CN114398709A - Cutting slope active reinforcement design method - Google Patents
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Abstract
The invention belongs to the technical field of geotechnical engineering, and particularly discloses a cutting slope active reinforcement design method. The method comprises the following steps: acquiring horizontal stress of geometric points of the cutting slope at different depths; calculating soil pressure values at different depths under the initial terrain; calculating horizontal stress loss values of different depth positions; calculating the stability coefficient of the cutting slope, calculating a horizontal loss force correction coefficient by using the ratio of the normal operation condition safety standard to the slope stability coefficient, and estimating the total horizontal reinforcement force corresponding to each grade of slope by using a depth-horizontal reinforcement force curve; and calculating the drawing force of the anchor cable according to the conventional spatial layout of the prestressed anchor cable to obtain the length of the anchor cable, calculating the position of the worst slip surface and the length of the free section of each grade of slope by utilizing the stability, and obtaining the length of the anchor cable by the free section and the anchor section. The invention has the active characteristic, is safe and guaranteed, is suitable for design and construction safety risk assessment of various cutting slopes, and can effectively guarantee the safety risk of the slopes.
Description
Technical Field
The invention belongs to the technical field of geotechnical engineering, and particularly relates to a cutting slope active reinforcement design method.
Background
Mountain traffic engineering, hydraulic engineering, mine engineering often can excavate the cutting side slope that forms different scales, and the excavation causes original level to restraint to disappear for the cutting side slope has strong off-load resilience + the deformation damage mechanism under the horizontal displacement combined action, and original stress field and the strong change in deformation field combine the stratum structure of the slope body, may cause it to be difficult to maintain stably. Therefore, the cutting slope is greatly different from other types of slopes, the stability of the cutting slope cannot be evaluated continuously by using a method specified by a specification, and a technical route of a traditional reinforcement design is used, otherwise, because the reinforcement force does not accord with the actual slope state, once the reinforcement force is insufficient, a great safety risk may be caused.
The traditional calculation of the reinforcing force is to determine the formation volume weight, the strength parameter and the deformation parameter through investigation, calculate the residual thrust according to the unbalanced force transfer coefficient method by utilizing the parameters, and indirectly obtain the reinforcing force of different reinforcing measures according to the residual thrust. The stratum parameters are before excavation, and disturbance deterioration caused by unloading resilience is not considered; the reinforcing force obtained by using old stratum parameter estimation is obviously smaller than the actual horizontal force loss value caused by excavation. Therefore, the traditional method has the previous defects and potential safety hazards aiming at the cutting slope. The conventional method is applicable to the evaluation of the stability under the deterioration or overload of the natural slope. However, excavation unloading causes great changes in the initial terrain stress field and deformation field, and at this time, stability evaluation and design by using the conventional method are not appropriate, and evaluation deviation and reinforcement design deviation which do not conform to the actual stable state are easily caused.
Based on the defects and shortcomings, a cutting slope active reinforcement design method needs to be provided in the field urgently, the spatial layout and the geometric dimension of reinforcement measures are determined scientifically and reasonably according to actually required reinforcement force, and the problems that in the prior art, an initial terrain stress field and a deformation field are greatly changed due to excavation unloading, and then evaluation deviation and reinforcement design deviation are prone to occurring are solved.
Disclosure of Invention
The invention provides a cutting slope active reinforcement design method aiming at the defects or the improvement requirements of the prior art, wherein the cutting slope active reinforcement design method is correspondingly designed by combining the cutting slope geological characteristics and the dynamic fixation process characteristics thereof, a cutting slope horizontal reinforcement force along depth distribution correction curve considering the compensation effect of the force is drawn according to the cutting slope horizontal stress along depth distribution curve after excavation, the static soil pressure along depth distribution curve and the cutting slope horizontal force loss value caused by excavation along depth distribution curve, the prestressed anchor cable (rod) active reinforcement design is carried out according to the correction curve, the compensation according to the actual horizontal stress loss can be correspondingly realized, the horizontal reinforcement force is considered through the correction, and the spatial layout and the geometric dimension of the reinforcement measures are scientifically and reasonably determined according to the actually required force. The invention has clear physical and mechanical mechanism, certain active characteristics and safety guarantee, is suitable for design and construction safety risk assessment of various cutting slopes, and can effectively guarantee the safety risk of the slopes.
In order to achieve the purpose, the invention provides a cutting slope active reinforcement design method, which comprises the following steps:
s1, calculating and acquiring horizontal stress of geometric point positions of the cutting slope at different depths in the excavation process, and drawing a cutting slope depth-horizontal stress curve graph;
s2, drawing a corresponding depth-static soil pressure curve according to the soil pressure at the geometric point positions of different depths of the cutting slope;
s3, subtracting the horizontal stress after excavation from the static soil pressure of the same geometric point at the same depth to obtain the horizontal stress loss value of the position, drawing a depth-horizontal stress loss value curve, estimating along height integral according to the stress difference between the top and the bottom of each grade of slope to obtain the horizontal loss force of the corresponding position, and drawing a depth-horizontal loss force curve;
s4, applying the horizontal loss force value reverse compensation of each grade of slope in the step S3 to the specified height position of the single grade of slope height, calculating to obtain a cutting slope stability coefficient, determining the engineering grade of the designed cutting slope and the corresponding safety standard of the normal operation working condition, constructing a horizontal compensation force correction coefficient model according to the safety standard corresponding to the normal operation working condition of the cutting slope, constructing a cutting slope horizontal reinforcement force calculation model according to the horizontal compensation force correction coefficient model, and calculating the total horizontal reinforcement force corresponding to each grade of slope;
s5, calculating the design drawing force of each anchor cable according to the determined total horizontal reinforcing force corresponding to each grade of slope and the horizontal reinforcing force required to be provided by each anchor cable on the slope at the corresponding position, and calculating the length of the anchoring section, the length of the free section of the anchor cable and the length of the designed prestressed anchor cable according to the design drawing force.
Preferably, in step S1, a numerical model of the cutting slope in consideration of excavation is established according to a designed profile of the cutting slope and formation physical and mechanical parameters provided by investigation, and the horizontal stress at the geometric points of different depths of the cutting slope in the excavation process is calculated.
Preferably, in step S2, the soil pressure at the geometric point positions of different depths is obtained according to the cutting slope design profile given by design, the provided formation physical and mechanical parameters obtained by survey, and the numerical model of the original terrain slope.
More preferably, step S3 specifically includes the following steps:
s31, solving horizontal stress loss values corresponding to different depths, subtracting the horizontal stress of the corresponding position after the excavation of the cutting slope is finished from the static soil pressure of the corresponding position to obtain the horizontal stress loss value of the depth position, and drawing a depth-horizontal stress loss value curve according to the horizontal stress loss value;
s32, solving the horizontal force loss values corresponding to different depths, obtaining the horizontal stress loss value corresponding to the top and the foot of each grade of slope according to the depth-horizontal stress loss value curve drawn in the step S31, estimating the horizontal stress loss value along the height integral to obtain the horizontal loss force at the corresponding position, and drawing the depth-horizontal loss force curve.
Further preferably, the calculation model of the horizontal stress loss value is as follows:
Ph＝σh1-σh2 (1)
in the formula, PhTo a horizontal stress loss value, σh1Horizontal stress of original terrain, sigma, obtained for finite element numerical simulationh2The horizontal stress of the excavated terrain is obtained by finite element numerical simulation;
the calculation model of the horizontal loss force is as follows:
in the formula, Fi+1The horizontal force loss value is the horizontal force loss value corresponding to the width of the i +1 grade slope per meter, and the unit is kN, Ph,iThe horizontal stress loss value P corresponding to the width of the i-th grade slope per meter of cross slopeh,i+1The unit of the horizontal stress loss value is kPa for the horizontal stress loss value corresponding to each meter of transverse slope width of the i +1 grade slope, h is the horizontal distance from the top of the slope, namely h is the abbreviation of horizontal level, the top of the slope starting point i is 0, and the total grade is i +1 grade slope.
More preferably, step S4 specifically includes the following steps:
s41 horizontal compensation force correction coefficient calculation, namely searching the safety standard of the normal operation condition corresponding to the cutting slope according to the standard, establishing a cutting slope numerical model considering the compensation force by using a limit balance method, calculating to obtain a slope stability coefficient, and establishing a horizontal compensation force correction coefficient model according to the slope stability coefficient;
s42, considering the corrected horizontal reinforcing force of the compensation effect, changing the direction of the horizontal reinforcing force to point into a slope on the basis of solving the horizontal loss force, namely, the horizontal reinforcing force is preliminarily determined; and multiplying by a correction coefficient to obtain the horizontal reinforcing force with safety guarantee.
More preferably, the correction coefficient formula is as follows:
wherein C is a horizontal compensation force correction coefficient, FsFor the safety standard corresponding to the normal operation condition of the cutting slope, the formula (3) ensures reasonable compensation, namely the engineering stability standard cannot be corrected and complemented, the excessive compensation is reduced to meet the requirement, and F is the slope stability coefficient calculated by considering the lower limit balance method of the horizontal compensation force for the normal operation condition of the cutting slope;
the calculation model of the horizontal reinforcing force is as follows:
the calculation model of the horizontal reinforcing force is as follows:
Fj+1＝-C×Fi+1 (4)
in the formula, Fj+1And j and i are equal in magnitude and opposite in direction for the corrected horizontal reinforcing force considering the compensation effect of the force corresponding to the width of the cross slope of the (i + 1) th grade, and are used for distinguishing the horizontal reinforcing force from the horizontal force loss value.
More preferably, step S5 specifically includes the following steps:
s51, estimating the length of an anchoring section, estimating the total horizontal reinforcing force corresponding to the 3m width of each grade of slope in the transverse direction according to the 3m multiplied by 3m layout, and dividing the single-grade slope height by 3 times of the sine of the design slope angle to obtain the number of anchor cables designed for the grade of slope;
s52 calculation of length of prestressed anchor cable with horizontal reinforcing force Fj+1Multiplying by 3m to obtain the total horizontal reinforcing force of the grade of slope corresponding to the transverse slope width of 3m, dividing the total horizontal reinforcing force by the number of the anchor cables to obtain the horizontal reinforcing force provided by each anchor cable, dividing the horizontal reinforcing force of each anchor cable by the cosine of the incident angle to obtain the drawing force of each anchor cable, dividing the drawing force of each anchor cable by the polar friction resistance of the hole wall and the unit side surface area pi d to obtain the length L of the anchoring sectionaDetermining the length L of the free section of the anchor cable according to the number of the anchor cables with the incidence angle alpha of the anchor cables arranged on the slope surface and the potential worst slip surfacefAnd calculating the length of the pre-stressed anchor cable according to the length;
wherein the length L of the anchoring sectionaIs a length required below the sliding surfaceLength L of free section of anchor cablefThe distance from the slope surface to the slide surface.
Preferably, the calculation model of the number of anchor cables is:
in the formula, nj+1The number of anchor cables h is longitudinally distributed for every 3m of cross slope width of the i +1 th grade slopei+1Is grade i +1, height of slope, betai+1Designing a slope angle for the (i + 1) th grade slope;
the anchor cable design length calculation model is as follows:
Li+1,m＝Li+1,m,a+Li+1,m,f+1 (7)
in the formula, Li+1，m，aThe length of the anchoring section of the mth anchor cable for the (i + 1) th grade slope from the top of the grade slope to the bottom is calculated by using a formula (6), and Li+1，m，fThe length of the mth anchor cable free section is counted from the top of the single-stage slope to the bottom of the (i + 1) th slope, and m is less than or equal to nj+1And measuring the slope surface to the slip surface to obtain the angle alpha, beta and d, wherein alpha is the angle of incidence of the anchor cable, beta is the slope angle designed for the grade slope, and d is the aperture of the anchor cable drilling hole.
As a further preference, the process of the invention also comprises the following steps:
s6, according to the control indexes that the pulling force provided by a single anchor cable is not more than 3000kN, the length is not more than 50m, the anchoring section is not more than 10m and the free section is not less than 3m, rechecking the length of the anchoring section, the length of the free section of the anchor cable and the length of the designed prestressed anchor cable which are obtained by calculation in the step S5, if the pulling force of the single anchor cable is too large or the length of the anchoring section obtained by calculation is too large, the layout of the anchor cables is sealed, but the distance between adjacent anchor cables is not less than 1.5m, and the step S5 is returned until all the indexes meet the requirements.
Generally, compared with the prior art, the above technical solution conceived by the present invention mainly has the following technical advantages:
1. according to the invention, a cutting slope horizontal reinforcement force along-depth distribution correction curve considering the compensation effect of the force is drawn according to a cutting slope horizontal stress along-depth distribution curve after excavation, a static soil pressure along-depth distribution curve and a cutting slope horizontal force loss value along-depth distribution curve caused by excavation, and the prestressed anchor cable (rod) active reinforcement design is carried out according to the correction curve, so that the compensation according to the actual horizontal stress loss and the correction considering the horizontal reinforcement force can be correspondingly realized, and the spatial layout and the geometric dimension of reinforcement measures can be scientifically and reasonably determined according to the actually required reinforcement force. The invention has clear physical mechanical mechanism, active characteristic and high safety performance. The method can be used as a basis for reinforcing design of the mountain road cutting slope.
2. According to the method for determining the horizontal reinforcing force, a finite element numerical simulation technology considering the excavation construction process of the cutting slope and the conversion of a series of actual elements are utilized to obtain a corrected horizontal reinforcing force curve considering the depth of the cutting slope and the compensation effect, the reinforcing force has certain safety reserve characteristics, and the characteristic of actual horizontal stress loss is also met. The method is different from the technical route determined by the side (slide) slope reinforcement force specified by the specification, namely, the method utilizes the stratum physical and mechanical parameters determined by investigation before excavation, substitutes the stratum physical and mechanical parameters into a cutting slope model formed by excavation to calculate the residual thrust, and combines different reinforcement measures to indirectly obtain the reinforcement force. The former conforms to the actual stress loss and compensation mechanism; the latter parameters have no deformation disturbance caused by unloading resilience, and the mechanical application standard method does not conform to the compensation and reinforcement mechanism of the actual slope force. The safety of the former is guaranteed, and the space difference characteristics of force loss and compensation are met; the latter is disadvantageous and insufficient force compensation may cause design concerns.
3. The invention adopts the active reinforcement design of the cutting slope, namely, the compensation is considered before excavation, the construction is not continued without compensation, and the safety risk can be effectively controlled. The design fully considers the space distribution characteristics of horizontal stress loss caused by excavation, and provides basis for targeted reinforcement design. The traditional reinforcement design is reinforcement according to the spatial distribution characteristics of the residual thrust, the distribution characteristics are obtained by calculation under the stratum parameters before excavation and under the cutting slope after excavation, the parameters are inaccurate, and the model is solidified, so that the result of the model is inevitably deviated from the stress loss characteristics caused by the dynamic excavation of the actual cutting slope. The invention actively reinforces, the reinforcing force is considered fully, and the spatial distribution of the reinforcing measures is reasonable; traditional reinforcement is slightly passive, reinforcement force is not considered sufficiently, and reinforcement measures are distributed unreasonably in space.
In summary, the patent provides a cutting slope active reinforcement design method, a horizontal force loss space distribution rule is obtained by utilizing a finite element numerical simulation technology, and the design drawing force and the design length of a single anchor cable (rod) after being rechecked by 4 indexes such as the minimum layout size, the minimum free segment length, the maximum anchor segment length, the single maximum drawing force and the like are comprehensively determined by combining the space geometric layout, the incident angle, the design slope angle, the stratum characteristic, the anchor cable (rod) drilling characteristic and the potential worst slip surface space distribution characteristic.
Drawings
Fig. 1 is a flowchart of a cutting slope active reinforcement design method according to a preferred embodiment of the present invention;
FIG. 2 is a graph of the pressure intensity of original slope soil and horizontal stress after excavation according to the present invention;
FIG. 3 is a graph of the original terrain soil pressure and excavation horizontal loss force involved in the present invention;
FIG. 4 is a schematic illustration of slope stability under consideration of the slope reinforcement force of the compensating force in the present invention;
FIG. 5 is a graph of slope reinforcement force corrected to account for the compensation force specification safety factor as referred to in the present invention;
fig. 6 is a schematic diagram of slope stability when the slope reinforcement force is corrected by considering the standard safety factor of the compensation force.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, a cutting slope active reinforcement design method provided in an embodiment of the present invention includes: (1) after excavation, calculating to obtain horizontal stress at different depths of the cutting slope caused by excavation of each grade of slope by utilizing a cutting slope finite element numerical simulation technology considering graded excavation, and drawing a depth-horizontal stress curve; (2) calculating the soil pressure values at different depths under the initial terrain by utilizing a finite element numerical simulation technology along the depth distribution curve of the static soil pressure, and drawing a depth-static soil pressure intensity curve; (3) the horizontal force loss value of the cutting slope caused by excavation is distributed along the depth, the static soil pressure intensity of the corresponding depth position is used for subtracting the corresponding horizontal stress after excavation to obtain the horizontal stress loss value of the different depth positions, a depth-horizontal stress loss value curve is drawn, and the horizontal width 1m of each grade of slope is used for integrating along the depth direction to obtain a depth-horizontal loss force curve; (4) taking the horizontal reinforcing force of the cutting slope along the depth distribution correction curve of the force compensation effect into consideration, establishing a cutting slope limit balance method calculation model by using slide software, applying the depth-horizontal loss force curve to the numerical model, calculating to obtain a cutting slope stability coefficient, calculating to obtain a horizontal loss force correction coefficient by using the ratio of the normal operation condition safety standard to the slope stability coefficient, and obtaining a corrected depth-horizontal reinforcing force curve; (5) and (3) performing active reinforcement design on the prestressed anchor cables (rods), and estimating the number of the anchor cables (rods) distributed in the 3m width direction of each grade of slope cross slope according to the conventional 3 m-by-3 m spatial layout. And estimating the total horizontal reinforcing force corresponding to each grade of slope by using the depth-horizontal reinforcing force curve, and dividing the total horizontal reinforcing force by the number of the total horizontal reinforcing force to obtain the horizontal reinforcing force required to be provided by each anchor cable (rod). The design pull force provided by each cable (rod) is the horizontal reinforcement force divided by the cosine of the angle of incidence (the angle of incidence of the cable is typically 15-30 °, and the display method is typically 15 °). Checking the limit side friction resistance (the general rock pore wall friction resistance is 600-. And determining the length of the free section of each grade of slope by using the worst slip surface position determined by stability calculation. The free section and the anchoring section obtain the length of the designed prestressed anchor cable (rod). (6) The design parameters of the rechecking anchor cable are that the drawing force provided by a single cable is not more than 3000kN, the length is not more than 50m, and the anchoring section is not more than 10 m. The invention has clear physical and mechanical mechanism, certain active characteristics and safety guarantee, is suitable for design and construction safety risk assessment of various cutting slopes, and can effectively guarantee the safety risk of the slopes.
More specifically, the method comprises the steps of:
the method comprises the steps of firstly, drawing a depth distribution curve of horizontal stress of the excavated cutting slope, establishing a numerical model of the cutting slope considering excavation by utilizing a design profile of the cutting slope and formation physical mechanical parameters provided by investigation, calculating the horizontal stress of geometric points at different depths of the cutting slope in the excavation process, and drawing a depth-horizontal stress curve of the cutting slope.
And secondly, drawing a depth-static soil pressure distribution curve under the terrain, obtaining soil pressures of geometric point positions at different depths according to a numerical model of the original terrain slope by utilizing a designed and given cutting slope design profile and prospecting provided stratum physical and mechanical parameters, and drawing a corresponding depth-static soil pressure curve.
Step three, drawing a distribution curve of the horizontal force loss value of the cutting slope along the depth caused by excavation, and utilizing the static soil pressure sigma of the same depth and the same geometric pointh1Minus horizontal stress sigma after excavationh2Obtaining the horizontal stress loss value of the position, and drawing a depth-horizontal stress loss value curve; according to the stress difference between the top and the bottom of each grade of slope, the horizontal loss force at the corresponding position is obtained by integral estimation along the height, and the horizontal loss force is drawnDepth-horizontal loss force curve. In the step, the horizontal stress loss values corresponding to different depths are solved, the horizontal stress at the corresponding position after the excavation of the cutting slope is finished is subtracted from the static soil pressure at the corresponding position to obtain the horizontal stress loss value at the depth position, and a depth-horizontal stress loss value curve is drawn according to the horizontal stress loss value. And then solving the horizontal force loss values corresponding to different depths, obtaining the horizontal stress loss value corresponding to the top and the foot of each grade of slope according to the drawn depth-horizontal stress loss value curve, estimating the horizontal stress loss value along the height integral to obtain the horizontal loss force at the corresponding position, and drawing the depth-horizontal loss force curve according to the horizontal stress loss value corresponding to the top and the foot of each grade of slope.
The third step specifically comprises the following steps:
step 3.1, solving horizontal stress loss values corresponding to different depths, and subtracting the horizontal stress of the corresponding position after the excavation of the cutting slope is completed from the static soil pressure of the corresponding position to obtain the horizontal stress loss value of the depth position, wherein the specific formula is as follows:
Ph＝σh1-σh2 (1)
in the formula, PhIs the horizontal stress loss value in kPa; sigmah1The method comprises the steps of obtaining original terrain horizontal stress in unit of kPa for finite element numerical simulation; sigmah2And (4) carrying out excavation terrain horizontal stress obtained by finite element numerical simulation.
Step 3.2, solving the horizontal force loss values corresponding to different depths, obtaining the horizontal stress loss value corresponding to the top and the foot of each grade of slope on the basis of 3.1 calculation, and estimating the horizontal stress loss value along the height integral to obtain the horizontal loss force at the corresponding position, wherein the specific formula is as follows:
in the formula, Fi+1The horizontal force loss value is a horizontal force loss value corresponding to the width of each meter of cross slope of the (i + 1) th grade slope in kN unit; ph,iThe horizontal stress loss value P corresponding to the width of the i-th grade slope per meter of cross slopeh,i+1The horizontal stress loss value is the horizontal stress loss value corresponding to the width of each meter of cross slope of the i +1 grade slope, the unit is kPa, and h is horiAbbreviation of zontal level, top of slope starting point i is 0, for grade i +1 slope.
Step four, drawing a cutting slope horizontal reinforcement force depth distribution correction curve considering the force compensation effect, establishing a cutting slope limit balance method calculation model by using slide software, applying the horizontal loss value of each grade of slope to one third height position of the single grade of slope in a reverse compensation manner, and calculating to obtain a cutting slope stability coefficient; looking up relevant highway standards, and determining the engineering grade of the designed cutting slope and the corresponding safety standard of the normal operation condition; and if the safety standard is larger than the slope stability coefficient, dividing the safety standard by the stability coefficient to obtain a horizontal loss force correction coefficient. And if the safety standard is less than or equal to the slope stability coefficient, the correction coefficient is 1, and the horizontal loss force at different height positions is multiplied by the correction coefficient to obtain the corrected horizontal compensation reinforcing force with safety guarantee, namely the horizontal reinforcing force for short, wherein the direction is opposite to the horizontal loss force and points into the slope. In the step, calculating a horizontal compensation force correction coefficient, searching a safety standard of a normal operation condition corresponding to the cutting slope according to the standard, establishing a cutting slope numerical model considering the compensation force by using a limit balance method, calculating to obtain a slope stability coefficient, and establishing a horizontal compensation force correction coefficient model according to the slope stability coefficient. Then, considering the corrected horizontal reinforcing force of the compensation effect, and changing the direction of the horizontal reinforcing force to point into a slope on the basis of solving the horizontal loss force, namely the primarily determined horizontal compensation force; and multiplying by a correction coefficient to obtain the horizontal reinforcing force with safety guarantee. The method comprises the following specific steps:
step 4.1, horizontally compensating force correction coefficients, searching safety standards Fs of normal operation conditions corresponding to the cutting slopes according to the specifications, establishing a cutting slope numerical model considering the compensation force by using a limit balance method, and calculating to obtain slope stability coefficients F, wherein the formula of the correction coefficients is as follows:
in the formula, C is a horizontal compensation force correction coefficient and has no dimensional quantity; fsCuttingAccording to the safety standard corresponding to the normal operation condition of the side slope, the formula (3) ensures reasonable compensation, namely, the engineering stability standard cannot be corrected and complemented, and the excessive compensation is reduced to meet the requirement, so that the safety standard is determined by checking the standard and is a dimensionless quantity; f, calculating the slope stability coefficient by considering the lower limit balance method of the horizontal compensation force under the normal operation condition of the cutting slope, wherein the slope stability coefficient is a dimensionless quantity.
Step 4.2, considering the corrected horizontal reinforcing force of the compensation effect, and changing the direction of the horizontal reinforcing force to point into a slope on the basis of solving the horizontal loss force, namely the primarily determined horizontal compensation force; multiplying by a correction coefficient to obtain the horizontal reinforcing force with safety guarantee, wherein the specific formula is as follows:
Fj+1＝-C×Fi+1 (4)
in the formula, Fj+1The corrected horizontal reinforcing force is the corrected horizontal reinforcing force which is corresponding to the width of each meter of cross slope of the (i + 1) th grade and takes the compensation effect of the force into consideration, and the unit kN is obtained; j is i, which is mainly used for distinguishing horizontal reinforcing force and horizontal force loss values, and the horizontal reinforcing force and the horizontal force loss values are equal in size and opposite in direction; the other criteria are as above.
Step five, performing active reinforcement design on the prestressed anchor cables (rods), and estimating the number of the anchor cables (rods) needing to be distributed in the longitudinal direction with the width of 3m in the cross slope direction of each grade of slope according to the conventional 3 m-by-3 m spatial layout; dividing the total horizontal reinforcing force corresponding to each grade of slope by the number to obtain the horizontal reinforcing force required to be provided by each anchor cable (rod) on the slope at the corresponding position, and dividing the horizontal reinforcing force by the cosine of the incident angle cos alpha DEG to obtain the design drawing force of each anchor cable (rod); drawing force divided by ultimate side frictional resistance qsikDividing by the unit side surface area (pi x d) to obtain the length L of the anchoring sectiona(i.e. the length of cable required below the slip plane). Determining the length L of the free section of the anchor cable (rod) according to the potential worst frame position determined by the computation model of the limit balance methodf(i.e., the distance of the ramp surface from the slip surface). And obtaining the length L of the designed prestressed anchor cable (rod) according to the rule that the free section enters the position below the sliding surface and is not less than 1m and the length of the free section plus 1m plus the length of the anchoring section. The method comprises the following specific steps:
step 5.1, estimating the length of the anchoring section, and estimating the total horizontal reinforcing force corresponding to the width of each grade of slope in the direction of 3m according to the 3 m-by-3 m layout; dividing the single-stage slope height by 3 times of the sine (3 x sin beta) of the design slope angle to obtain the number of anchor cables (rods) designed by the single-stage slope, wherein if a decimal place exists in the result, the specific number can be considered according to the integral number +1 of the result, and the specific formula is as follows:
in the formula, nj+1Longitudinally arranging the number of anchor cables (rods) for each 3m cross slope width of the i +1 th grade slope, wherein the number is unit; h isi+1Is the i +1 th grade slope height, unit m; beta is ai+1Designing a slope angle for the (i + 1) th grade slope in unit degree; the other criteria are as above.
Step 5.2 prestressed anchorage cable (rod) length, 3m multiplied by Fj+1Obtaining the total horizontal reinforcing force of the grade of slope corresponding to the transverse slope width of 3 m; dividing the total horizontal reinforcing force by the number of the anchor cables (rods) to obtain the horizontal reinforcing force provided by each anchor cable (rod); dividing the horizontal reinforcing force of each anchor cable (rod) by the cosine of the incident angle to obtain the drawing force of each anchor cable (rod); as shown in figure 4 of the drawings,
the drawing force of each anchor cable (rod) is divided by the hole wall polar friction qsikDividing the length by the unit side surface area pi d to obtain the length L of the anchoring sectiona(ii) a Determining the length L of the free section of the anchor cable (rod) according to the number of alpha incidence anchor cables (rods) distributed on the slope surface and the potential worst slip surfacefThe formula for solving the design length of the anchor cable (rod) is as follows:
Li+1,m＝Li+1,m,a+Li+1,m,f+1 (7)
in the formula, Li+1，m，aThe length of the anchoring section of the mth anchor cable (rod) from the top of the grade slope to the bottom of the grade slope (i + 1) in unit m; l isi+1，m，fThe length of the free segment of the mth anchor cable (rod) from the top of the single-stage slope to the bottom of the (i + 1) th slope, wherein m is less than or equal to nj+1Obtaining the unit m by measuring the slope surface to the sliding surface; alpha is the incidence angle of the anchor cable (rod), and beta is the slope designed for the grade slopeAngle, in degrees; d is the bore diameter of the anchor cable (rod) bore hole, generally referred to as diameter, unit m; the other criteria are as above.
And sixthly, rechecking the design parameters of the anchor cable, wherein the drawing force provided by a single cable is not more than 3000kN, the length is not more than 50m, the anchoring section is not more than 10m, the free section is not less than 3m, and the design is finished after rechecking according to the control indexes. And if the single drawing force is too large or the calculated length of the anchoring section is too large, the adjustment layout is improved, but the distance is not smaller than 1.5m until all indexes meet the requirements.
The active reinforcing design method for the cutting slope formed by the steps considers the horizontal reinforcing force according to the compensation and correction of the actual horizontal stress loss, the safety is guaranteed, the physical and mechanical mechanism is clear, all the parts are organically matched, the spatial layout and the geometric dimension of the reinforcing measure are scientifically and reasonably determined according to the actually required reinforcing force, and the method can be used as the basis for reinforcing design of the cutting slope of the highway in the mountainous area.
Example 1
In this embodiment, the active reinforcing design method for cutting slope includes the following steps:
step 1, drawing a depth-along-depth distribution curve of the excavated cutting slope, establishing a numerical model of the cutting slope considering excavation by using a design profile and survey provided stratigraphic physical mechanical parameters of the cutting slope as shown in the following table 1, calculating the horizontal stress of the geometric points of the cutting slope at different depths in the excavation process, and drawing a depth-horizontal stress curve of the cutting slope as shown in fig. 2.
TABLE 1 physical mechanics and geometrical parameters of slope
And 2, drawing a depth-to-static soil pressure distribution curve under the initial terrain, calculating the static soil pressure of the corresponding geometric point positions at different depths according to a static soil pressure formula by utilizing a designed and given cutting slope design profile and prospecting provided stratum physical and mechanical parameters, and drawing a corresponding depth-to-static soil pressure curve, wherein the curve is shown in figure 3.
Step 3, excavating the horizontal force loss value of the cutting slope along the depth distribution curve, and utilizing the static soil pressure sigma of the same depth and the same geometric pointh1Minus horizontal stress sigma after excavationh2Obtaining the horizontal stress loss value of the position, and drawing a depth-horizontal stress loss value curve; and (4) according to the stress difference between the top and the bottom of each grade of slope, obtaining the horizontal loss force at the corresponding position by integral estimation along the height, and drawing a depth-horizontal loss force curve. The method comprises the following specific steps:
step 3.1, solving horizontal stress loss values corresponding to different depths, and subtracting the horizontal stress of the corresponding position after the excavation of the cutting slope is completed from the static soil pressure of the corresponding position to obtain the horizontal stress loss value of the depth position, wherein the specific formula is as follows:
Ph＝σh1-σh2 (1)
in the formula, PhIs the horizontal stress loss value in kPa; sigmah1The method comprises the steps of obtaining original terrain horizontal stress in unit of kPa for finite element numerical simulation; sigmah2And (4) carrying out excavation terrain horizontal stress obtained by finite element numerical simulation.
Step 3.2, solving the horizontal force loss values corresponding to different depths, obtaining the horizontal stress loss value corresponding to the top and the foot of each grade of slope on the basis of 3.1 calculation, and estimating the horizontal stress loss value along the height integral to obtain the horizontal loss force at the corresponding position, wherein the specific formula is as follows:
in the formula, Fi+1The horizontal force loss value is a horizontal force loss value corresponding to the width of each meter of cross slope of the (i + 1) th grade slope in kN unit; the other criteria are as above.
Step 4, drawing a cutting slope horizontal reinforcement force depth distribution correction curve considering the force compensation effect, establishing a cutting slope limit balance method calculation model by using slide software, applying the horizontal loss value of each grade of slope to one third height position of the single grade of slope in a reverse compensation manner, and calculating to obtain a cutting slope stability coefficient; looking up relevant highway standards, and determining the engineering grade of the designed cutting slope and the corresponding safety standard of the normal operation condition; and if the safety standard is larger than the slope stability coefficient, dividing the safety standard by the stability coefficient to obtain a horizontal loss force correction coefficient. And if the safety standard is less than or equal to the slope stability coefficient, the correction coefficient is 1, and the horizontal loss force at different height positions is multiplied by the correction coefficient to obtain the corrected horizontal compensation reinforcing force with safety guarantee, namely the horizontal reinforcing force for short, wherein the direction is opposite to the horizontal loss force and points into the slope. The method comprises the following specific steps:
step 4.1, horizontally compensating force correction coefficients, searching safety standards Fs of normal operation conditions corresponding to the cutting slopes according to the specifications, establishing a cutting slope numerical model considering the compensation force by using a limit balance method, and calculating to obtain slope stability coefficients F, wherein the formula of the correction coefficients is as follows:
in the formula, C is a horizontal compensation force correction coefficient and has no dimensional quantity; fsThe safety standard corresponding to the normal operation condition of the cutting slope is checked, standardized and determined, and no dimensional quantity exists; f, calculating to obtain a slope stability coefficient by considering the lower limit balance method of the horizontal compensation force under the normal operation condition of the cutting slope, wherein the slope stability coefficient is free of dimensional quantity.
Step 4.2, considering the corrected horizontal reinforcing force of the compensation effect, and changing the direction of the horizontal reinforcing force to point into a slope on the basis of solving the horizontal loss force, namely the primarily determined horizontal compensation force; multiplying by a correction coefficient to obtain the horizontal reinforcing force with safety guarantee, wherein the specific formula is as follows:
Fj+1＝-C×Fi+1 (4)
in the formula, Fj+1The corrected horizontal reinforcement force, which is the compensation effect of the consideration force corresponding to the width of each meter of cross slope of the (i + 1) th grade, is represented by a table in table 2, and has a unit of kN; the other criteria are as above.
The horizontal compensation force correction coefficient is calculated from the following map,the stability factor safety factor is 1.684, as shown in fig. 4, so the horizontal compensation force correction factor is 1.0. Corrected horizontal reinforcement force F for each grade of slope, corresponding to each meter of cross slope width, taking into account the compensation effect of the forcej+1Is 10208 KN.
Table 2 slope reinforcement force considering compensation force
Step 5, performing active reinforcement design on the prestressed anchor rods, and estimating the number of the anchor rods needing to be distributed in the longitudinal direction with the width of 3m in the cross slope direction of each grade of slope according to the conventional 3m by 3m space layout; dividing the total horizontal reinforcing force corresponding to each grade of slope by the number to obtain the horizontal reinforcing force required to be provided by each anchor rod on the slope at the corresponding position, and dividing the horizontal reinforcing force by the cosine of the incident angle cos alpha to obtain the design drawing force of each anchor rod; drawing force divided by ultimate side frictional resistance qsikDividing by the unit side surface area (pi x d) to obtain the length L of the anchoring sectiona. Determining the length L of the free section of the anchor rod according to the potential worst picture position determined by the calculation model of the limit balance methodf. And obtaining the length L of the designed prestressed anchor rod according to the rule that the free section enters the position below the sliding surface and is not less than 1m, and the length of the free section plus 1m plus the length of the anchoring section. The method comprises the following specific steps:
step 5.1, estimating the length of the anchoring section, and estimating the total horizontal reinforcing force corresponding to the width of each grade of slope in the direction of 3m according to the 3 m-by-3 m layout; the single-stage slope height is divided by 3 times of the sine (3 x sin beta) of the design slope angle to obtain the number of the anchor rods designed by the single-stage slope, if a decimal place exists, the specific number can be considered according to the integral number plus 1 of the result, and the specific formula is as follows:
in the formula, nj+1Longitudinally arranging anchor rods for each 3m cross slope width of the i +1 th grade slope, wherein the number of the anchor rods is unit; h isi+1Is the i +1 th grade slope height, unit m; beta is ai+1Designing a slope angle for the (i + 1) th grade slope in unit degree; the other criteria are as above.
Step 5.2 prestressed anchor rod length, 3m times Fj+1Obtaining the total horizontal reinforcing force of the grade of slope corresponding to the transverse slope width of 3 m; dividing the total horizontal reinforcing force by the number of the anchor rods to obtain the horizontal reinforcing force provided by each anchor rod; dividing the horizontal reinforcing force of each anchor rod by the cosine of the incident angle to obtain the drawing force of each anchor rod; the drawing force of each anchor rod is divided by the hole wall polar friction qsikDividing the length by the unit side surface area pi d to obtain the length L of the anchoring sectiona(ii) a Determining the length L of the free section of the anchor rod according to the number of alpha incident anchor rods distributed on the slope surface and the potential most unfavorable slip surfacefThe formula for calculating the designed length of the anchor rod is as follows:
Li+1,m＝Li+1,m,a+Li+1,m,f+1 (7)
in the formula, Li+1，m，aThe anchoring length of the mth anchor rod is the length of the (i + 1) th grade slope from the top of the grade slope to the bottom in a unit of m; l isi+1，m，fThe length of the mth anchor rod free section of the (i + 1) th grade slope from the top of the single-grade slope to the bottom is measured and obtained in a unit of m; alpha is the anchor rod incidence angle, beta is the slope angle of the grade slope design, and the unit degree is; d is the bore diameter of the anchor hole, generally the diameter, in m; the other criteria are as above.
And (3) reducing the reinforcing force of each stage obtained in the step (4) according to the requirement of the specification safety factor 1.35 to obtain the horizontal reinforcing force (shown in figure 5) of the active reinforcing design of the anchor cable and the designed value of the length of the anchor cable, wherein the anchoring force is 5930KN, the length of the free section of the anchor cable is determined by a slide automatic search sliding surface, and the length of the anchoring section is calculated by the horizontal reinforcing force, which is shown in table 3.
TABLE 3 active reinforcing design for prestressed anchor cable
And 6, rechecking the design parameters of the anchor cable, wherein the drawing force provided by a single cable is not more than 3000kN, the length is not more than 50m, the anchoring section is not more than 10m, the free section is not less than 3m, and the design is finished after rechecking according to the control indexes. If the single-piece drawing force is too large or the calculated length of the anchoring section is too large, the adjustment layout is improved, but the distance is not smaller than 1.5m until all indexes meet the requirements, as shown in fig. 6.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A cutting slope active reinforcement design method is characterized by comprising the following steps:
s1, calculating and acquiring horizontal stress of geometric point positions of the cutting slope at different depths in the excavation process, and drawing a cutting slope depth-horizontal stress curve graph;
s2, drawing a corresponding depth-static soil pressure curve according to the soil pressure at the geometric point positions of different depths of the cutting slope;
s3, subtracting the horizontal stress after excavation from the static soil pressure of the same geometric point at the same depth to obtain the horizontal stress loss value of the position, drawing a depth-horizontal stress loss value curve, estimating along height integral according to the stress difference between the top and the bottom of each grade of slope to obtain the horizontal loss force of the corresponding position, and drawing a depth-horizontal loss force curve;
s4, applying the horizontal loss force value reverse compensation of each grade of slope in the step S3 to the specified height position of the single grade of slope height, calculating to obtain a cutting slope stability coefficient, determining the engineering grade of the designed cutting slope and the corresponding safety standard of the normal operation working condition, constructing a horizontal compensation force correction coefficient model according to the safety standard corresponding to the normal operation working condition of the cutting slope, constructing a cutting slope horizontal reinforcement force calculation model according to the horizontal compensation force correction coefficient model, and calculating the total horizontal reinforcement force corresponding to each grade of slope;
s5, calculating the design drawing force of each anchor cable according to the determined total horizontal reinforcing force corresponding to each grade of slope and the horizontal reinforcing force required to be provided by each anchor cable on the slope at the corresponding position, and calculating the length of the anchoring section, the length of the free section of the anchor cable and the length of the designed prestressed anchor cable according to the design drawing force.
2. The active reinforcing design method for cutting slopes according to claim 1, wherein in step S1, a numerical model of the cutting slope in consideration of excavation is established according to a designed profile of the cutting slope and stratigraphic physical mechanical parameters provided by investigation, and horizontal stress at different depth geometric points of the cutting slope in the excavation process is calculated.
3. The active reinforcing design method for cutting slopes according to claim 1, wherein in step S2, the earth pressure at different depth geometric point positions is obtained according to a designed and given cutting slope design profile, and the provided formation physical and mechanical parameters are investigated, and according to an original terrain slope numerical model.
4. The cutting slope active reinforcement design method according to claim 1, wherein the step S3 specifically includes the steps of:
s31, solving horizontal stress loss values corresponding to different depths, subtracting the horizontal stress of the corresponding position after the excavation of the cutting slope is finished from the static soil pressure of the corresponding position to obtain the horizontal stress loss value of the depth position, and drawing a depth-horizontal stress loss value curve according to the horizontal stress loss value;
s32, solving the horizontal force loss values corresponding to different depths, obtaining the horizontal stress loss value corresponding to the top and the foot of each grade of slope according to the depth-horizontal stress loss value curve drawn in the step S31, estimating the horizontal stress loss value along the height integral to obtain the horizontal loss force at the corresponding position, and drawing the depth-horizontal loss force curve.
5. The cutting slope active reinforcement design method according to claim 4, wherein the calculation model of the horizontal stress loss value is:
Ph＝σh1-σh2 (1)
in the formula, PhTo a horizontal stress loss value, σh1Horizontal stress of original terrain, sigma, obtained for finite element numerical simulationh2The horizontal stress of the excavated terrain is obtained by finite element numerical simulation;
the calculation model of the horizontal loss force is as follows:
in the formula, Fi+1The horizontal force loss value P corresponding to the width of the i +1 th grade slope per meter of cross slopeh,iThe horizontal stress loss value P corresponding to the width of the i-th grade slope per meter of cross slopeh,i+1The horizontal stress loss value is corresponding to the width of each meter of cross slope of the i +1 grade slope, and h is the horizontal distance from the starting point of the top of the slope.
6. The cutting slope active reinforcement design method according to claim 1, wherein the step S4 specifically includes the steps of:
s41 horizontal compensation force correction coefficient calculation, namely searching the safety standard of the normal operation condition corresponding to the cutting slope according to the standard, establishing a cutting slope numerical model considering the compensation force by using a limit balance method, calculating to obtain a slope stability coefficient, and establishing a horizontal compensation force correction coefficient model according to the slope stability coefficient;
s42, considering the corrected horizontal reinforcing force of the compensation effect, changing the direction of the horizontal reinforcing force to point into a slope on the basis of solving the horizontal loss force, namely, the horizontal reinforcing force is preliminarily determined; and multiplying by a correction coefficient to obtain the horizontal reinforcing force with safety guarantee.
7. The active reinforcing design method for cutting slopes according to claim 6, wherein the correction coefficient formula is as follows:
wherein C is a horizontal compensation force correction coefficient, FsCalculating a slope stability coefficient by considering a lower limit balance method of a horizontal compensation force under the normal operation condition of the cutting slope;
the calculation model of the horizontal reinforcing force is as follows:
Fj+1＝-C×Fi+1 (4)
in the formula, Fj+1And j and i are equal in magnitude and opposite in direction for the corrected horizontal reinforcing force considering the compensation effect of the force corresponding to the width of the cross slope of the (i + 1) th grade, and are used for distinguishing the horizontal reinforcing force from the horizontal force loss value.
8. The cutting slope active reinforcement design method according to claim 1, wherein the step S5 specifically includes the steps of:
s51, estimating the length of an anchoring section, estimating the total horizontal reinforcing force corresponding to the 3m width of each grade of slope in the transverse direction according to the 3m multiplied by 3m layout, and dividing the single-grade slope height by 3 times of the sine of the design slope angle to obtain the number of anchor cables designed for the grade of slope;
s52 calculation of length of prestressed anchor cable with horizontal reinforcing force Fj+1Multiplying by 3m to obtain the total horizontal reinforcing force of the grade of slope corresponding to the transverse slope width of 3m, dividing the total horizontal reinforcing force by the number of the anchor cables to obtain the horizontal reinforcing force provided by each anchor cable, dividing the horizontal reinforcing force of each anchor cable by the cosine of the incident angle to obtain the drawing force of each anchor cable, dividing the drawing force of each anchor cable by the polar friction resistance of the hole wall and the unit side surface area pi d to obtain the length L of the anchoring sectionaDetermining the length L of the free section of the anchor cable according to the number of the anchor cables with the incidence angle alpha of the anchor cables arranged on the slope surface and the potential worst slip surfacefAnd calculating the length of the pre-stressed anchor cable according to the length;
wherein the length L of the anchoring sectionaThe length L of the free section of the anchor cable is the length required below the sliding surfacefIs a slopeFace to sliding face distance.
9. The cutting slope active reinforcement design method according to claim 8, wherein the calculation model of the number of anchor cables is:
in the formula, nj+1The number of anchor cables h is longitudinally distributed for every 3m of cross slope width of the i +1 th grade slopei+1Is grade i +1, height of slope, betai+1Designing a slope angle for the (i + 1) th grade slope;
the anchor cable design length calculation model is as follows:
Li+1,m＝Li+1,m,a+Li+1,m,f+1 (7)
in the formula, Li+1，m，aThe length of the anchoring section of the mth anchor cable for the (i + 1) th grade slope from the top of the grade slope to the bottom is calculated by using a formula (6), and Li+1，m，fThe length of the mth anchor cable free section is counted from the top of the single-stage slope to the bottom of the (i + 1) th slope, and m is less than or equal to nj+1And measuring the slope surface to the slip surface to obtain the angle alpha, beta and d, wherein alpha is the angle of incidence of the anchor cable, beta is the slope angle designed for the grade slope, and d is the aperture of the anchor cable drilling hole.
10. The active reinforcing design method for cutting slopes according to any one of claims 1 to 9, further comprising:
s6, according to the control indexes that the pulling force provided by a single anchor cable is not more than 3000kN, the length is not more than 50m, the anchoring section is not more than 10m and the free section is not less than 3m, rechecking the length of the anchoring section, the length of the free section of the anchor cable and the length of the designed prestressed anchor cable which are obtained by calculation in the step S5, if the pulling force of the single anchor cable is too large or the length of the anchoring section obtained by calculation is too large, the layout of the anchor cables is sealed, but the distance between adjacent anchor cables is not less than 1.5m, and the step S5 is returned until all the indexes meet the requirements.
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