CN111814369A - 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 PDF

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CN111814369A
CN111814369A CN202010558700.8A CN202010558700A CN111814369A CN 111814369 A CN111814369 A CN 111814369A CN 202010558700 A CN202010558700 A CN 202010558700A CN 111814369 A CN111814369 A CN 111814369A
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strip
slope
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CN111814369B (en
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苏爱军
冯明权
鲁志春
林宇
许泽坤
毛浩然
林世权
杨世文
邵晨
关力豪
甘昭文
仝德富
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China University of Geosciences
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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 the slope survey data, S2 dividing the slide body of the slope into a plurality of vertical stripes, S3 calculating the inclination angle of the acting force between the stripes, and S4 calculating the slope stability safety coefficient by adopting a semi-accurate stripe method or an accurate stripe 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

Strip division method capable of accurately calculating force inclination angle between strips and stability safety coefficient of side slope
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 segmentation method 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 developed based on a limit balance theory, and is widely applied to slope stability analysis and slope protection engineering design. Over the last hundred years, tens of fractionation methods have emerged, and the differences of the various 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):
firstly, counting the integral stability coefficient fos along the shearing surface as 1;
normal counter force and tangential counter force at the bottom of the stripping are counted to be 2 n;
and thirdly, counting the horizontal acting force and the vertical acting force among the strips to be 2 n-2.
The load and the counter force of the strip satisfy the balance condition (Sigma F)x＝0,∑Fy0) and ultimate equilibrium condition on shear plane
Figure BDA0002545480860000011
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:
firstly, assuming that n-1 vertical force values between strips are 0, namely, only horizontal force exists between strips, such as a simplified simple distribution method, a simplified common method and the like;
secondly, the ratio of n-1 vertical force values to horizontal force values among the strips is assumed, such as an improved transfer coefficient method, a American army and army law and the like;
and thirdly, assuming that n-1 vertical force values and horizontal force values among the strips reach a critical state, the method is called a block limit balancing method, namely, an upper limit solution meeting the static balance condition.
(2) The solving stability coefficient of the precise strip method which simultaneously meets the static 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):
the integral stability coefficient k along the shearing surface is counted as 1;
counting the normal counter force and the tangential counter force of the bottom of the stripe and the moment of the midpoint of the bottom of the stripe by 3 n;
thirdly, the horizontal acting force, the vertical acting force and the gravity among the strips act on the moment of the central point of the bottom of the strip, and the number is n +2 (n-1).
The load and the counter force of the strip satisfy the balance condition (Sigma F)x＝0,∑Fy0), ultimate equilibrium condition on shear plane
Figure BDA0002545480860000021
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)i0) the moment induced at the bottom of the bar can be ignored and the undetermined variable is reduced by n. Compared with 6n-1 unknown variables, the method has n-1 unknown conditions, and is an essentially static and uncertain problem, and traditionally solves the problem by assuming n-1 unknown conditions:
-assuming the position of the inter-bar force action, e.g. the method of Janbu;
secondly, the ratio of n-1 vertical force values to horizontal force values among the strips is assumed, and the ratio is adjusted by equal proportion or through a certain linear relation, so that static balance conditions and moment balance conditions are met simultaneously, 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 assumption of the direction of force application between the bars (ratio of force between bars) or the position of the point of application determines the accuracy of the various semi-accurate and accurate bar methods.
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 strip division method capable of accurately calculating a force inclination angle between strips and a slope stability safety coefficient, which comprises the following steps of:
s1, determining calculation parameters according to the slope survey data;
s2, dividing the slide body of the side slope into a plurality of vertical strips;
s3, calculating by using the calculation parameters of 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 semi-precise striping method or a precise striping method, stopping calculation after obtaining the slope stability safety coefficient if the semi-precise striping method is adopted, and setting an adjustment coefficient v after obtaining the slope stability safety coefficient if the precise striping method is adopted1Simultaneously 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 v2；
S6, setting a calculation precision delta, when | v |1-v2When | is ≦ Δ, the calculation is stopped, and when | v ≦ Δ1-v2If | > Δ, proceed to step S7;
s7, comparing v1V and v2The value of (a) is recorded as v1Let v stand for1＝v1+0.618|v1-v2And then returns to S4, the command of S4-S6 is repeatedly executed until | v is satisfied1-v2|≤Δ。
Further, formula (1) -formula (8) are combined to calculate the inclination of the inter-bar acting force in S3, wherein the expressions of formula (1) -formula (8) are respectively as follows:
Figure BDA0002545480860000041
Figure BDA0002545480860000042
Figure BDA0002545480860000043
Figure BDA0002545480860000044
Figure BDA0002545480860000045
Ci＝ci/k (6)
Figure BDA0002545480860000046
Figure BDA0002545480860000047
in the above formula, i is 0,1,2, …, n, n is a natural number, i represents a bar number, HEiIs EiArm of force of alphaiAngle of inclination of sliding surface (P degree) corresponding to ith stripdIs horizontal seismic force (kN), ξiThe calculated gradient (°) corresponding to the ith strip is provided, theta is a side slope angle (°),
Figure BDA0002545480860000048
the internal friction angle (°) of the soil slide at the bottom of the ith strip,
Figure BDA00025454808600000412
the slope angle (degree) of the slope at the position designated for the ith strip, rho is a correction coefficient for calculating the slope, and is the inclination angle (degree) of the underground water line, gamma and gammawRespectively, the natural gravity and the saturated gravity (kN) of the synovial body, and sin lambda is the ratio of the shear stress to the average stress in the soil body, and
Figure BDA0002545480860000049
wherein σ1And σ3Maximum and minimum principal stress (kPa) in the earth respectively, snss denotes the earth (thin strip) in the area of the slide adjacent to the slide, sin lambdasnssiIs sin lambda at the ith stripesnss，αcThe upper anti-slip force snss in the sliding body is equal to the inclination angle (DEG) of the sliding belt at the lower slip force,
Figure BDA00025454808600000410
and ciThe internal friction angle (DEG) and cohesive force (kPa), phi of the soil slide-in at the bottom of the ith stripeiAnd CiIs an intermediate variable, hcAnd
Figure BDA00025454808600000411
the dip angle of the finger sliding belt is alphacThickness (m) of sliding body and height (m), b) of underground water leveliIs the width (m), U of the ith stripeiIs 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:
Figure BDA0002545480860000051
in the formula: alpha is alphaiRepresenting the slope angle (°) of the slide corresponding to the ith slice,
Figure BDA0002545480860000052
indicating the normal force, T, acting on the centroid of the ith bar bottom slip surfacei semiShowing the shear resistance acting on the centroid of the ith strip bottom slip surface,
Figure BDA0002545480860000053
represents the normal component of the acting force between the stripes on the left side surface of the ith stripe,
Figure BDA0002545480860000054
represents the normal component of the acting force between the stripes on the right side surface of the ith stripe,
Figure BDA0002545480860000055
representing the horizontal force acting on the centroid of the ith bar;
the equilibrium equation for the forces in the vertical direction is:
Figure BDA0002545480860000056
in the formula:
Figure BDA0002545480860000057
representing the tangential component of the force between the bars on the left side of the ith stripe,
Figure BDA0002545480860000058
represents the tangential component of the force between the bars on the right side of the ith stripe, Wi semiRepresenting 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:
Figure BDA0002545480860000059
in the formula: c. CiShows the cohesive force (kPa), phi of the slip-band soil at the position of the ith stripe surfaceiThe effective stress internal friction angle (DEG), l, of the sliding zone soil at the position of the ith strip surfaceiThe length of the bottom sliding surface of the ith stripe surface is shown;
when the safety coefficient of slope stability is obtainedk, adopting quasi-overload method to multiply the slip force parallel to the slip surface by the stability safety coefficient k, or adopting strength storage method to multiply the cohesive force c and the internal friction angle of the soil body
Figure BDA00025454808600000511
Dividing by k, the yield condition calculation formula for the bottom slip surface varies as follows:
Figure BDA00025454808600000510
and combining the formulas (12) - (14) and (17), and obtaining the slope stability coefficient k through iterative operation.
Further, the specific method for calculating the slope stability safety coefficient by adopting the accurate segmentation method in the step S4 is as follows:
s42, setting the adjusting coefficient v1An initial value, by equation (15), is calculated for the stability factor k and the n-1 horizontal components of the force between the bars, E1、E2…En-1And continuing to the next operation, wherein the expression of equation (15) is as follows:
Ai＝(Wi-Qi)sinαi+Pdicosαi-Ptisin(αi+θpti)-(Uti-Uti-1)cosαi(9)
Figure BDA0002545480860000061
Figure BDA0002545480860000062
in the above formula, EiAnd XiThe horizontal component and the vertical component (kN) of the interaction force between the ith and (i + 1) th branches, respectively, and when E isi<0, order EiWhen i is 0, Ei-1＝E0＝0；AiAnd BiAre all intermediate variables, v is the adjustment factor, WiIs the ith stripe dead weight (kN), QiExternal load applied to ith stripe(kN)，PdiHorizontal seismic forces (kN), P, to which the ith stripe is subjectedtiSlip resistance (kN), θ, provided for the ith sectional soil guard structureptiIs PtiAngle (°) from horizontal, c)iEffective cohesive force (kPa), U of soil of the bottom slide zone of the ith stripetiWater pressure (kN) to which the ith stripe was subjected.
Further, the n-1 horizontal components of the inter-division force obtained in the step S4 are substituted into the formulas (11) and (16) to obtain the moment arms (taking the midpoint of the bottom surface of the division as the centroid) corresponding to the n-1 horizontal components of the inter-division force, and HE1、HE2、…、HEn-1While obtaining the adjustment coefficient v2Wherein the expressions of formula (11) and formula (16) are as follows:
Figure BDA0002545480860000063
Figure BDA0002545480860000064
in the above formula, HEiThe moment arm (m) of the horizontal force component between the ith slitting strip is set as H when i is equal to 0E0＝0，Ei-1＝E0＝0；DiIs an intermediate variable, HUtiThe moment arm (m) of the water pressure of the ith stripe side surface is HpdiMoment arm (m), H of horizontal earthquake acting force of ith stripptiMoment arm (m), g) of anti-sliding force provided for ith sub-soil retaining structureiMoment arms (m), e) of buoyancy force borne by the bottom of the ith stripeiIs 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 beneficial effects that: 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 conditions are different, and the magnitude and the distribution of the shear force and normal force ratio between 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 conditions and loads of the sliding body;
(3) according to the method, the ratio of the shearing force to the normal force between 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 by segmentation, hi、ΔXiAnd LiRespectively showing the height, width and length of the i-th stripe, Wi、QiRespectively representing the weight and top of the ith bar, Ei、XiAnd MiRespectively 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 slittingi、TiAnd
Figure BDA0002545480860000071
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 landslide leading edge abscissa (m) and b is the landslide trailing edge abscissaThe symbol (m), xiThe abscissa (m) of the midpoint of the ith stripe ground;
FIG. 4 is an engineering geological profile of a circular arc sliding surface landslide: (a) east wind bridge landslide, (b) east bay landslide, (c) apricot tree bay east landslide;
FIG. 5 is a geological section of a large dam landslide project with a polygonal sliding surface;
FIG. 6 shows a scheme for dividing the slip body into strips for the circular arc sliding surface: (a) east wind bridge landslide, (b) east bay landslide, (c) apricot tree bay east 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) east wind bridge landslide, (b) east bay landslide, (c) apricot tree bay east landslide;
FIG. 8 is a calculated profile of a large river dam landslide;
FIG. 9 is a graph showing 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:
Figure BDA0002545480860000081
Figure BDA0002545480860000082
Figure BDA0002545480860000083
Figure BDA0002545480860000084
Figure BDA0002545480860000085
Ci＝ci/k (6)
Figure BDA0002545480860000086
Figure BDA0002545480860000087
Ai＝(Wi-Qi)sinαi+Pdicosαi-Ptisin(αi+θpti)-(Uti-Uti-1)cosαi(9)
Figure BDA0002545480860000088
Figure BDA0002545480860000089
Figure BDA0002545480860000091
Figure BDA0002545480860000092
in the above formula, i is 0,1,2, …, n, n is a natural number, i represents a section number, k is a slope stability safety factor, psiiIs the angle of interaction force inclination (degree), E, between the ith and (i + 1) th slicesiAnd XiThe 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, HEiIs EiThe moment arm (the invention takes the midpoint of the bottom surface of the stripe as the centroid, the same applies below) when Ei<0, order EiWhen i is 0, let HE0＝0，Ei-1＝E0＝0，αiAngle of inclination of sliding surface (degree), A, corresponding to ith divisioni、BiAnd DiAre all intermediate variables, WiIs the ith stripe dead weight (kN), QiFor external loads (kN), U, to which the ith strip is subjectedtiWater pressure (kN), P, to which the ith stripe is subjecteddIs horizontal seismic acting force (kN), PdiHorizontal seismic forces (kN), P, to which the ith stripe is subjectedtiSlip resistance (kN) provided for ith sectional soil retaining structure, e.g. anti-slip pile, thetaptiIs PtiAngle (°) with horizontal plane, HEiThe moment arm (m), H of the horizontal force component between the ith slitting barsUtiThe moment arm (m) of the water pressure of the ith stripe side surface is HpdiMoment arm (m), H of horizontal earthquake acting force of ith stripptiMoment arm (m), g) of anti-sliding force provided for ith sub-soil retaining structureiMoment arms (m), e) of buoyancy force borne by the bottom of the ith stripeiThe moment arm (m) and xi of the ith strip dead weight and external loadiThe calculated gradient (°) corresponding to the ith strip is provided, theta is a side slope angle (°),
Figure BDA0002545480860000093
the slope angle (°) at the designated position for the ith division, ρ is the correction factor for calculating the slope, see figure 3,
Figure BDA0002545480860000094
and ciThe internal friction angle (DEG) and cohesive force (kPa) of the soil slide at the bottom of the ith stripe are the inclination angle (DEG) of the underground water line, gamma and gammawRespectively, the natural gravity and the saturated gravity (kN) of the synovial body, and sin lambda is the ratio of the shear stress to the average stress in the soil body, and
Figure BDA0002545480860000095
wherein sigma1And σ3Refers to the maximum and minimum principal stresses (kPa) in the earth, snss denotes the earth (thin strip) in the area of the slide adjacent to the slide, sin λsnssiIs sin lambda at the ith stripesnss，αcThe 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, phicAnd CcFor the slide belt with an inclination angle of alphacInternal friction angle (DEG) and cohesive force (kPa), phi after soil breaking of sliding zone is reduced (divided by safety factor)iAnd CiIs an intermediate variable, hcAnd
Figure BDA0002545480860000096
the dip angle of the finger sliding belt is alphacThickness (m) of sliding body and height (m), b) of underground water leveliIs the width (m), U of the ith stripeiIs 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 wind bridge sliding slope (fig. 4(a)), eastern bay sliding slope (fig. 4(b)) and apricot tree bay eastern sliding slope (fig. 4(c)), and the 1 fold-line sliding surface is dam sliding slope (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 the 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 flow line 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 is 0kN, and other calculation parameters are shown in a table 1;
TABLE 1 landslide and sliding bed rock physical and mechanical parameter design suggestion values
Figure BDA0002545480860000101
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 surface embodiments provided by the invention are respectively divided into 18 (Dongfeng bridge landslide), 16 (Dongwei landslide) and 14 (Wandong landslide of apricot tree) vertical strips, as shown in FIG. 6;
s3, according to the formula (1) -formula (8), inputting calculation parameters, and acquiring the inclination angle (°), tan ψ of the acting force between the strips1、tanψ2、…、tanψiWherein the input calculation parameters include sliding surface effective shear strength parameters at corresponding slitting positions
Figure BDA0002545480860000102
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 is alpha)c) The corresponding slide thickness, the corresponding groundwater level height, slope inclination angle, side slope angle and correction coefficient of the calculated slope (which can be calculated according to the slide and the geometric information of the strips, see figure 3 in detail); wherein, the position of the position on 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 the limit balance state, namely the stability safety factor is equal to 1, according to Mohr-Coulomb theorem,
Figure BDA0002545480860000111
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 division method, namely a Su method is adopted, the inter-strip force and slope stability safety coefficient are calculated by combining a static equilibrium 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:
Figure BDA0002545480860000112
in the formula: alpha is alphaiRepresenting the slope angle (°) of the slide corresponding to the ith slice,
Figure BDA0002545480860000113
indicating the normal force, T, acting on the centroid of the ith bar bottom slip surfacei semiShowing the shear resistance acting on the centroid of the ith strip bottom slip surface,
Figure BDA0002545480860000114
represents the normal component of the acting force between the stripes on the left side surface of the ith stripe,
Figure BDA0002545480860000115
represents the normal component of the acting force between the stripes on the right side surface of the ith stripe,
Figure BDA0002545480860000116
representing the horizontal force acting on the centroid of the ith bar;
the equilibrium equation for the forces in the vertical direction is:
Figure BDA0002545480860000117
in the formula:
Figure BDA0002545480860000118
representing the tangential component of the force between the bars on the left side of the ith stripe,
Figure BDA0002545480860000119
represents the tangential component of the force between the bars on the right side of the ith stripe, Wi semiRepresenting 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:
Figure BDA00025454808600001110
in the formula: c. CiShows the cohesive force (kPa), phi of the slip-band soil at the position of the ith stripe surfaceiThe effective stress internal friction angle (DEG), l, of the sliding zone soil at the position of the ith strip surfaceiThe 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
Figure BDA0002545480860000121
Dividing by k, the yield condition calculation formula for the bottom slip surface varies as follows:
Figure BDA0002545480860000122
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 strip method, namely an S-F method is adopted, an adjusting coefficient v is given1An initial value, e.g. let v1By formula (9), formula (10) and formula (15), stability safety factor k and n-1 horizontal component of force between bars, E, are calculated1、E2…En-1And 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 stripn-1Corresponding to the self weight and external load of the branch, horizontal earthquake acting force, anti-sliding force provided by the soil retaining structure, included angle between the anti-sliding force and the horizontal plane, and water pressure U on the side surface of the branchtiAnd the buoyancy of the bottom surface of the sectioni。
S5, converting the data obtained in S4The n-1 horizontal components of the inter-division force are substituted into the formulas (11) and (16) to obtain the force arms (taking the midpoint of the bottom surface of the division as the centroid) corresponding to the n-1 horizontal components of the inter-division force, HE1、HE2、…、HEn-1Meanwhile, obtaining an adjusting coefficient v 2;
s6, setting a calculation precision delta, when | nu1-ν2When | < delta, stopping calculation, at the moment, showing that the static force and moment equations are simultaneously satisfied, and the corresponding stability safety coefficient, the horizontal force component between the strips and the adjustment coefficient are target values; when v is greater than1-ν2If the value is greater than delta, continuing to execute the next command;
s7, comparing v1V and v2The value of (a) is recorded as v1By using the golden section method, let v1＝v1+0.618|v1-v2And then returns to S42, the command of S42-S6 is repeatedly executed until | ν is satisfied in S61-ν2|≤Δ。
In order to make the advantages of the present invention clearer, the inter-stripe force inclination and stability safety factor of the 3 examples with arc sliding surfaces were calculated using the numerical simulation (finite difference method) method and other existing stripe methods, such as the transfer coefficient method, the lue method, the army engineering faculty method and the simplified simple distribution method, and compared with the results calculated by the method of the present invention, see table 2, table 3, table 4 and fig. 7.
Numerical simulations were performed using Flac3D (Itasca,2005) (fig. 6). And determining the size of the corresponding numerical model according to the geometric information of the geological section of the 3 arc-shaped 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), 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 5 m. 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 slip band 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
Figure BDA0002545480860000131
In the table, R represents a correlation coefficient, and Q represents an euclidean distance.
TABLE 3 correlation statistical table of numerical simulation statistical strip force dip angle and the method of the present invention and each strip method under extreme equilibrium state
Figure BDA0002545480860000132
Table 4 stability coefficient results comparison table
Figure BDA0002545480860000141
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 simulated by Flac 3D. 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 method and S-F method are equal to Pearson' S correlation coefficient of the dip angle of force between bars of numerical simulation statistics, and equal to or more than 0.98; the euclidean distances have little difference and are 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 111.72 as large as the maximum. 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 the Su method and the 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
Figure BDA0002545480860000142
Figure BDA0002545480860000151
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 as local sliding. The position of the dangerous sliding surface can be accurately searched out by commercial landslide stability calculation and analysis software (Su Scien, Von Ming, full compilation) (figure 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 transfer 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)
Figure BDA0002545480860000152
Further, fig. 9(a) shows the distribution of the inter-bar force inclination 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 total trend of the change of the force inclination angle between the S-F normal strips along with the horizontal distance is from small to large, the force inclination angle between the S-F normal strips is slightly reduced near the shearing outlet, and the force inclination angle is influenced by the slope gradient between the 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-shear 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 is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (5)

1. A strip division method capable of accurately calculating a force inclination angle between strips and a slope stability safety coefficient is characterized by comprising the following steps of:
s1, determining calculation parameters according to the slope survey data;
s2, dividing the slide body of the side slope into a plurality of vertical strips;
s3, calculating by using the calculation parameters of 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 semi-precise striping method or a precise striping method, stopping calculation after obtaining the slope stability safety coefficient if the semi-precise striping method is adopted, and setting an adjustment coefficient v after obtaining the slope stability safety coefficient if the precise striping method is adopted1Simultaneously acquiring horizontal force components among the n-1 strips, and continuing to perform the step S5;
s5, respectively obtaining n-1 inter-strip force horizontal component correspondences according to the n-1 inter-strip force horizontal components in S4While obtaining the adjustment coefficient v2；
S6, setting a calculation precision delta, when | v |1-v2When | is ≦ Δ, the calculation is stopped, and when | v ≦ Δ1-v2If | > Δ, proceed to step S7;
s7, comparing v1V and v2The value of (a) is recorded as v1Let v stand for1＝v1+0.618|v1-v2And then returns to S4, the command of S4-S6 is repeatedly executed until | v is satisfied1-v2|≤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 following expressions (1) to (8):
Figure FDA0002545480850000011
Figure FDA0002545480850000012
Figure FDA0002545480850000013
Figure FDA0002545480850000014
Figure FDA0002545480850000021
Ci＝ci/k (6)
Figure FDA0002545480850000022
Figure FDA0002545480850000023
in the above formula, i is 0,1,2, …, n, n is a natural number, i represents a division number, ψiIs the angle of interaction force (degree), alpha, between the ith and (i + 1) th slicesiAngle of inclination of sliding surface (P degree) corresponding to ith stripdIs horizontal seismic force (kN), ξiThe calculated gradient (°) corresponding to the ith strip is provided, theta is a side slope angle (°),
Figure FDA00025454808500000210
the slope angle (degree) of the slope at the position designated for the ith strip, rho is a correction coefficient for calculating the slope, and is the inclination angle (degree) of the underground water line, gamma and gammawRespectively, the natural gravity and the saturated gravity (kN) of the synovial body, and sin lambda is the ratio of the shear stress to the average stress in the soil body, and
Figure FDA0002545480850000024
wherein σ1And σ3Maximum 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 lambdasnssiIs sin lambda at the ith stripesnss，αcThe upper anti-slip force snss in the sliding body is equal to the inclination angle (DEG) of the sliding belt at the lower slip force,
Figure FDA0002545480850000025
and ciThe internal friction angle (DEG) and cohesive force (kPa), phi of the soil slide-in at the bottom of the ith stripecAnd CcFor the slide belt with an inclination angle of alphacInternal friction angle (DEG) and cohesive force (kPa), phi after soil reduction in sliding zoneiAnd CiIs an intermediate variable, hcAnd
Figure FDA0002545480850000026
for the slide belt with an inclination angle of alphacThickness (m) of sliding body and height (m), b) of underground water leveliIs the width (m), U of the ith stripeiIs the ithBuoyancy (kN) of the bottom surface of the stripe.
3. The segmentation method capable of accurately calculating the inter-segment force inclination angle and the slope stability safety coefficient according to claim 1, wherein the specific method for calculating the slope stability safety coefficient by adopting the semi-precise segmentation method in S4 is as follows:
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:
Figure FDA0002545480850000027
in the formula: alpha is alphaiRepresenting the slope angle (°) of the slide corresponding to the ith slice,
Figure FDA0002545480850000028
indicating the normal force, T, acting on the centroid of the ith bar bottom slip surfacei semiShowing the shear resistance acting on the centroid of the ith strip bottom slip surface,
Figure FDA0002545480850000029
represents the normal component of the acting force between the stripes on the left side surface of the ith stripe,
Figure FDA0002545480850000031
represents the normal component of the acting force between the stripes on the right side surface of the ith stripe,
Figure FDA0002545480850000032
water acting on centroid of i-th stripeLeveling force;
the equilibrium equation for the forces in the vertical direction is:
Figure FDA0002545480850000033
in the formula:
Figure FDA0002545480850000034
representing the tangential component of the force between the bars on the left side of the ith stripe,
Figure FDA0002545480850000035
represents the tangential component of the force between the bars on the right side of the ith stripe, Wi semiRepresenting 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:
Figure FDA0002545480850000036
in the formula: c. CiShows the cohesive force (kPa) of the slip-band soil at the position of the ith stripe surface,
Figure FDA0002545480850000037
the effective stress internal friction angle (DEG), l, of the sliding zone soil at the position of the ith strip surfaceiThe 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
Figure FDA0002545480850000038
Dividing by k, the yield condition calculation formula for the bottom slip surface varies as follows:
Figure FDA0002545480850000039
and combining the formulas (12) - (14) and (17), and obtaining the slope stability coefficient k through iterative operation.
4. The segmentation method capable of accurately calculating the inter-segment force inclination angle and the slope stability safety coefficient according to claim 1, wherein the specific method for calculating the slope stability safety coefficient by adopting the precise segmentation method in S4 is as follows:
s42, setting the adjusting coefficient v1An 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、E2…En-1And continuing to the next operation, wherein the expressions of formula (9), formula (10) and formula (15) are as follows:
Ai＝(Wi-Qi)sinαi+Pdicosαi-Ptisin(αi+θpti)-(Uti-Uti-1)cosαi(9)
Figure FDA00025454808500000310
Figure FDA0002545480850000041
in the above formula, k is the slope stability safety factor, EiAnd XiThe horizontal component and the vertical component (kN) of the interaction force between the ith and (i + 1) th branches, respectively, and when E isi<0, order EiWhen i is 0, Ei-1＝E0＝0；AiAnd BiAre all intermediate variables, v is the adjustment factor, WiIs the ith stripe dead weight (kN), QiExternal load (kN), P, to which the ith strip is subjecteddiHorizontal seismic forces (kN), P, to which the ith stripe is subjectedtiSlip resistance (kN), θ, provided for the ith sectional soil guard structureptiIs PtiFrom the horizontal planeAngle (°), c)iEffective cohesive force (kPa), U of soil of the bottom slide zone of the ith stripetiWater pressure (kN) to which the ith stripe was subjected.
5. The strip method capable of accurately calculating the dip angle of the strip force and the slope stability safety factor according to claim 4, wherein n-1 horizontal components of the strip force obtained in S4 are substituted into the formula (11) and the formula (16) to obtain the force arms corresponding to the n-1 horizontal components of the strip force, HE1、HE2、…、HEn-1While obtaining the adjustment coefficient v2Wherein the expressions of formula (11) and formula (16) are as follows:
Figure FDA0002545480850000042
Figure FDA0002545480850000043
in the above formula, HEiThe moment arm (m) of the horizontal force component between the ith slitting strip is set as H when i is equal to 0E0＝0，Ei-1＝E0＝0；DiIs an intermediate variable, HUtiThe moment arm (m) of the water pressure of the ith stripe side surface is HpdiMoment arm (m), H of horizontal earthquake acting force of ith stripptiMoment arm (m), g) of anti-sliding force provided for ith sub-soil retaining structureiMoment arms (m), e) of buoyancy force borne by the bottom of the ith stripeiIs the moment arm (m) of the self weight and the external load of the ith branch.
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