Method and system for predicting stability of anti-inclined rock slope under slope top load action

Abstract

The present application provides a method and system for predicting the stability of an anti-inclined rock slope under the action of slope top load, proposes a slope collapse failure surface determination criterion that conforms to actual conditions, and can quickly and accurately determine the failure surface and slope stability through the geometric boundary conditions and rock mass mechanical parameters of the anti-inclined rock slope. The method for predicting the stability of an anti-inclined rock slope under the action of slope top load comprises the following steps: Step 1: constructing a two-dimensional anti-inclined rock slope analysis model based on the geometric parameters and rock mass mechanical parameters of the anti-inclined rock slope; Step 2: determining the failure surface of the anti-inclined rock slope collapse based on the slope collapse failure surface determination criterion for the two-dimensional anti-inclined rock slope analysis model; Step 3: establishing a relationship formula for the normal force between rock layers based on the size and stress condition of the rock mass, and determining the stress condition between rock layers; Step 4: judging the stability of the anti-inclined rock slope under the action of slope top load according to the stress condition between rock layers.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of geological disaster prevention and control, and particularly relates to a method and system for predicting the stability of an anti-dip rock slope under the action of slope top load. BACKGROUND

[0002] With the construction of highways, water conservancy and hydropower and other infrastructure, a large number of natural slopes have been artificially exposed and disturbed, and landslides occur frequently. The collapse and destruction of anti-dip rock slopes is a typical slope failure mode, and it is crucial to evaluate the stability of anti-dip rock slopes under the action of slope top load.

[0003] The anti-dip rock slope is characterized by one or more sets of bedding or foliation consistent with the slope direction and opposite to the slope direction. The non-linear large deformation characteristics of the failure process are prominent, and it is difficult to analyze the stability using the finite element method. At present, the main method for evaluating the stability of anti-dip rock slopes is the limit equilibrium method, which analyzes the forces between rock blocks step by step from top to bottom. However, this method has some limitations. It assumes that the bottom of the rock layer is a complete straight line and does not consider the influence of interlayer cohesion and slope top load, which does not match the actual situation. In addition, the tensile strength of the rock layer is one of the decisive factors for collapse and destruction, but the limit equilibrium method does not consider it. Furthermore, under the action of slope top load, most existing methods assume that the failure surface passes through the slope toe and forms a certain angle with the normal line of the layer surface. However, the actual failure surface is often a curved surface, and the failure surface does not necessarily pass through the slope toe. This assumption is obviously not in line with the actual situation. SUMMARY

[0004] To solve the above technical problems, the present application provides a method and system for predicting the stability of an anti-dip rock slope under the action of slope top load, which proposes a slope collapse and destruction surface determination criterion that conforms to the actual situation. The stability is evaluated through the geometric boundary conditions and rock mass mechanical parameters of the anti-dip rock slope, which can quickly and accurately determine the failure surface and the stability of the slope.

[0005] <Method>

[0006] The method for predicting the stability of an anti-dip rock slope under the action of slope top load provided by the present application is characterized by the following steps:

[0007] Step 1: Construct a two-dimensional anti-dip rock slope analysis model based on the geometric parameters and rock mass mechanical parameters of the anti-dip rock slope;

[0008] Step 2: Determine the failure surface of the anti-dip rock slope collapse and destruction based on the slope collapse and destruction surface determination criterion for the two-dimensional anti-dip rock slope analysis model; the slope collapse and destruction surface determination criterion is:

[0009] 1) As the slope top load loading range increases, the failure area increases;

[0010] 2) Initial failure vertically downward, and the vertical joint direction failure is generated when the joint is reached;

[0011] 3) After reaching the maximum reference surface, failure along the maximum reference surface;

[0012] 4) The intersection point of the vertical line on the right side of the slope top load loading range and the straight line of the vertical joint is the turning point of the failure surface;

[0013] 5) After exceeding the maximum loading length, the failure mode is fixed, and the failure surface does not change;

[0014] The failure surface is different when the slope top load loading range is divided, and it is generally divided into three failure periods, the first and second periods are distributed, and the third period appears last; and the division follows the principle that the larger the slope top load loading range, the larger the landslide volume; the slope top load loading range is the loading range under the slope top load of the counter-inclined rock slope;

[0015] First period: corresponding to criteria 1), 2), and 4); the rightmost point of the loading range is in the first half of the rock mass, and the vertical downward intersection with the reference surface of the vertical joint forms a failure surface; but as the loading range increases, the slope body that occurs toppling failure should increase, and simply dividing the failure surface according to criterion 2) will make the landslide volume smaller, so criterion 1) should also be followed, so the initial failure vertically downward line should intersect the lower surface of the n-1 rock layer, thereby dividing the first failure period;

[0016] Second period: corresponding to criteria 1), 2), and 4); when the slope top load loading range falls in the second half of the rock layer, the slope top load loading range increases, the initial failure vertically downward directly intersects the lower surface of the rock layer n, and intersects the reference surface of the vertical joint to form a failure surface, thereby dividing the second period;

[0017] Third period: corresponding to criteria 1), 3), and 5); when the slope top load loading range is large enough, the initial failure position vertically downward can always intersect the maximum reference surface, and the maximum reference surface is a straight line passing through the slope angle and the joint, and this range is divided into the third period; when the initial failure position vertically downward can always intersect the maximum reference surface, it is the starting point of the third period division range, and the endpoint is the intersection point of the maximum reference surface and the slope top; when the slope top load loading range exceeds the intersection point of the maximum reference surface and the slope top, the failure mode is fixed and does not change, and it always fails along the maximum reference surface;

[0018] The failure surface and the slope surface together form a landslide body region, and based on the failure surface, each rock layer in the landslide body region is segmented to disperse the corresponding rock mass;

[0019] Step 3: Establish a relationship formula for the normal force between rock layers based on the size and stress of the rock mass, and determine the stress between rock layers;

[0020] Step 4: Determine the stability of the reverse-dip rock slope under the load at the top of the slope based on the stress between the rock strata.

[0021] Preferably, in the method for predicting the stability of a reverse-dip rock slope under top load provided by the present invention, in step 1, the geometric parameters and rock mechanics parameters of the reverse-dip rock slope include: the slope height of the reverse-dip rock slope. slope angle Rock layer thickness and rock strata dip angle Cohesion of layered or structural surfaces and internal friction angle The cohesion of the rock mass internal friction angle and tensile strength Length of load at the top of the slope and load size .

[0022] Preferably, in the method for predicting the stability of a reverse-dip rock slope under top load provided by the present invention, in step 2, for each period, when a special case occurs that conflicts with criterion 1) when the division based on criterion 2) or criterion 3) occurs, the failure point should extend to the next bedding layer when it is vertically downward, rather than the bedding layer of the current rock layer.

[0023] Preferably, in the method for predicting the stability of a reverse-dip rock slope under top load provided by the present invention, after determining the landslide area in step 2, the rock blocks are numbered from left to right. Let the rightmost rock block that has collapsed be numbered n and the leftmost rock block be numbered 1. When the right end of the loading range falls on the (n+1)th rock block, the small part of the rock block that was cut is merged into the nth rock block.

[0024] Preferably, in the method for predicting the stability of a reverse-dip rock slope under top load provided by the present invention, the relationship between the normal forces between rock layers in step 3 is as follows:

[0025] ,

[0026] In the formula: and They are rock blocks The normal forces acting on the left and right sides, It is a rock. The maximum tensile stress subjected to It is a rock. Self-respect It is a rock. The upper surface is subjected to a uniformly distributed external load; It is the structural surface cohesion after strength reduction. It is the internal friction angle of the structural surface after strength reduction. is the thickness of the rock block , , are the right height and the left height of the rock block , , is the dip angle of the rock block , is the length of the upper surface of the rock block , is the force concentration coefficient of the normal force.

[0027] Preferably, the method for predicting the stability of the anti-dip rock slope under the slope top load provided by the present application, in step 3, is .

[0028] Preferably, the method for predicting the stability of the anti-dip rock slope under the slope top load provided by the present application, in step 4, based on step 3, the size of the normal force between the rock layers is continuously changed by the strength reduction method, the size of the anti-sliding force and the sliding force of the outermost rock block is calculated, and the stability of the slope is judged by comparing the anti-sliding force and the sliding force of the outermost rock block;

[0029] The calculation formula of the anti-sliding force and the sliding force is:

[0030] ,

[0031] In the formula, and represent the anti-sliding force and the sliding force of the outermost rock block, is the normal force at the bottom of the outermost rock block, is the weight of the outermost rock block, and are the cohesion and the internal friction angle of the rock mass after strength reduction, is the normal force inside the outermost rock block, and are the thickness and the dip angle of the outermost rock block; according to the size relationship between and , the stability of the anti-dip rock slope is judged, and the judgment criteria are as follows:

[0032] I) , the slope is in a stable state;

[0033] II) , the slope is in a limit equilibrium state;

[0034] III) , the slope is in an unstable state;

[0035] When the slope is in limit equilibrium state, the reduction factor at this time is the safety factor of the anti-dumping rock slope; the safety factor is greater than 1.0, which is a stable slope; the safety factor is greater than 1.0, which is an unstable slope.

[0036] <Device>

[0037] Further, the present application also provides a system for predicting the stability of an anti-dumping rock slope under the action of slope top load, which automatically implements the above-mentioned <method>, comprising:

[0038] A model initial construction unit constructs a two-dimensional anti-dumping rock slope analysis model based on the geometric parameters and rock mass mechanical parameters of the anti-dumping rock slope.

[0039] A failure surface determination unit determines the failure surface of the anti-dumping rock slope based on the slope dumping failure surface determination criterion for the two-dimensional anti-dumping rock slope analysis model; the slope dumping failure surface determination criterion is:

[0040] 1) As the slope top load loading range increases, the failure area increases;

[0041] 2) The initial failure is vertically downward, and when the joint is reached, the vertical joint direction failure is generated;

[0042] 3) After reaching the maximum reference surface, the failure along the maximum reference surface is generated;

[0043] 4) The intersection point of the vertical line on the right side of the slope top load loading range and the vertical joint line is the turning point of the failure surface;

[0044] 5) After exceeding the maximum loading length, the failure mode is fixed, and the failure surface does not change;

[0045] The failure surfaces divided by different slope top load loading ranges are different, and are generally divided into three failure periods, the first period and the second period are distributed at intervals, and the third period appears last; and the division follows the principle that the larger the slope top load loading range, the larger the landslide volume; the slope top load loading range is the loading range under the slope top load of the anti-dumping rock slope;

[0046] The first period corresponds to criteria 1), 2), and 4); the rightmost point of the loading range is in the first half of the rock block, vertically downward and intersects with the reference surface of the vertical joint to form a failure surface; but as the loading range increases, the slope body that occurs dumping failure should increase, and simply dividing the failure surface according to criterion 2) will make the landslide volume smaller, so criterion 1) should also be followed, so the vertically downward line should intersect with the lower surface of the n-1 rock layer, thereby dividing the first failure period;

[0047] The second period corresponds to criteria 1), 2), and 4). When the load range at the top of the slope falls on the latter half of the rock layer, the load range at the top of the slope increases. The initial failure is vertically downward and directly intersects the lower surface of rock layer n, intersecting with the reference plane perpendicular to the bedding to form a failure surface, thus dividing the second period.

[0048] The third period corresponds to criteria 1), 3), and 5). When the load range at the top of the slope is sufficiently large, the initial failure location vertically downwards will always intersect with the maximum reference plane. The maximum reference plane is the straight line passing through the slope angle and perpendicular to the bedding. This range is defined as the third period. When the initial failure location vertically downwards always intersects with the maximum reference plane, it marks the starting point of the third period's division, and its ending point is the intersection of the maximum reference plane and the top of the slope. When the load range at the top of the slope exceeds the intersection of the maximum reference plane and the top of the slope, the failure mode remains fixed and always fails along the maximum reference plane.

[0049] The rock block division section, the failure surface and the slope surface together form the landslide area. Based on the failure surface, the rock layers in the landslide area are divided and the corresponding rock blocks are separated.

[0050] The interlayer stress determination section establishes the relationship between the normal forces between rock layers based on the size and stress conditions of the rock blocks, and determines the stress conditions between the rock layers.

[0051] The stability prediction department determines the stability of the reverse-dip rock slope under the action of the slope top load based on the stress between the rock strata.

[0052] The control unit is connected in communication with the model initialization unit, failure surface determination unit, rock block division unit, interlayer stress determination unit, and stability prediction unit, and controls their operation.

[0053] Preferably, the stability prediction system for anti-dip rock slopes under top load provided by the present invention may further include: an input display unit, which is communicatively connected to the model initialization unit, the failure surface determination unit, the rock block division unit, the interlayer stress determination unit, the stability prediction unit, and the control unit, for allowing users to input operation commands, and displaying the data and files of the corresponding units in the form of text, tables, graphics, static or dynamic models according to the operation commands.

[0054] Preferably, in the stability prediction system for reverse-dip rock slopes under top load provided by the present invention, the relationship between the normal forces between rock layers in the interlayer force determination section is as follows:

[0055] ,

[0056] In the formula: and They are rock blocks The normal forces acting on the left and right sides, It is a rock. The maximum tensile stress subjected to It is a rock. Self-respect It is a rock. The upper surface is subjected to a uniformly distributed external load; It is the structural surface cohesion after strength reduction. It is the internal friction angle of the structural surface after strength reduction. It is a rock. thickness, , They are rock blocks Right side height and left side height , It is a rock. The angle of inclination, It is a rock. The length of the upper surface subjected to external load, It is the force concentration factor of the normal force.

[0057] The role and effect of invention

[0058] This invention fully considers the structural strength, rock mass strength, and force distribution characteristics, proposing a criterion for determining the slope toppling failure surface. This allows for rapid and accurate identification of the failure surface, thereby improving the stability analysis model under slope crest load. Furthermore, it proposes a relationship between the normal forces between rock layers to determine the stress conditions between them and assess the stability of reverse-dipping rock slopes under slope crest load. This approach better reflects the actual situation of reverse-dipping rock slopes toppling under slope crest load, improving calculation accuracy and making the prediction results more accurate and reliable. This invention provides a scientific and reliable new approach for stability prediction of reverse-dipping rock slopes in highway slopes, open-pit mines, and hydropower facilities, offering advantages such as simple algorithm structure, accurate calculation results, easy programmability, and high computational efficiency. Attached Figure Description

[0059] Figure 1 This is a flowchart of the method for predicting the stability of a reverse-dip rock slope under top load according to an embodiment of the present invention;

[0060] Figure 2 This is a schematic diagram of the slope failure zone involved in an embodiment of the present invention;

[0061] Figure 3 This is a diagram showing the loading cycle division for different load lengths in an embodiment of the present invention;

[0062] Figure 4 The rock block subjected to external load involved in the embodiments of the present invention Force analysis diagram;

[0063] Figure 5 The rock block involved in the embodiments of the present invention is not subjected to external load. Force analysis diagram;

[0064] Figure 6 This is a stress analysis diagram of rock block 1 involved in an embodiment of the present invention;

[0065] Figure 7 The failure modes of the anti-dip rock slope top load experiment with different rock strata dip angles involved in the embodiments of the present invention are shown in (a) to (d), where the rock strata dip angles are 45°, 50°, 55° and 60° respectively.

[0066] Figure 8 The embodiments of the present invention involve displacements of different rock strata dip angles predicted by the present invention, wherein the rock strata dip angles of (a) to (d) are 45°, 50°, 55°, and 60° respectively.

[0067] Figure 9 This is a simplified diagram illustrating the loading process in an embodiment of the present invention.

[0068] In the picture:

[0069] - Load application length, -Load size -Slope height, - Rock layer thickness, -Rock block number, - Rock strata dip angle Slope angle, - Rock Upper surface load length, and -These are rock blocks Normal force distribution on the right and left sides and -These are rock blocks Surface friction on the right and left sides and -These are rock blocks Right and left side heights and -These are rock blocks Right-side normal force and left normal force Simplified concentration -Normal force concentration factor, - Rock torque, - Rock Anti-slip strength - Rock Bottom normal force, - Rock Self-respect and - Rock Right-side normal force and left normal force The simplified point of application. Detailed Implementation

[0070] The following description, in conjunction with the accompanying drawings, details the method and system for predicting the stability of a reverse-dip rock slope under top load, as per the present invention.

[0071] <Example 1>

[0072] like Figure 1 As shown in this embodiment, the method for predicting the stability of a reverse-dip rock slope under top load includes the following steps:

[0073] Step 1: Based on the anti-dip rock slope for which the stability of the project will be evaluated, obtain the slope height through field investigation and laboratory tests. slope angle Rock layer thickness and rock strata dip angle Cohesion of bedding or result surfaces and internal friction angle The cohesion of the rock mass and internal friction angle ,tensile strength and rock density ;like Figure 2 As shown, the magnitude and range of the load to be applied at the top of the slope are determined according to engineering needs. If no load is required, the value is 0. Rock blocks affected by the load at the top of the slope are represented by white areas, rock blocks on the slope surface are represented by gray areas, and rock block 1 is represented by black. In step 1, a numerical model of the reverse-dip rock slope is established based on the basic geometric parameters and rock mechanics parameters of the reverse-dip rock slope, which is used for the calculation in step 2.

[0074] Step 2: Determine the failure surface criteria, combine the digital model from Step 1 with the load loading length at the top of the slope (loading range, for example, if a foundation building is constructed on the top of the slope, then the free surface of the foundation building relative to the reverse-dipping rock slope is the loading range), establish the failure surface of the reverse-dipping rock slope, and obtain a numerical model of the reverse-dipping rock slope with the failure surface, which is used for the calculation in Step 3.

[0075] Within the slope crest area, the larger the loading range, the larger the landslide mass that will collapse. Therefore, different loading lengths result in different failure surfaces, such as... Figure 3 As shown, the criteria for determining the failure surface are as follows:

[0076] 1) As the loading length increases, the damaged area increases.

[0077] 2) The initial damage is vertically downward, and damage occurs in the direction perpendicular to the joint when it reaches the joint.

[0078] 3) After reaching the maximum datum plane, it fails along the maximum datum plane.

[0079] 4) The point where the perpendicular line drawn to the right side of the loading range intersects with the straight line perpendicular to the bedding plane is the turning point of the failure surface.

[0080] 5) After exceeding the maximum loading length, the failure mode is fixed and the failure surface remains unchanged.

[0081] According to the above criteria, the failure surfaces differ depending on the loading length, but generally they are divided into three failure cycles: the first and second cycles are interspersed, and the third cycle occurs last. Furthermore, the division follows the principle that the larger the loading range, the larger the landslide volume. Figure 3 As shown:

[0082] First cycle: Area numbered ①; the rightmost endpoint of the loading range is in the front half of the rock block, vertically downwards and intersecting with the reference plane of the vertical bedding to form a failure surface; however, as the loading range increases, the slope body that will collapse should increase. Simply dividing the failure surface according to criterion 2) will make the landslide volume smaller, so criterion 1) should be followed at the same time. Therefore, the vertically downward line of the initial failure should intersect with the lower surface of the n-1 rock layer to ensure that the failure range increases, thus dividing it into the first failure cycle.

[0083] Second period: Region numbered ②; when the loading range falls on the latter half of the rock layer, the loading range increases, and the initial failure is vertically downward and directly intersects the lower surface of rock layer n, intersecting with the reference plane perpendicular to the bedding to form a failure surface, thus dividing the second period.

[0084] The third period: Region ③; when the loading range is large enough, the initial failure location vertically downwards will always intersect the maximum datum plane, which is the straight line passing through the slope angle and perpendicular to the bedding plane. This range is designated as the third period. When the loading range exceeds the maximum datum plane, the failure mode remains fixed and always fails along the maximum datum plane. The point where the initial failure location vertically downwards always intersects the maximum datum plane marks the starting point of the third period's division, and its endpoint is the intersection of the maximum datum plane and the slope crest, as shown below. Figure 3 The reference plane refers to the maximum reference plane. Secondly, when the loading length exceeds the intersection of the maximum reference plane and the slope crest, the failure surface always fails along the maximum reference plane of the third cycle. When the loading range does not exceed the maximum reference plane, it is determined based on the fact that the initial failure position, when vertically downward, always intersects the maximum reference plane.

[0085] The first and second halves mentioned above are determined based on the midpoint of the rock block corresponding to the rock layer, with each rock layer corresponding to one rock block.

[0086] The failure surface is composed of two straight lines, forming a structure like... Figure 3 The line segment is shown in the diagram. Based on engineering requirements, the loading range at the top of the reverse-dip rock slope is determined. Then, combining this with the criteria and periodic distribution patterns, the location of the failure surface can be determined.

[0087] Based on the fact that the failure surface and the slope surface together form a landslide area, and based on the distribution of slope joints in the landslide area, the landslide area is divided into multiple rock layers, and corresponding rock blocks are separated from each rock layer based on the failure surface.

[0088] Step 3: Establish the relationship between the normal forces between rock layers. Based on the established relationship between the normal forces between rock layers and the digital model of the reverse-dip rock slope with the failure surface established in Step 2, calculate the interlayer forces of each rock block and output the interlayer forces of each rock block for the next step of judging the slope stability.

[0089] Step 3-1: After determining the scope of damage according to Step 2, such as... Figure 2 As shown, the rock blocks are numbered from right to left. The rightmost rock block that collapsed is numbered n, and the leftmost rock block is numbered 1, which facilitates the unified expression of the formula. At the same time, the geometric dimensions of each rock block and the loading length at the top are calculated.

[0090] Step 3-2, as follows Figure 4 and 5 As shown, Figure 4 This indicates that there is an external load on the upper surface of the rock block at the top of the slope. Figure 5 This indicates that there is no external load on the upper surface of the rock blocks on the slope. A force analysis is performed on each rock block to establish its force balance equations and moment balance equations. Figure 4 For example, from the force balance equation along the centerline of the rock block, we can obtain:

[0091] ,

[0092] ,

[0093] In the above formula, It is a rock. The formula for calculating its own weight is: , , and It is a rock. The normal forces on the right and left sides, the normal force on the right side is: The normal force on the left is: .

[0094] At the same time, according to the torque balance equation, we can obtain:

[0095] ,

[0096] ,

[0097] In the above formula, is a dimensionless number representing the interlayer normal force of the rock mass. The point of application is at a distance from the bottom of the rock block. Place.

[0098] Step 3-3: The reverse-dip rock slope to be analyzed consists of rock strata and structural planes. Based on the cantilever beam method, the relationship between the rock strata moment and the tensile strength of the rock mass can be established:

[0099] ,

[0100] In the formula, Let the moment of inertia of the rock block be... , It refers to the cross-sectional area of ​​the rock block, because the established analysis model is a two-dimensional model. .

[0101] Step 3-4: Establish the force transmission relationship of the rock strata in the reverse-dip rock slope. Substitute the moment balance equation and force balance equation into the relationship established in step 3-3 to establish the normal force between the rock strata. Relationship:

[0102] ,

[0103] In the formula: and They are rock blocks The normal forces acting on the left and right sides, It is a rock. The maximum tensile stress subjected to It is a rock. Self-respect It is a rock. The upper surface is subjected to a uniformly distributed external load; It is the structural surface cohesion after strength reduction. It is the internal friction angle of the structural surface after strength reduction. It is a rock. thickness, and They are rock blocks Right side height and left side height It is a rock. The angle of inclination, It is a rock. The length of the upper surface subjected to external load, This refers to the force concentration factor of the normal force. Existing techniques typically take the force concentration factor of the normal force as 1 or 0.5, but this does not reflect the actual situation. This invention has discovered... Values It is more in line with the actual situation.

[0104] Based on the stress analysis of the rock block, it can be seen that the rightmost fault line is... If the rock block is a stable rock block and will not tip over, then the first... rock block to rock block The normal force is 0, that is Therefore, we can obtain the result from the above formula. The magnitude of the normal force can be deduced by analogy; based on this equation, the normal forces on the right and left sides of the rock block can be calculated sequentially from right to left. and size.

[0105] Steps 3-5: To evaluate the stability of the reverse-dip rock slope, a strength reduction method needs to be introduced into the rock stratum normal force relationship to change the magnitude of the rock stratum normal force; firstly, the strength of the structural surface is reduced:

[0106] ,

[0107] Furthermore, a reduction calculation is performed on the rock mass strength:

[0108] ,

[0109] ,

[0110] Substituting the reduced rock mass strength into the relationship of the normal force of the rock block, we can obtain the following formula:

[0111] ,

[0112] Step 4: Calculate the safety factor of the reverse-dip rock slope based on interlayer forces. Predict stability. If stable, increase the safety factor and return to step 3 to recalculate; if unstable, decrease the safety factor and return to step 3 to recalculate; if in a limiting equilibrium state, stop the calculation and output the safety factor.

[0113] After introducing the strength reduction method into the normal force relationship of rock blocks, such as Figure 6 As shown, through the force analysis of rock block 1, the force balance equation is established:

[0114] ,

[0115] In the formula: and These represent the anti-sliding force and sliding force of rock block 1, respectively, according to and The relative sizes of these elements can be used to determine the stability of a reverse-dip rock slope. The criteria for this determination are as follows:

[0116] I) The slope is in a stable state;

[0117] II) The slope is in a state of limit equilibrium;

[0118] III) The slope is in an unstable state.

[0119] When a slope is in a state of limit equilibrium, the reduction factor at this point is the safety factor of the reverse-dip rock slope. A safety factor greater than 1.0 indicates a stable slope; a safety factor greater than 1.0 indicates an unstable slope.

[0120] The predictions of this invention were verified through experiments:

[0121] like Figure 7 The figure shows the failure phenomena of four reverse-dip rock slope indoor experimental models under slope crest load. The models were designed according to similarity theory, and the results of the indoor experiments show a high degree of similarity to actual engineering conditions. Therefore, the results of the model experiments can directly reflect the failure phenomena in the field. The rock strata dip angles of the four reverse-dip rock slopes are 45°, 50°, 55°, and 60°, and the other experimental conditions are the same. It can be seen that when the slope crest load is applied, the cracks in the rock strata of the reverse-dip rock slope begin to propagate, and the failure surface is different under different rock strata dip angles.

[0122] like Figure 8 As shown, the displacement was simulated using the method of this invention via PFC software. The rock mass mechanics parameters of the model were set the same as those in the laboratory experiment, with dip angles of the rock strata of 45°, 50°, 55°, and 75°. Figure 8 The simulation results show that the results are consistent with... Figure 7 The results of the indoor experiments shown are basically consistent, proving that the present invention can effectively study the failure mechanism of reverse-dip rock slopes under engineering loads, and well presents the failure mode and failure mechanism of reverse-dip rock slopes in actual engineering, solving the problem of evaluating the stability of reverse-dip rock slopes under top loads.

[0123] To more intuitively demonstrate the effects of this invention, the analytical model is applied to an example calculation, such as a reverse-dip rock slope. Figure 9 As shown.

[0124] Step 1: Because a highway may be built above the top of the slope or there may be residential areas, the top of the slope is considered to be under load. Assume the loading length is 16m and the load is 500KN / m. The geometric parameters and rock mechanics parameters of the slope are summarized in Table 1 below:

[0125] Table 1. Slope geometric parameters and rock mechanics parameters

[0126]

[0127] Step 2: Based on the loading range and failure surface criteria of the slope, the failure surface is located in the first cycle and consists of two straight segments, such as... Figure 9 As shown by the dashed line; because falling in the first period will cause a small-scale cutting of the rock block, the rock block n is an irregular quadrilateral, such as... Figure 9 As shown in the image.

[0128] Step 3: Based on the limit equilibrium method and cantilever beam method, establish the normal force relationship between rock strata. Assume the reduction factor is equal to 1 in the first calculation. Figure 9 In the middle, because the region to the right of rock block n is a stable region, the normal force of rock block n is... =0, so The calculation formula is:

[0129] ,

[0130] By analogy, the normal force on each rock block on the failure surface can be calculated using the following formula:

[0131] ,

[0132] Step 4: After completing Step 3, the normal force of rock block 1 is known. Calculate the anti-sliding force of rock block 1. and downward force :

[0133] ,

[0134] Comparison of anti-slip forces and downward force The size, when:

[0135] I) The slope is in a stable state.

[0136] II) The slope is in a state of limit equilibrium.

[0137] III) The slope is in an unstable state.

[0138] When rock block 1 is in the first scenario, increase the reduction factor and repeat step 3 until the second scenario occurs. When rock block 1 is in the second scenario, the reduction factor at this point is the safety factor of the slope, and the calculation can be stopped. When rock block 1 is in the third scenario, decrease the reduction factor and repeat step 3 until the second scenario occurs. The calculated safety factor of the slope is 0.820, which is less than 1.0, indicating an unstable slope that may experience instability. This prediction is consistent with the actual situation.

[0139] <Example 2>

[0140] This embodiment 2 provides a stability prediction system for anti-dip rock slopes under top load that can automatically implement the above-described method of the present invention. The system includes a model initialization unit, a failure surface determination unit, a rock block division unit, an interlayer stress determination unit, a stability prediction unit, an input display unit, and a control unit.

[0141] The initial model construction section follows the steps described in step 1 above, constructing a two-dimensional analysis model of the reverse-dip rock slope based on the geometric and rock mechanics parameters of the reverse-dip rock slope.

[0142] The failure surface determination process follows the steps described in step 2 above. For the two-dimensional reverse-dip rock slope analysis model, the failure surface of the reverse-dip rock slope is determined based on the slope failure surface determination criteria. Specifically, the criteria and the period are combined, and then automatically divided by computer. First, based on the data obtained from the slope's loading length, the right end of the loading range is determined to fall within a specific period. Starting from that point, the slope moves vertically downwards until a failure surface perpendicular to the joint is generated. The period division is as follows: Figure 3 As shown, once the right end of the loading range falls within a given period, the larger the loading range, the larger the damage volume. Then, starting vertically downwards from that point, after contacting the bedding plane, the damage propagates perpendicular to that bedding plane, as shown... Figure 4 The diagram shows a case where the failure surface is determined, meaning the failure surface can be identified.

[0143] The initial model building section first needs to construct a numerical model of the reverse-dip rock slope based on the input slope geometric parameters, sketch the actual shape of the slope, and store it using numerical equations. Then, the failure surface determination section can automatically divide the failure surface based on the range and periodic distribution of the loading and the failure surface criterion.

[0144] The rock block division section performs the steps described in step 3 above. The failure surface and the slope surface together form a landslide area. Based on the failure surface, the rock layers in the landslide area are divided to separate the corresponding rock blocks.

[0145] The interlayer stress determination section performs the steps described in step 4 above, establishes the relationship between the normal forces between rock layers based on the size and stress conditions of the rock blocks, and determines the interlayer stress conditions.

[0146] The stability prediction department determines the stability of the reverse-dip rock slope under the action of the slope top load based on the stress between the rock strata.

[0147] The input display unit is used to allow users to input operation commands and to display the data and files of the corresponding unit in the form of text, tables, graphics, static or dynamic models according to the operation commands.

[0148] The control unit is communicatively connected to the model initialization unit, failure surface determination unit, rock block division unit, interlayer stress determination unit, and stability prediction unit, and controls their operation.

[0149] The above embodiments are merely illustrative examples of the technical solutions of the present invention. The method and system for predicting the stability of anti-dip rock slopes under top loads involved in this invention are not limited to the content described in the above embodiments, but are defined by the scope of the claims. Any modifications, additions, or equivalent substitutions made by those skilled in the art based on these embodiments are within the scope of protection claimed by the claims of this invention.

Claims

1. A method for predicting the stability of a reverse-dip rock slope under top load, characterized in that, Includes the following steps: Step 1: Construct a two-dimensional analysis model of the reverse-dip rock slope based on the geometric and rock mechanics parameters of the reverse-dip rock slope; Step 2: For the two-dimensional reverse-dip rock slope analysis model, determine the failure surface of the reverse-dip rock slope based on the slope toppling failure surface determination criteria; the slope toppling failure surface determination criteria are: 1) As the load range at the top of the slope increases, the failure area increases; 2) Initial failure is vertically downward, and failure occurs perpendicular to the joint direction upon reaching the joint; 3) After reaching the maximum datum plane, it fails along the maximum datum plane; 4) The point where the perpendicular line drawn to the right side of the load loading range at the top of the slope intersects with the straight line perpendicular to the bedding is the turning point of the failure surface; 5) Once the maximum loading length is exceeded, the failure mode remains fixed, and the failure surface remains unchanged; The failure surfaces are divided differently depending on the loading range of the slope crest load. Generally, there are three failure cycles. The first and second cycles are distributed alternately, and the third cycle appears last. Furthermore, the division follows the principle that the larger the loading range of the slope crest load, the larger the landslide volume. The loading range of the slope crest load is the loading range under the load on the slope crest of the anti-dip rock slope. The first cycle corresponds to criteria 1), 2), and 4). The rightmost endpoint of the loading range is in the front half of the rock block, vertically downwards and intersecting with the reference plane perpendicular to the bedding, forming the failure surface. However, as the loading range increases, the slope that will collapse should increase. Simply dividing the failure surface according to criterion 2) will make the landslide volume smaller. Criterion 1) should also be followed. Therefore, the vertically downward line of the initial failure should intersect with the lower surface of the n-1 rock layer, thus defining the first failure cycle. The second period corresponds to criteria 1), 2), and 4). When the load range at the top of the slope falls on the latter half of the rock layer, the load range at the top of the slope increases. The initial failure is vertically downward and directly intersects the lower surface of rock layer n, intersecting with the reference plane perpendicular to the bedding to form a failure surface, thus dividing the second period. The third period corresponds to criteria 1), 3), and 5). When the load range at the top of the slope is sufficiently large, the initial failure location vertically downwards will always intersect with the maximum reference plane. The maximum reference plane is a straight line passing through the slope angle and perpendicular to the bedding. This range is defined as the third period. When the initial failure location vertically downwards always intersects with the maximum reference plane, it marks the starting point of the third period's division, and its ending point is the intersection of the maximum reference plane and the top of the slope. When the load range at the top of the slope exceeds the intersection of the maximum reference plane and the top of the slope, the failure mode remains fixed and always fails along the maximum reference plane. The failure surface and the slope surface together form a landslide area. Based on the failure surface, the rock layers in the landslide area are divided and the corresponding rock blocks are separated. Step 3: Based on the size and stress conditions of the rock blocks, establish the relationship between the normal forces between the rock layers to determine the stress conditions between the rock layers; Step 4: Determine the stability of the reverse-dip rock slope under the load at the top of the slope based on the stress between the rock strata.

2. The method for predicting the stability of a reverse-dip rock slope under top load as described in claim 1, characterized in that: in, In step 1, the geometric and rock mechanics parameters of the reverse-dip rock slope include: the slope height of the reverse-dip rock slope. slope angle Rock layer thickness and rock strata dip angle The cohesion of layered or structural surfaces and internal friction angle The cohesion of the rock mass internal friction angle and tensile strength Length of load at the top of the slope and load size .

3. The method for predicting the stability of a reverse-dip rock slope under top load as described in claim 1, characterized in that: in, In step 2, for each period, if a special case arises that conflicts with criterion 1) when dividing based on criterion 2) or criterion 3), the failure point should extend vertically downwards to the next bedding layer, rather than the bedding layer of the current bedding layer.

4. The method for predicting the stability of a reverse-dip rock slope under top load as described in claim 1, characterized in that: in, In step 2, after determining the landslide area, the rock blocks are numbered from left to right. Let the rightmost rock block that has collapsed be numbered n and the leftmost rock block be numbered 1. When the right end of the loading range falls on the (n+1)th rock block, the cut part of the rock block is merged into the nth rock block.

5. The method for predicting the stability of a reverse-dip rock slope under top load according to claim 1, characterized in that: in, In step 3, the relationship between the normal forces between the rock strata is as follows: ， In the formula: and They are rock blocks The normal forces acting on the left and right sides, It is a rock. The maximum tensile stress subjected to It is a rock. Self-respect It is a rock. The upper surface is subjected to a uniformly distributed external load; It is the structural surface cohesion after strength reduction. It is the internal friction angle of the structural surface after strength reduction. It is a rock. thickness, and They are rock blocks Right side height and left side height , It is a rock. The angle of inclination, It is a rock. The length of the upper surface subjected to external load, It is the force concentration factor of the normal force.

6. The method for predicting the stability of a reverse-dip rock slope under top load according to claim 5, characterized in that: in, In step 3, Values .

7. The method for predicting the stability of a reverse-dip rock slope under top load as described in claim 5, characterized in that: in, In step 4, based on step 3, the magnitude of the normal force between the rock layers is continuously changed by the strength reduction method. The magnitude of the anti-sliding force and sliding force of the outermost rock block is calculated. The anti-sliding force and sliding force of the outermost rock block are compared to determine whether the slope is stable. The formulas for calculating anti-slip force and sliding force are: ， In the formula: and These represent the anti-sliding force and sliding force of the outermost rock block, respectively. It is the normal force at the bottom of the outermost rock block. It is the weight of the outermost rock block. and These are the cohesion and friction angle after reducing the rock mass strength. It is the normal force on the inner side of the outermost rock block. and These are the thickness and dip angle of the outermost rock block, respectively; according to and The relationship between the magnitudes of the rock slopes is used to determine the stability of the reverse-dip rock slope. The criteria for this determination are as follows: I) The slope is in a stable state; II) The slope is in a state of limit equilibrium; III) The slope is in an unstable state; When a slope is in a state of limit equilibrium, the reduction factor at this time is the safety factor of the reverse-dip rock slope; a safety factor greater than 1.0 indicates a stable slope; a safety factor greater than 1.0 indicates an unstable slope.

8. A stability prediction system for reverse-dip rock slopes under top load, characterized in that, include: The initial model building section constructs a two-dimensional analysis model of the reverse-dip rock slope based on the geometric and rock mechanics parameters of the reverse-dip rock slope. The failure surface determination section, for a two-dimensional reverse-dip rock slope analysis model, determines the failure surface of the reverse-dip rock slope based on the slope collapse failure surface determination criteria; the slope collapse failure surface determination criteria are: 1) As the load range at the top of the slope increases, the failure area increases; 2) Initial failure is vertically downward, and failure occurs perpendicular to the joint direction upon reaching the joint; 3) After reaching the maximum datum plane, it fails along the maximum datum plane; 4) The point where the perpendicular line drawn to the right side of the load loading range at the top of the slope intersects with the straight line perpendicular to the bedding is the turning point of the failure surface; 5) Once the maximum loading length is exceeded, the failure mode remains fixed, and the failure surface remains unchanged; The failure surfaces are divided differently depending on the loading range of the slope crest load. Generally, there are three failure cycles. The first and second cycles are distributed alternately, and the third cycle appears last. Furthermore, the division follows the principle that the larger the loading range of the slope crest load, the larger the landslide volume. The loading range of the slope crest load is the loading range under the load on the slope crest of the anti-dip rock slope. The first cycle corresponds to criteria 1), 2), and 4). The rightmost endpoint of the loading range is in the front half of the rock block, vertically downwards and intersecting with the reference plane perpendicular to the bedding, forming the failure surface. However, as the loading range increases, the slope that will collapse should increase. Simply dividing the failure surface according to criterion 2) will make the landslide volume smaller. Criterion 1) should also be followed. Therefore, the vertically downward line of the initial failure should intersect with the lower surface of the n-1 rock layer, thus defining the first failure cycle. The second period corresponds to criteria 1), 2), and 4). When the load range at the top of the slope falls on the latter half of the rock layer, the load range at the top of the slope increases. The initial failure is vertically downward and directly intersects the lower surface of rock layer n, intersecting with the reference plane perpendicular to the bedding to form a failure surface, thus dividing the second period. The third period corresponds to criteria 1), 3), and 5). When the load range at the top of the slope is sufficiently large, the initial failure location vertically downwards will always intersect with the maximum reference plane. The maximum reference plane is the straight line passing through the slope angle and perpendicular to the bedding. This range is defined as the third period. When the initial failure location vertically downwards always intersects with the maximum reference plane, it marks the starting point of the third period's division, and its ending point is the intersection of the maximum reference plane and the top of the slope. When the load range at the top of the slope exceeds the intersection of the maximum reference plane and the top of the slope, the failure mode remains fixed and always fails along the maximum reference plane. The rock block division section, the failure surface and the slope surface together form the landslide area. Based on the failure surface, the rock layers in the landslide area are divided and the corresponding rock blocks are separated. The interlayer stress determination section establishes the relationship between the normal forces between rock layers based on the size and stress conditions of the rock blocks, and determines the stress conditions between the rock layers. The stability prediction department determines the stability of the reverse-dip rock slope under the action of the slope top load based on the stress between the rock strata. The control unit is connected in communication with the model initialization unit, failure surface determination unit, rock block division unit, interlayer stress determination unit, and stability prediction unit, and controls their operation.

9. The stability prediction system for anti-dip rock slopes under top load as described in claim 8, characterized in that, Also includes: The input display unit is connected in communication with the model initialization unit, failure surface determination unit, rock block division unit, interlayer stress determination unit, stability prediction unit, and control unit. It is used to allow users to input operation commands and to display the data and files of the corresponding units in the form of text, tables, graphics, static or dynamic models according to the operation commands.

10. The stability prediction system for reverse-dip rock slopes under top load as described in claim 8, characterized in that: in, In the section on interlayer stress determination, the relationship between the normal forces between rock strata is: ， In the formula: and They are rock blocks The normal forces acting on the left and right sides, It is a rock. The maximum tensile stress subjected to It is a rock. Self-respect It is a rock. The upper surface is subjected to a uniformly distributed external load; It is the structural surface cohesion after strength reduction. It is the internal friction angle of the structural surface after strength reduction. It is a rock. thickness, , They are rock blocks Right side height and left side height , It is a rock. The angle of inclination, It is a rock. The length of the upper surface subjected to external load, It is the force concentration factor of the normal force.

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