8) are combined to calculate the inclination of the inter-stripe forces in S3, wherein the expressions of formula (1) -formula (8) are respectively as follows:
C i ＝c i /k (6)
in the above formula, i =0,1,2, \8230, n, n is a natural number, i represents a bar number, H Ei Is E i Arm of force of alpha i Angle of inclination of sliding surface (P degree) corresponding to ith strip d Is horizontal seismic force (kN), ξ i The calculated gradient (°) corresponding to the ith strip is provided, theta is a side slope angle (°),
is the inner friction angle (°) of the soil sliding at the bottom of the ith stripe>
The slope angle (degree) of the slope at the position designated for the ith strip, rho is a correction coefficient for calculating the slope, delta is the inclination angle (degree) of the underground water line, and gamma are w Respectively, the natural severe degree and the saturated severe degree (kN) of the synovial body, sin lambda is the ratio of the shear stress to the average stress in the soil body, and->
Wherein σ 1 And σ 3 Maximum and minimum principal stress (kPa) in the earth respectively, snss denotes the earth in the region of the slide adjacent to the slide (thin strip), sin λ snssi Is sin lambda at the ith stripe snss ，α c The slide angle (°) of the slide belt where the snss upper anti-slide force in the slide body is equal to the lower slide force, and the position is selected as->
And c i The internal friction angle (°) of the soil sliding at the bottom of the ith strip) And cohesion force (kPa), phi i And C i Is an intermediate variable, h c And &>
The dip angle of the finger sliding belt is alpha c Thickness (m) of sliding body and height (m), b) of underground water level i Is the width (m), U of the ith stripe i The buoyancy (kN) of the ith stripe bottom surface.
Further, the concrete method for calculating the slope stability safety coefficient by adopting the semi-precise segmentation method in the S4 comprises the following steps:
s41, solving the inter-strip force and slope stability safety coefficient by combining a static balance equation:
the static balance condition comprises balance of force in the horizontal direction and balance of force in the vertical direction;
establishing an xoy coordinate system, wherein the positive direction of an x axis is the horizontal direction of sliding of a sliding body, the positive direction of a y axis is the vertical downward direction, the strips are kept in limit balance by external force and acting force of the left side surface and the right side surface of the adjacent strips, the pulling force of the normal force is defined as negative, the pressure of the normal force is defined as positive, and the balance equation of the forces in the horizontal direction is as follows:
in the formula: alpha is alpha i Representing the slope angle (°) of the sliding surface corresponding to the ith strip,
indicating the normal force, T, acting on the centroid of the ith bar bottom slip surface i semi Represents the shear resistance acting on the centroid of the i-th stripe bottom sliding surface>
Represents the normal component of the force between the lines on the left side of the ith branch, and is based on the value of the normal component of the force between the lines on the left side of the ith branch>
Showing the acting force between the upper strips on the right side of the ith stripNormal component,. Based on>
Represents the horizontal force acting on the centroid of the ith stripe;
the equilibrium equation for the forces in the vertical direction is:
in the formula:
represents the tangential component of the force between the bars on the left side of the ith bar, is greater than or equal to>
Represents the tangential component of the force between the bars on the right side of the ith stripe, W i semi Representing the vertical force acting on the centroid of the ith stripe.
The strip reaches ultimate balance along the sliding surface, the sliding surface at the bottom of the strip meets the Mohr-Coulomb yield criterion, and the yield condition of the sliding surface at the bottom of the strip is as follows:
in the formula: c. C i Shows the cohesive force (kPa), phi of the slip-band soil at the position of the ith stripe surface i The effective stress internal friction angle (DEG), l, of the sliding zone soil at the position of the ith strip surface i The length of the bottom sliding surface of the ith stripe surface is shown;
when the slope stability safety coefficient k is obtained, the sliding force parallel to the sliding surface is multiplied by the stability safety coefficient k by adopting a quasi-overload method, or the cohesive force c and the internal friction angle of the soil body are multiplied by adopting a strength storage method
Dividing by k, the yield condition calculation formula for the bottom slip surface varies as follows:
combining the formulas (12) - (14) and (17), obtaining the slope stability coefficient k through iterative operation.
Further, the specific method for calculating the slope stability safety coefficient by adopting the accurate strip method in the S4 comprises the following steps:
s42, setting the adjusting coefficient v 1 An initial value, by equation (15), is calculated for the stability factor k and the n-1 horizontal components of the force between the bars, E 1 、E 2 …E n-1 And continuing to the next operation, wherein the expression of equation (15) is as follows:
A i ＝(W i -Q i )sinα i +P di cosα i -P ti sin(α i +θ pti )-(U ti -U ti-1 )cosα i (9)
in the above formula, E i And X i The horizontal component and the vertical component (kN) of the interaction force between the ith and (i + 1) th branches, respectively, and when E is i <0, order E i =0, when i =0, e i-1 ＝E 0 ＝0；A i And B i Are all intermediate variables, v is the adjustment coefficient, W i Is the ith strip dead weight (kN), Q i External load (kN), P, to which the ith strip is subjected di Horizontal seismic forces (kN), P, to which the ith stripe is subjected ti Slip resistance (kN), θ, provided for the ith segmented soil retaining structure pti Is P ti Angle (°) from horizontal, c) i Effective cohesive force (kPa), U of soil of the bottom slide zone of the ith stripe ti For the ith stripeWater pressure (kN).
Further, the n-1 horizontal components of the inter-division force obtained in the step S4 are substituted into a formula (11) and a formula (16) to obtain force arms (taking the midpoint of the bottom surface of the division as a centroid) corresponding to the n-1 horizontal components of the inter-division force, and H E1 、H E2 、…、H En-1 While obtaining the adjustment coefficient v 2 Wherein the expressions of formula (11) and formula (16) are as follows:
in the above formula, H Ei The moment arm (m) of the horizontal force component between the ith stripe when i =0 is set as H E0 ＝0，E i-1 ＝E 0 ＝0；D i Is an intermediate variable, H Uti The moment arm (m), H of the water pressure of the ith stripe side surface pdi Moment arm (m), H of horizontal earthquake acting force of ith strip pti Moment arm (m), g) of anti-sliding force provided for ith sub-soil retaining structure i Moment arms (m), e) of buoyancy force borne by the bottom of the ith stripe i Is the moment arm (m) of the self weight and the external load of the ith branch.
The technical scheme provided by the invention has the following beneficial effects: the strip division method capable of accurately calculating the force inclination angle between strips and the stability safety coefficient of the side slope has the following advantages:
(1) The method breaks through the bottleneck that the existing strip division method solves the statically indeterminate problem by means of the direction or the position of the assumed strip-to-strip force, theoretically deduces the ratio of the shearing force and the normal force between the strips, the inclination angle of the sliding surface, the shearing strength parameter, the functional relation between the strip-to-strip physical property parameter and the load based on the Mohr-Coulomb criterion, and ensures that the statically indeterminate problem is obtained. The theoretical basis is solid, the physical significance is very clear, and the method is more scientific and reasonable;
(2) The method of the invention has the biggest difference with the existing striping method that: for the same slope, the calculation working conditions are different, and the magnitude and the distribution of the ratio of the shearing force to the normal force among the strips are also different. The ratio of the shearing force between strips to the normal force is not only related to the shearing strength of the sliding surface, but also influenced by the geometrical boundary condition and the load of the sliding body;
(3) According to the method, the ratio of the shearing force to the normal force among the strips is adjusted by introducing the adjustment coefficient, so that static force and moment balance can be achieved simultaneously for the strips and the whole, and therefore the stability safety coefficient of the landslide or the side slope is obtained, and compared with the existing strip division method, the calculation precision is improved;
(4) The method is suitable for calculating the stability of the landslide of the circular arc sliding surface and the broken line type sliding surface, and can completely solve the problem that the moment balance equation of the existing strip division method is not converged based on the calculated force inclination angle between the strips.
Drawings
FIG. 1 is a flow chart of a striping method for accurately calculating the force inclination angle between stripes and the safety coefficient of slope stability according to the present invention;
FIG. 2 is a graph of force analysis of the strip, h i 、ΔX i And L i Respectively showing the height, width and length of the i-th stripe, W i 、Q i Respectively representing the weight and top of the ith bar, E i 、X i And M i Respectively representing the horizontal acting force and the vertical acting force (kN) between the ith slitting and the moment (kN) N of the gravity acting on the central point of the bottom of the slitting i 、T i And
respectively representing the normal reaction force and the tangential reaction force (kN) of the ith strip bottom and the moment (kN & m) of the ith strip bottom to the midpoint of the strip bottom;
FIG. 3 is a graphical representation of the calculation of slope correction factors, where a is the abscissa (m) of the leading edge of the landslide, b is the abscissa (m) of the trailing edge of the landslide, x i The abscissa (m) of the center point of the ith stripe ground is taken;
FIG. 4 is an engineering geological profile of a circular arc sliding surface landslide: (a) Dongfeng bridge landslide, (b) Dongwan landslide, (c) Dongzhu east landslide;
FIG. 5 is a geological section of a large dam landslide engineering with a broken-line shaped slip surface;
FIG. 6 shows a scheme for dividing the slip body into strips for the circular arc sliding surface: (a) Dongfeng bridge landslide, (b) Dongfuwan landslide, (c) Xingzhu bay landslide;
FIG. 7 shows the inclination angle of the acting force between the slip surface and the strip of the circular arc sliding surface calculated by the method and the numerical simulation method of the present invention: (a) Dongfeng bridge landslide, (b) Dongwan landslide, (c) apricot Bayong landslide;
FIG. 8 is a calculated profile of a large river dam landslide;
FIG. 9 is a graph of the variation of the force inclination angle between bars under different working conditions calculated by the method (S-F method) and the M-P method of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be further described with reference to the accompanying drawings.
The invention provides a striping method capable of accurately calculating a force inclination angle between stripes and a slope stability safety coefficient, which comprises the following calculation formula:
C i ＝c i /k (6)
A i ＝(W i -Q i )sinα i +P di cosα i -P ti sin(α i +θ pti )-(U ti -U ti-1 )cosα i (9)
in the above formula, i =0,1,2, \ 8230;, n, n is a natural number, i represents a division number, k is a slope stability safety factor, ψ i Is the angle of interaction force inclination (degree), E, between the ith and (i + 1) th slices i And X i The horizontal component and the vertical component (kN) of the interaction force of the ith and (i + 1) th branches respectively, v is an adjustment coefficient, H Ei Is E i The moment arm (the invention takes the midpoint of the bottom surface of the stripe as the centroid, the same applies below) when E i <0, order E i =0, let H when i =0 E0 ＝0，E i-1 ＝E 0 ＝0，α i The slide surface inclination angle (DEG), A, corresponding to the ith division i 、B i And D i Are all intermediate variables, W i Is the ith strip dead weight (kN), Q i For external loads (kN), U, to which the ith strip is subjected ti Water pressure (kN), P, to which the ith stripe is subjected d Is horizontal seismic acting force (kN), P di Horizontal seismic forces (kN), P, to which the ith stripe is subjected ti Slip resistance (kN) provided for ith sectional soil retaining structure, e.g. anti-slip pile, theta pti Is P ti Angle (°) with horizontal plane, H Ei The moment arm (m), H of the horizontal force component between the ith slitting bars Uti The moment arm (m) of the water pressure of the ith stripe side surface is H pdi Moment arm (m), H of horizontal earthquake acting force of ith strip pti Moment arm (m), g) of anti-sliding force provided for ith sub-soil retaining structure i Moment arm (m), e) of buoyancy force borne by the bottom of the ith stripe i The moment arm (m) and xi of the ith strip dead weight and external load i The calculated gradient (°) corresponding to the ith strip is provided, theta is a side slope angle (°),
the slope angle (°) at the designated position for the ith division, ρ is the correction factor for calculating the slope, see fig. 3, based on the slope angle p>
And c i The inner friction angle (DEG) and cohesive force (kPa) of the soil sliding at the bottom of the ith stripe are shown, delta is the inclination angle (DEG) of the underground water line, gamma w Respectively is the natural weight and the saturation weight (kN) of a sliding body, sin lambda is the ratio of shear stress to average stress in a soil body, and->
Wherein sigma 1 And σ 3 Refers to the maximum and minimum principal stresses (kPa) in the earth, snss denotes the earth in the region of the slide adjacent to the slide (thin strip), sin λ snssi Is sin lambda at the ith stripe snss ，α c The inclination angle (degree) of the sliding belt at the position where the snss upper sliding resistance force in the sliding body is equal to the lower sliding force, phi c And C c For the slide belt with an inclination angle of alpha c Internal friction angle (DEG) and cohesive force (kPa), phi after soil breaking of sliding zone is reduced (divided by safety factor) i And C i Is an intermediate variable, h c And &>
The dip angle of the finger sliding belt is alpha c Thickness (m) of sliding body and height (m), b) of underground water level i Is the width (m), U of the ith stripe i Is the buoyancy (kN) of the ith stripe bottom surface.
In order to make the purpose and technical solution of the present invention clearer, the following will further describe the embodiments of the present invention with reference to 4 examples, wherein 3 sliding surfaces of the 4 examples are circular arc-shaped, and 1 sliding surface is zigzag-shaped. The 3 circular arc sliding surfaces are eastern bridge sliding (fig. 4 (a)), eastern bay sliding (fig. 4 (b)) and apricot bay eastern sliding (fig. 4 (c)), and the 1 fold-line sliding surface is dam sliding (fig. 5).
Firstly, the strip division method capable of accurately calculating the inter-strip force inclination angle and the slope stability safety coefficient is used for calculating the inter-strip force inclination angles and the corresponding stability safety coefficients of 3 arc-shaped sliding surface landslides, and comprises the following specific implementation steps of:
s1, determining calculation parameters according to slope survey data;
acquiring measured values of a terrain line, a water line and a sliding surface according to drilling data, and modeling in calculation software; according to the geometric information of the model, software can automatically acquire the sliding surface inclination angle of the position of each vertical stripe surface, the underground water streamline inclination angle, the stripe top surface calculation gradient and the correction coefficient thereof, the thickness of a sliding body and the height of underground water; the working condition is a natural working condition, the seismic force is not considered, pd =0kN, and other calculation parameters are shown in table 1;
TABLE 1 landslide and sliding bed rock physical and mechanical parameter design suggestion values
S2, dividing the slide body of the side slope into a plurality of vertical strips;
when dividing the vertical strips, selecting points with larger fluctuation to divide the strips according to the fluctuation condition of the slope. The 3 circular arc sliding surfaces provided by the invention are divided into 18 (Dongfeng bridge landslide), 16 (Dongwan landslide) and 14 (Wandong landslide of apricot tree) vertical strips respectively, as shown in figure 6;
s3, according to the formula (1) -the formula (8), inputting calculation parameters, and acquiring the inclination angle (°), tan psi of the acting force between the strips 1 、tanψ 2 、…、tanψ i Wherein the input calculation parameters include sliding surface effective shear strength parameters at corresponding slitting positions
The dip angle of the sliding surface, the natural gravity of the sliding body, the saturation gravity of the sliding body, the dip angle of the groundwater waterline, the earthquake acting force and the sliding resistance on the sliding surface are equal to the sliding resistance (alpha = alpha) c ) The corresponding slide thickness, the corresponding groundwater level height, slope inclination angle, side slope angle and correction coefficient of the calculated slope (can be calculated according to the slide and the geometric information of the strips, see figure 3 for details); the position of the sliding surface where the anti-sliding force is equal to the lower sliding force is special but easy to obtain, and the specific method is that when the side slope or the sliding slope is in a limit balance state, namely the stability safety coefficient is equal to 1, according to the Moro-Coulomb theorem, the position of the side slope or the sliding slope is greater than or equal to the lower sliding force>
Obtained through trial calculation; the other parameters can be directly obtained according to the survey data;
s4, calculating a slope stability safety coefficient;
s41, if a semi-precise strip method, namely a Su method is adopted, combining a static balance equation to obtain the safety coefficients of strip force and slope stability:
the static balance condition comprises balance of force in the horizontal direction and balance of force in the vertical direction;
establishing an xoy coordinate system, wherein the positive direction of an x axis is the horizontal direction of sliding of a sliding body, the positive direction of a y axis is the vertical downward direction, the strips are kept in limit balance by external force and acting force of the left side surface and the right side surface of the adjacent strips, the pulling force of the normal force is defined as negative, the pressure of the normal force is defined as positive, and the balance equation of the forces in the horizontal direction is as follows:
in the formula: alpha is alpha i Representing the slope angle (°) of the slide corresponding to the ith slice,
indicating the normal force, T, acting on the centroid of the ith bar bottom slip surface i semi Represents the shear resistance acting on the centroid of the i-th stripe bottom sliding surface>
Represents the normal component of the force between the lines on the left side of the ith branch, and is based on the value of the normal component of the force between the lines on the left side of the ith branch>
Represents the normal component of the force between the lines on the right side surface of the ith division and is combined with the normal component of the force between the lines>
Represents the horizontal force acting on the centroid of the ith stripe;
the equilibrium equation for the forces in the vertical direction is:
in the formula:
represents the tangential component of the force between the bars on the left side of the ith bar, is greater than or equal to>
Represents the tangential component of the force between the bars on the right side of the ith stripe, W i semi Vertical direction representing the action on the centroid of the ith divisionForce.
The strip reaches limit balance along the sliding surface, the sliding surface at the bottom of the strip meets the Mohr-Coulomb yield criterion, and the yield condition of the sliding surface at the bottom of the strip is as follows:
in the formula: c. C i Shows the cohesive force (kPa), phi of the slip-band soil at the position of the ith stripe surface i The effective stress internal friction angle (DEG), l, of the sliding zone soil at the position of the ith strip surface i The length of the ith stripe bottom sliding surface is shown;
when the slope stability safety coefficient k is obtained, the stability safety coefficient k is multiplied by the downward sliding force parallel to the sliding surface by adopting a quasi-overload method, or the cohesive force c and the internal friction angle of the soil body are multiplied by adopting a strength storage method
Dividing by k, the yield condition calculation formula for the bottom slip surface varies as follows:
and combining the formulas (12) - (14) and (17), and obtaining the slope stability coefficient k through iterative operation.
After the slope stability coefficient k is obtained, the calculation is stopped;
s42, if an accurate segmentation method, namely an S-F method is adopted, setting an adjusting coefficient v 1 An initial value, e.g. let v 1 =1, stability factor k and n-1 horizontal components of force between bars, E, are calculated by equation (9), equation (10) and equation (15) 1 、E 2 …E n-1 And continuing to execute the next command;
the calculation parameters related to the formula are known, and comprise a sliding surface inclination angle and a sliding strip soil internal friction angle corresponding to the nth strip, and a force inclination angle psi between the n-1 th strip n-1 Anti-skid provided by corresponding strip dead weight, external load, horizontal earthquake acting force and soil retaining structureForce and included angle with horizontal plane, and water pressure U of side surface of division bar ti And the buoyancy of the bottom surface of the section i 。
S5, substituting the n-1 horizontal components of the inter-stripe force obtained in the S4 into the formulas (11) and (16) to obtain the moment arms (taking the midpoint of the bottom surfaces of the stripes as a centroid) corresponding to the n-1 horizontal components of the inter-stripe force, H E1 、H E2 、…、H En-1 Meanwhile, obtaining an adjusting coefficient v2;
s6, setting a calculation precision delta when v 1 -ν 2 When | < delta, the calculation is stopped, and at the moment, the static force and moment equations are satisfied at the same time, and the corresponding stability safety coefficient, the horizontal component of the force between the strips and the adjustment coefficient are target values; when | v 1 -ν 2 If the value is greater than delta, continuously executing the next command;
s7, comparing v 1 V and v 2 The value of (a) is recorded as v 1 By using the golden section method, let v 1 ＝v 1 +0.618|v 1 -v 2 And then returning to S42, and repeatedly executing the commands of S42-S6 until the nu is satisfied in S6 1 -ν 2 |≤Δ。
In order to make the advantages of the invention more clear, the inter-stripe acting force inclination angle and the stability safety factor of the 3 calculation examples with arc sliding surfaces are calculated by using a numerical simulation (finite difference method) method and other existing stripe methods, such as a transmission coefficient method, a luoeu method, a army engineering faculty method and a simplified simple distribution method, and are compared with the results calculated by the method disclosed by the invention, and the results are shown in tables 2, 3, 4 and 7.
Numerical simulations were performed using Flac3D (Itasca, 2005) (FIG. 6). And determining the size of a corresponding numerical model according to the geometrical information of the geological section of the 3 circular arc sliding surface landslides. Their lengths (X direction) correspond to 78m (east wind bridge landslide), 86m (east bay landslide) and 61m (apricot tree bay east landslide), respectively, and heights (Z direction) are 34 (east wind bridge landslide), 42 (east bay landslide) and 29m (apricot tree bay east landslide), respectively, and the width (Y direction) of each model is 5m. Each vertical slice is divided into a plurality of computing units: for thicker strips, dividing 5 units along the X direction and 10 units along the Z direction; for thinner strips, dividing 5 units along the X direction, and dividing 5 units along the Z direction; as the thickness of the slipperiness soil is small (0.3-0.6 m), 5 units are divided along the X direction, and 1 unit is divided along the Z direction. For the slider bed, 5 cells are divided in the X direction and 10 cells are divided in the Z direction. For bedrock and slick, an elastic model was used, and for slick strip, a Mohr-Coulomb model was used. The calculated parameters are summarized in table 1. The shear strength parameters of the slip bands were gradually reduced to obtain the extreme equilibrium state for each model. Setting the calculation accuracy of the model to be 1 multiplied by 10 < -5 >, and simulating the stress distribution on the strip surface when three circular arc sliding surface landslides are in a limit balance state by reducing the shear strength parameter of the sliding belt. The horizontal and vertical stresses of each cell along a vertical slice can be obtained. The direction of the interlayer force can be obtained by calculating the ratio of the force of the horizontal cell to the sum of the forces of the vertical cells.
When the stability safety coefficient of the landslide with 3 arc sliding surfaces is calculated by other existing striping methods, the same striping scheme as the method is adopted, and the scheme is shown in figure 6.
TABLE 2 Interstrip dip angle and numerical simulation statistical angle calculated by the method of the present invention when the landslide is in the extreme equilibrium state
* In the table, R represents a correlation coefficient, and Q represents an euclidean distance.
TABLE 3 correlation statistical table of force inclination between numerical simulation statistical bars in extreme equilibrium state and the method of the invention and each bar dividing method
Table 4 stability coefficient results comparison table
As can be seen from tables 2, 3, and 4, for three circular arc-shaped sliding surface landslides, the stability coefficient calculated by the Su method is between the simplified simple distribution method and the M-P method; the stability coefficient is 0.00-7.5% larger than that of the Flac3D simulation. The stability coefficient calculated by the S-F method is 0.65 to 0.77 percent larger than that of the Su method, is 0.00 to 0.68 percent larger than that of the M-P method, and is closer to the M-P method. Su and S-F methods are equal to Pearson' S correlation coefficient of the force tilt angle between bars of numerical simulation statistics and equal to or more than 0.98; the euclidean distances have little difference and are all less than 17.77, the smallest being only 6.38. The inter-strip force dip angle assumed by the reverse transfer coefficient method, the Roue method, the American army engineering Master method and the simplified simple layout method is in a negative correlation relationship or is not correlated with the inter-strip force dip angle of numerical simulation statistics, and the Euclidean distance is 44.55 as small as the minimum and is as large as 111.72 as possible. The Pearson correlation coefficient of the force inclination angle between the closest M-P method and the numerical simulation statistic is only 0.627 at the maximum, and the minimum Euclidean distance is 33.754, which is inferior to Su method and S-F method.
Compared with the existing main strip method, the stability coefficients calculated by the Su method, the M-P method and the S-F method are closest to each other, and the difference is not more than 1%. Two of the stable safety factors of the three landslides calculated by the S-F method are more urgent and closer to the numerical analysis result than those calculated by the M-P method. No matter the Pearson correlation coefficient and the Euclidean distance of the inter-strip force dip angle compared with the numerical simulation statistics, the Su method and the S-F are superior to M-P and superior to other existing main strip division methods, namely the inter-strip force dip angle calculated by the Su method and the S-F method is more accurate.
Furthermore, in order to investigate whether the method of the present invention is suitable for analyzing the stability of the polygonal-shaped side (slide) slope, the inter-strip acting force inclination angle and the stability safety coefficient (see the calculated section in fig. 8) of the large dam slide slope (the calculated parameters are shown in table 5) are calculated by the method of the present invention, and compared with the current strip division method M-P method and other methods. The calculation takes into account two conditions. Working condition 1: surface load plus dead weight of the slider in a natural state (the slider and the sliding belt both adopt natural shear strength parameters and have no underground water); working condition 2: the earth surface load +20 years of rainfall (20 years of rainfall, drilling hole monitoring water level) + the self weight of the sliding body are adopted (the natural shear strength parameters of the sliding body and the sliding belt are adopted above the underground water level, and the saturated shear strength parameters of the sliding body and the sliding belt are adopted below the underground water level).
TABLE 5 landslide and sliding bed rock physical and mechanical parameter design suggestion values
The calculated landslide stability safety factors are shown in table 6. In the table, the sliding as a whole refers to a case where the entire sliding body slides along the bedrock face. The sliding speed of the front edge in the sliding body is higher than that of the middle and rear edges, so that a pulling crack is generated in the middle of the sliding body, and the sliding from the crack to the front edge part is called local sliding. The position of the risk-slip plane was searched out comparatively accurately using commercial "landslide stability calculation and analysis software" (Soviet, von Ming et al) in FIG. 8. The calculation results of Su and S-F methods are most suitable for practical conditions, and the characteristic of typical 'flat-pushing type landslide' traction type sliding deformation of the large river dam is well explained from the perspective of quantitative evaluation. The stability safety factors calculated by the Su method and the S-F method under the condition of the working condition 2 are less than 1 (0.988 and 0.991 respectively). The stability factor calculated in the local sliding mode is less than 1, and also comprises an M-P method 0.991 and a simplified simple distribution method 0.941 (which is too small and not suitable for weak deformation characteristics). The other three methods are all more than or equal to 1, the transmission coefficient method is 1.075, the Laue method is 1.052, and the American army Master method is 1.006.
Table 6 stability factor of safety results comparison table (consider surface loading)
Further, fig. 9 (a) shows the distribution of the inter-bar force tilt angles calculated by the S-F method and the M-P method (condition one) and fig. 9 (b) shows the partial slip mode. (1) From the rear edge of the landslide to a shearing outlet (the inclination angle of the sliding surface is reduced from large to small), the general trend of the change of the force inclination angle between S-F normal strips along with the horizontal distance is changed from small to large, the force inclination angle is slightly reduced near the shearing outlet, and the force inclination angle is influenced by the slope gradient between strips; at a slip plane angle of greater than about 45 deg. +/2, the strip-to-strip force angle is negative. The dip angle of the force between the M-P normal bars is constantly larger than zero, is a sine function symmetrical along the horizontal distance and is irrelevant to the dip angle of the sliding surface and the gradient of the slope between the sub-bars. (2) Generally, at the rear edge of the landslide, the force inclination angle between S-F normal bars is smaller than that of an M-P normal; the middle part is slightly larger than that of the M-P method; the near-shearing outlet is far larger than that of the M-P method. For a broken-line type sliding surface, the S-F method is different from the M-P method, the inter-strip force inclination angle is a non-smooth broken line, and the larger the variation of the sliding surface inclination angle is, the larger the variation width of the inter-strip force inclination angle is (FIG. 9 (a)).
In this document, the terms front, back, upper and lower are used to define the components in the drawings and the positions of the components relative to each other, and are used for clarity and convenience of the technical solution. It is to be understood that the use of the directional terms should not be taken to limit the scope of the claims.
The features of the embodiments and embodiments described herein above may be combined with each other without conflict.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the scope of the present invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.
Claims (2)
1. A strip division method capable of accurately calculating an inter-strip force inclination angle and a slope stability safety coefficient is characterized by comprising the following steps of:
s1, determining calculation parameters according to slope survey data;
s2, dividing a slide body of the side slope into a plurality of vertical strips;
s3, calculating by using the calculation parameters in the step S1 to obtain the inclination angle of the acting force between the strips;
s4, calculating the slope stability safety coefficient by adopting a precise segmentation method through a semi-precise segmentation method, and setting an adjustment coefficient v 1 Simultaneously obtain n-1 horizontal force components between the stripsMeasuring, and continuing to step S5; the method comprises the following specific steps:
s41, solving the inter-strip force and slope stability safety coefficient by combining a static balance equation:
the static balance condition comprises balance of force in the horizontal direction and balance of force in the vertical direction;
establishing an xoy coordinate system, wherein the positive direction of an x axis is the horizontal direction of sliding of a sliding body, the positive direction of a y axis is the vertical downward direction, the sub-strips are kept in limit balance by external force and acting force of the left side surface and the right side surface of the adjacent sub-strips, the tensile force of the normal force is defined as negative, the pressure of the normal force is defined as positive, and the balance equation of the forces in the horizontal direction is as follows:
in the formula: alpha is alpha i Representing the slope angle (°) of the sliding surface corresponding to the ith strip,
indicating the normal force, T, acting on the centroid of the ith bar bottom slip surface i semi Represents the shear resistance acting on the centroid of the i-th stripe bottom sliding surface>
Represents the normal component of the force between the lines on the left side of the ith branch, and is based on the value of the normal component of the force between the lines on the left side of the ith branch>
Represents the normal component of the force between the lines on the right side surface of the ith division and is combined with the normal component of the force between the lines>
Representing the horizontal force acting on the centroid of the ith bar;
the equilibrium equation for the forces in the vertical direction is:
in the formula:
represents the tangential component of the force between the bars on the left side of the ith bar, is greater than or equal to>
Represents the tangential component of the force between the bars on the right side of the ith stripe, W i semi Representing the vertical force acting on the centroid of the ith stripe.
The strip reaches ultimate balance along the sliding surface, the sliding surface at the bottom of the strip meets the Mohr-Coulomb yield criterion, and the yield condition of the sliding surface at the bottom of the strip is as follows:
in the formula: c. C i Shows the cohesive force (kPa) of the slip-band soil at the position of the ith stripe surface,
the inner friction angle (DEG), l of the effective stress of the sliding zone soil at the position of the ith stripe surface i The length of the bottom sliding surface of the ith stripe surface is shown;
when the slope stability safety coefficient k is obtained, the stability safety coefficient k is multiplied by the downward sliding force parallel to the sliding surface by adopting a quasi-overload method, or the cohesive force c and the internal friction angle of the soil body are multiplied by adopting a strength storage method
Dividing by k, the yield condition calculation formula for the bottom slip surface varies as follows:
combining the formulas (12) - (14) and (17), and obtaining a slope stability coefficient k through iterative operation;
s42, setting the adjusting coefficient v 1 An initial value, stability safety factor k and n-1 horizontal components of the force between the bars, E, are calculated by equations (9), (10) and (15) 1 、E 2 …E n-1 And continuing to the next operation, wherein expressions of formula (9), formula (10) and formula (15) are as follows:
A i ＝(W i -Q i )sinα i +P di cosα i -P ti sin(α i +θ pti )-(U ti -U ti-1 )cosα i (9)
in the above formula, k is the slope stability safety factor, E i And X i The horizontal component and the vertical component (kN) of the interaction force between the ith and (i + 1) th branches, respectively, and when E i <0, order E i =0, when i =0 i-1 ＝E 0 ＝0；A i And B i Are all intermediate variables, v is the adjustment coefficient, W i Is the ith strip dead weight (kN), Q i External load (kN), P, to which the ith strip is subjected di Horizontal seismic forces (kN), P, to which the ith stripe is subjected ti Slip resistance (kN), θ, provided for the ith sectional soil guard structure pti Is P ti Angle (°) from horizontal, c) i Effective cohesive force (kPa), U of soil of the bottom slide zone of the ith stripe ti Water pressure (kN) to which the ith strip is subjected;
s5, respectively obtaining force arms corresponding to the n-1 horizontal components of the inter-strip force according to the n-1 horizontal components of the inter-strip force in the S4, and simultaneously obtaining an adjustment coefficient v 2 (ii) a The method specifically comprises the following steps:
substituting the n-1 horizontal components of the force between the strips obtained in the step S4 into a formula (11) and a formula (16) to obtain force arms corresponding to the n-1 horizontal components of the force between the strips, and H E1 、H E2 、…、H En-1 While obtaining the adjustment coefficient v 2 Wherein the expressions of formula (11) and formula (16) are as follows:
in the above formula, H Ei The moment arm (m) of the horizontal force component between the ith stripe when i =0 is set as H E0 ＝0，E i-1 ＝E 0 ＝0；D i Is an intermediate variable, H Uti The moment arm (m) of the water pressure of the ith stripe side surface is H pdi Moment arm (m), H of horizontal earthquake acting force of ith strip pti Moment arm (m), g) of anti-sliding force provided for ith sub-soil retaining structure i Moment arms (m), e) of buoyancy force borne by the bottom of the ith stripe i The moment arm (m) is the self weight of the ith branch and the external load;
s6, setting a calculation precision delta, when | v 1 -v 2 When | is ≦ Δ, the calculation is stopped, and when | v ≦ Δ 1 -v 2 |>If delta, continuing to step S7;
s7, comparing v 1 V and v 2 The value of (a) is recorded as v 1 Let v stand for 1 ＝v 1 +0.618v 1 -v 2 And then returns to S4, and repeatedly executes the commands of S4-S6 until | v is satisfied 1 -v 2 |≤Δ。
2. The strip method for accurately calculating the dip angle of force between strips and the safety factor of slope stability according to claim 1, wherein the dip angle of force between strips in S3 is calculated by combining the expressions (1) to (8), wherein the expressions (1) to (8) are respectively as follows:
C i ＝c i /k (6)
in the above formula, i =0,1,2, ..., n, n is a natural number, i represents a division number,. Psi i Is the angle of interaction force (degree), alpha, between the ith and (i + 1) th slices i Angle of inclination of sliding surface (P degree) corresponding to ith strip d Is horizontal seismic force (kN), ξ i The calculated gradient (°) corresponding to the ith strip is provided, theta is a side slope angle (°),
the slope angle (degree) of the slope at the position designated for the ith strip, rho is a correction coefficient for calculating the slope, delta is the inclination angle (degree) of the underground water line, and gamma are w Respectively, the natural severe degree and the saturated severe degree (kN) of the synovial body, sin lambda is the ratio of the shear stress to the average stress in the soil body, and->
Wherein σ 1 And σ 3 Maximum and minimum principal stress (kPa) in the soil, respectively, snss denotes the soil in the region of the slide adjacent to the sliding strip, sin lambda snssi Is sin lambda at the ith stripe snss ，α c The sliding resistance on the snss in the sliding body is equal to the inclination angle (°) of the sliding belt at the sliding force, and the part is combined with the sun or the sun>
And c i The internal friction angle (DEG) and cohesive force (kPa), phi of the soil slide-in at the bottom of the ith stripe c And C c For the sliding belt with an inclination angle alpha c The internal friction angle (DEG) and cohesive force (kPa), phi after the soil in the sliding zone is reduced i And C i Is an intermediate variable, h c And &>
For the slide belt with an inclination angle of alpha c Thickness (m) of sliding body and height (m), b) of underground water level i Is the width (m), U of the ith stripe i Is the buoyancy (kN) of the ith stripe bottom surface. />
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