JP6693825B2 - Slope stability calculation device, method and program for bank body - Google Patents

Description

  The present invention relates to a slope stability calculation device, method and program for a bank.

  As is well known, in construction of roads, embankments, dams, etc., an artificial slope is formed by cutting or embankment. In order to prevent the slope from collapsing easily, a slope stability calculation is widely performed, in which a safety factor, which is an index showing the stability of the slope, is calculated and the design is evaluated when the slope is constructed.

  Slope failure usually occurs due to the sliding of earth and sand, etc. located above the slip surface along the slip surface, which is the boundary surface between the substances that occur below the surface of the earth. In the slope stability calculation, a slip surface is assumed for the slope, and the average pore water pressure between the slope and the slip surface is used as an input parameter to apply the publicly known Fellenius equation or the like to derive the safety factor. The higher the average pore water pressure is, the lower the safety factor is, that is, the stability is low and the result tends to be easily collapsed.

  Here, especially in a dike such as an embankment, water may be stored on the slope on one side of the dike, so unlike ordinary slope stability calculation, it is stored on the slope at an average pore water pressure. The safety factor is derived by using the sum of the water pressure generated by the generated water as the water pressure. Non-Patent Document 1 is an operation guide of a system capable of slope stability calculation when water is stored on the slope as described above. In the slope stability calculation system whose usage is explained in this operation guide, water pressure is calculated according to the following policy.

  FIG. 8A is a vertical cross-sectional view of an evaluation model 100 imitating a dam body 101 including two slopes 101a and 101b facing in mutually opposite directions. This figure assumes a case where the water level increases due to a flood or the like, and water is stored on the slope 101a on one side of the dam body 101, as represented by a water surface 103. The water has infiltrated into the inside of the bank 101, and the boundary between the infiltrated portion and the infiltrated portion is represented as an infiltration line 104. A single sliding surface 105 is provided on the slope 101a.

In such an example shown in FIG. 8A, with respect to the point P _S11 on the water surface 103 where the slope 101a is located below the water surface 103, the slip surface 105 located vertically below the point P _S11. The water pressure at the upper point Q _S11 is calculated based on the height direction difference h _S11 between the height position of the point P _S11 on the water surface 103 and the height position of the point Q _S11 on the slip surface 105. With respect to the point _{P S12} which is located on the infiltration line 104, located vertically below the point _{P S12,} the water pressure at the point _{Q S12} on the sliding surface 105, the height of the point _{P S12} on infiltration line 104 It is calculated based on the difference h _S12 in the height direction between the position and the height position of the point Q _S12 on the slip surface 105.

  Another method for calculating the water pressure is to perform permeation flow analysis. The seepage flow analysis is a method of deriving the water velocity and water pressure at each point in the levee by simulating the flow of water inside the levee against the model of the levee by the finite element method. .. According to this method, an accurate water pressure value can be derived.

"FUJITSU Construction Industry Solution COSTANA Slope Stable Calculation System Operation Guide (Specification Version)", Fujitsu FIP Limited, January 2015 Edition

  In order to reduce the risk of bank breakage, a material that can completely block water may be laid on the slope of the bank. FIG. 8B is a cross-sectional view of the evaluation model 110 of the dam body 111 in which the water shield 116 is laid on the slope 111a on the water storage side. The water shield 116 is, for example, a water shield sheet. When the water shield 116 is laid, the infiltration line 114 has a shape that extends from the lower end of the water shield 116 in the direction opposite to the side of the bank 111 where water is stored. Thereby, the continuous water boundary line formed by the water surface 103, the water shield 116, and the infiltration line 114 includes a turn-back such that the water surface 103 is once turned by the water shield 116 and continues to the infiltration line 114. It has a shape.

Such, when the boundary line is a shape including the folded, in such a way as non-patent document 1, for example with respect to the point P _S2 on the water surface 103 in FIG. 8 (b), vertically below the point P _S2 located, in the case of calculating the pressure at point Q _S2 on the sliding surface 105, the height position of the point Q _S2 on height as the sliding surface 105 of the point P _S2 on the water surface 103, a height direction The water pressure is calculated based on the difference h _S2 of However, since there is a part where water is not infiltrated under the water shield 116 and the height of this part is also included in the difference h _S2 , a water pressure value higher than the actual value is calculated, and as a result, An overly low safety factor is derived.

  On the other hand, if the water pressure is calculated by the permeation flow analysis, an accurate water pressure value can be calculated even in the case as shown in FIG. 8B, but as described above, in the permeation flow analysis, many calculation times such as the finite element method are required. Since the water pressure is derived by the method that requires, it takes a lot of time to calculate the water pressure. In particular, when the safety factor is derived many times for various models and trial and error is performed, such as in the initial stage of the design of the bank, the permeation flow analysis requires a long design period. Become.

  The problem to be solved by the present invention is to prevent the safety factor from being underestimated even if the boundary line of water includes folding, and to derive the safety factor at high speed, a slope stability calculation device for a bank, It is to provide a method and a program.

The present invention is a slope stability calculation device for a dam body for blocking water, the surface of which is provided with a water shield body, which is opposite to the side of the dam body where water is stored below the water shield body. When the lower infiltration line extends in the direction of and the slip surface is set with respect to the levee body, the water level surface of the water side of the levee body and the lower side of the water level surface Based on the upper difference that is the difference in the height direction with the surface of the water shield located in, to calculate the water pressure in the slip surface, and, at this time, the slip surface below the lower infiltration line If located, the difference in the height direction between the surface of the water shield and the lower infiltration line, if the slip surface is located above the lower infiltration line, the The difference in the height direction between the surface and the slip surface is the water level surface and the slip surface, respectively. Excluded from the height direction of the difference calculated with, a control unit for calculating the safety factor based on the water pressure, provide a slope stability calculation apparatus dam.
Here, the difference in the height direction is obtained by subtracting the height position of the point at the lower position from the height position of the point at the higher position of the two points positioned at intervals in the vertical direction. Means the resulting value.
According to the above configuration, the control unit of the slope stability calculation device for the dam is formed by the water level surface of the dam on the water storage side, the inclined surface of the water shield, and the lower infiltration line. In addition, in the case where the continuous water boundary line has a shape including folds such that the water level surface is once folded by the impermeable body and continues to the lower infiltration line, the water pressure on the slip surface referred to in the calculation of the safety factor Is calculated based on the upper difference that is the difference in the height direction between the water level surface of the bank body on the side where water is stored and the inclined surface of the water shield located below the water level surface. At this time, when the slip surface is located below the lower infiltration line, the difference in the height direction between the surface of the water shield and the lower infiltration line is calculated when the slip surface is located above the lower infiltration line. In the calculation, the difference in the height direction between the surface of the water shield and the slip surface is excluded from the difference in the height direction between the water level surface and the slip surface. Since each of these differences calculated by excluding them corresponds to the area where the stored water does not infiltrate in each case, these values are calculated in the height direction between the water level surface and the slip surface. By excluding it from the difference, it becomes possible to calculate a water pressure value closer to the actual value, derive an appropriate safety factor, and prevent the safety factor from being underestimated.
Further, even without using the permeation flow analysis, it is possible to derive an appropriate water pressure value that prevents the safety factor from being underestimated, so that the safety factor can be derived at high speed. This makes it possible to shorten the design period when it is desired to derive the safety factor many times for various models, for example, in the initial stage of the design of the bank.

In one aspect of the present invention, when the slip surface is located below the lower infiltration line, the control unit is a lower side which is a difference in a height direction between the lower infiltration line and the slip surface. The water pressure on the slip surface is calculated based on the sum of the difference and the upper difference.
According to the above configuration, when the slip surface is located below the lower infiltration line, the lower difference which is the difference in the height direction between the lower infiltration line and the slip surface, and the sum of the upper differences are Based on this, the difference in the height direction between the surface of the water shield and the lower infiltration line is excluded from the difference in the height direction between the water level surface and the slip surface, and the water pressure on the slip surface is calculated. That is, even when the slip surface is located below the lower infiltration line, it is possible to calculate a water pressure value that is closer to the actual value, derive an appropriate safety factor, and underestimate the safety factor. Can be prevented.

In one aspect of the present invention, the water shield is provided with the surface in the vicinity of the surface layer of the slope of the bank, along the slope, and the water level is the water surface of the stored water.
According to the above configuration, the water shield is more practical even when the sloped surface is provided along the slope near the surface of the slope of the dam body and the water level is the surface of the stored water. It becomes possible to calculate a water pressure value close to the value of, and it is possible to derive an appropriate safety factor and prevent the safety factor from being underestimated.

In one aspect of the present invention, the water shield is a water shield sheet.
According to the above configuration, even if the water shield is a water shield sheet, it is possible to calculate a water pressure value that is closer to the actual value, derive an appropriate safety factor, and calculate the safety factor. It is possible to prevent underestimation.

In one aspect of the present invention, the water shield is embedded in the dam body, and the water level surface is an upper surface that is continuous from the water surface of the stored water to the surface of the water shield body inside the dam body. Has an infiltration line.
According to the above configuration, the water shield is buried in the dam body, and the water level surface includes the water surface of the stored water and the upper infiltration line continuous from the water surface to the inclined surface of the water shield body inside the dam body. Even when the safety factor is present, it is possible to calculate a water pressure value that is closer to the actual value, derive an appropriate safety factor, and prevent the safety factor from being underestimated.

In one aspect of the present invention, the bank is a fill dam, and the water shield is a core of the fill dam.
According to the above configuration, even when the bank is a fill dam and the water shield is the core of the fill dam, it is possible to calculate a water pressure value that is closer to the actual value and derive an appropriate safety factor. Thus, it is possible to prevent the safety factor from being underestimated.

In one aspect of the present invention, the dam body is a reservoir dam body, and the water shield is a water shield layer.
According to the above configuration, even when the dam body is a reservoir dam body and the impermeable body is an impermeable layer, it is possible to calculate a water pressure value that is closer to the actual value, and an appropriate safety factor. Can be derived to prevent the safety factor from being underestimated.

Further, the present invention is a slope stability calculation method in a dam body for damming water, in which a water shield body having an inclined surface is provided, wherein a water side of the dam body is stored below the water shield body. When the lower side infiltration line extends in the opposite direction and a slip surface is set for the levee body, the water level surface of the water side of the levee body and the water level surface Based on the upper difference which is the difference in the height direction with the surface of the water shield located below, calculate the water pressure in the slip surface, and, at this time, the slip surface is more than the lower infiltration line. When located below, the difference in the height direction between the surface of the water shield and the lower infiltration line, when the slip surface is located above the lower infiltration line, the water shield. The difference in the height direction between the surface and the slip surface of the Excluded from the height direction of the difference between Beri surface calculated, to calculate the safety factor based on the water pressure, provide a slope stability calculation method of the dam.
According to the above configuration, the control unit of the slope stability calculation device for the dam is formed by the water level surface of the dam on the water storage side, the inclined surface of the water shield, and the lower infiltration line. In addition, in the case where the continuous water boundary line has a shape including folds such that the water level surface is once folded by the impermeable body and continues to the lower infiltration line, the water pressure on the slip surface referred to in the calculation of the safety factor Is calculated based on the upper difference that is the difference in the height direction between the water level surface of the bank body on the side where water is stored and the inclined surface of the water shield located below the water level surface. At this time, when the slip surface is located below the lower infiltration line, the difference in the height direction between the surface of the water shield and the lower infiltration line is calculated when the slip surface is located above the lower infiltration line. In the calculation, the difference in the height direction between the surface of the water shield and the slip surface is excluded from the difference in the height direction between the water level surface and the slip surface. Since each of these differences calculated by excluding them corresponds to the area where the stored water does not infiltrate in each case, these values are calculated in the height direction between the water level surface and the slip surface. By excluding it from the difference, it becomes possible to calculate a water pressure value closer to the actual value, derive an appropriate safety factor, and prevent the safety factor from being underestimated.
Further, even without using the permeation flow analysis, it is possible to derive an appropriate water pressure value that prevents the safety factor from being underestimated, so that the safety factor can be derived at high speed. This makes it possible to shorten the design period when it is desired to derive the safety factor many times for various models, for example, in the initial stage of the design of the bank.

In one aspect of the present invention, the slope stability calculation method for a bank is a difference in the height direction between the lower infiltration line and the slip surface when the slip surface is located below the lower infiltration line. The water pressure on the slip surface is calculated based on the sum of the lower difference and the upper difference.
According to the above configuration, when the slip surface is located below the lower infiltration line, the lower difference which is the difference in the height direction between the lower infiltration line and the slip surface, and the sum of the upper differences are Based on this, the difference in the height direction between the surface of the water shield and the lower infiltration line is excluded from the difference in the height direction between the water level surface and the slip surface, and the water pressure on the slip surface is calculated. That is, even when the slip surface is located below the lower infiltration line, it is possible to calculate a water pressure value that is closer to the actual value, derive an appropriate safety factor, and underestimate the safety factor. Can be prevented.

Further, the present invention is a slope stability calculation program for a dam body for damming water, wherein a water shield body having an inclined surface is provided, wherein the water side of the dam body is stored below the water shield body. When the lower side infiltration line extends in the opposite direction and a slip surface is set for the levee body, the water level surface of the water side of the levee body and the water level surface Based on the upper difference which is the difference in the height direction with the surface of the water shield located below, calculate the water pressure in the slip surface, and, at this time, the slip surface is more than the lower infiltration line. When located below, the difference in the height direction between the surface of the water shield and the lower infiltration line, when the slip surface is located above the lower infiltration line, the water shield. The difference in the height direction between the surface and the sliding surface of the Calculated by excluding from the difference in the height direction between said sliding surface, to calculate the safety factor based on the water pressure, provide a slope stability calculation program dam.
According to the above configuration, the control unit of the slope stability calculation device for the dam is formed by the water level surface of the dam on the water storage side, the inclined surface of the water shield, and the lower infiltration line. In addition, in the case where the continuous water boundary line has a shape including folds such that the water level surface is once folded by the water shield and continues to the lower infiltration line, the water pressure on the slip surface referred to in the calculation of the safety factor is Is calculated based on the upper difference that is the difference in the height direction between the water level surface of the bank body on the side where water is stored and the inclined surface of the water shield located below the water level surface. At this time, when the slip surface is located below the lower infiltration line, the difference in the height direction between the surface of the water shield and the lower infiltration line is calculated when the slip surface is located above the lower infiltration line. In the calculation, the difference in the height direction between the surface of the water shield and the slip surface is excluded from the difference in the height direction between the water level surface and the slip surface. Since each of these differences calculated by excluding them corresponds to the area where the stored water does not infiltrate in each case, these values are calculated in the height direction between the water level surface and the slip surface. By excluding it from the difference, it becomes possible to calculate a water pressure value that is closer to the actual value, derive an appropriate safety factor, and prevent the safety factor from being underestimated.
Further, even without using seepage flow analysis, it is possible to derive an appropriate water pressure value that prevents the safety factor from being underestimated, so that the safety factor can be derived at high speed. As a result, the design period can be shortened when it is desired to derive the safety factor for various models many times, for example, in the initial stage of the design of the bank.

In one aspect of the present invention, the slope stability calculation program for the dam body, when the slip surface is located below the lower infiltration line, the difference in the height direction between the lower infiltration line and the slip surface. The water pressure on the slip surface is calculated based on the sum of the lower difference and the upper difference.
According to the above configuration, when the slip surface is located below the lower infiltration line, the lower difference which is the difference in the height direction between the lower infiltration line and the slip surface, and the sum of the upper differences are Based on this, the difference in the height direction between the surface of the water shield and the lower infiltration line is excluded from the difference in the height direction between the water level surface and the slip surface, and the water pressure on the slip surface is calculated. That is, even when the slip surface is located below the lower infiltration line, it is possible to calculate a water pressure value that is closer to the actual value, derive an appropriate safety factor, and underestimate the safety factor. Can be prevented.

  ADVANTAGE OF THE INVENTION According to this invention, even if the boundary line of water contains a folding | turning, the safety factor can be prevented from being underestimated, a safety factor can be derived at high speed, the slope stability calculation apparatus, method, and program of a bank. , Can be provided.

It is a block diagram of the control part in the slope stability calculation device of the bank shown as an embodiment of the present invention. It is explanatory drawing of the 1st Example explaining the slope stability calculation apparatus, method, and program of the bank shown as the embodiment of this invention. It is explanatory drawing of the 1st Example explaining the slope stability calculation apparatus, method, and program of the bank shown as the embodiment of this invention. It is a flow chart explaining a slope stability calculation method of a dam body shown as an embodiment of the present invention. It is explanatory drawing of 2nd Example explaining the slope stability calculation apparatus of a bank, the method, and program shown as embodiment of this invention. It is explanatory drawing of 3rd Example explaining the slope stability calculation apparatus of a bank, the method, and program shown as embodiment of this invention. It is explanatory drawing of 4th Example explaining the slope stability calculation apparatus of a bank, the method, and program shown as embodiment of this invention. It is explanatory drawing of the conventional slope stability calculation method of a bank.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

(Configuration of control unit in slope stability calculation device)
FIG. 1 is a block diagram of a control unit 1 in the slope stability calculation device for a bank shown as an embodiment of the present invention. In the present embodiment, the control unit 1 is a computer such as a PC (Personal Computer), a server, or a mainframe, which is provided with an input device and an output device (not shown) such as a keyboard, a mouse, and a display. The computer executes a program for carrying out a slope stability calculation method for a bank, which will be described later. The control unit 1 includes a model input unit 2, a slip surface candidate set determination unit 3, a strip division unit 4, a water pressure calculation unit 5, a safety factor calculation unit 6, and an output unit 7.

  The model input unit 2 displays, for example, an appropriate user interface on an output device such as a display, while inputting an operator's input of an evaluation model of the bank for which the safety factor is to be evaluated, via an input device such as a keyboard or a mouse. Support. The slope stability calculation device, method, and program in the present embodiment are devices, methods, and programs for calculating the safety factor of a slope in a dam body that dams water, such as an embankment. Therefore, as an example of the levee body evaluation model that can be input to the model input unit 2, there is, for example, the evaluation model 10 shown in FIG. 2A as the first embodiment.

  FIG. 2A is an evaluation model 10 in which the bank body 11 formed on the ground G is viewed in a vertical cross section. In the first embodiment, the bank 11 is opposite to the upper surface 11c formed substantially parallel to the ground G and the water-side slope 11a (slope) extending diagonally downward from opposite ends of the upper surface 11c. The side slope 11b is provided, and the upper surface 11c, the water side slope 11a, the opposite side slope 11b, and the ground G are formed into a substantially trapezoidal shape.

  Water 12 is stored on the left side of the bank 11 in FIG. A water shield 15 having a surface 15a that is substantially parallel to the water slope 11a is provided on the water slope 11a on the side where the water 12 is stored. Thereby, the surface 15a of the water shield 15 is positioned to be inclined. In the first embodiment, the water shield 15 is a water shield sheet whose surface 15a is provided near the surface of the water side slope 11a of the bank 11 along the water side slope 11a. In each drawing, the water-side slope 11a and the surface 15a of the water shield 15 are drawn so as to coincide with each other, but the surface 15a may actually be shallowly buried near the surface of the bank 11. The water level surface 13, which is the upper surface of the water on the side where the water 12 of the bank 11 is stored, corresponds to the water surface 12a of the stored water 12 in the first embodiment, and is a point on the surface 15a of the water shield 15. It terminates at 15b.

  In the evaluation model 10, the lower part of the water-side slope 11a, which is located below the point 15b, is covered by the lower side 15c of the water shield 15 until reaching the ground G. The right side in FIG. 2A, which is in the opposite direction to the side where the water 12 is stored, with respect to the ground G that is not infiltrated inside the bank body 11 and is located under the water shield 15. Infiltrate from the lower end of the water shield 15 in the direction of. That is, the lower side infiltration line 16 which is a boundary between the portion infiltrated by the water 12 and the portion not infiltrated at a height lower than the water shield 15 is located below the water shield 15, more specifically, the water. It is provided so as to extend from the lower end of the water body 15 in a direction opposite to the side on which the water 12 is stored. The continuous water boundary line formed by the water surface 12a, that is, the water level surface 13, the lower side 15c of the water shield 15, and the lower wetting line 16 is a lower water wetting line 16 when the water surface 12a is once folded by the water shield 15. It has a shape that includes folds, such as to.

  The model input unit 2 receives the evaluation model 10 as described above and then saves it as data.

  The slip surface candidate set determination unit 3 determines, for the evaluation model 10 input by the model input unit 2, a set of a plurality of slip surfaces, which are targets for deriving a safety factor. In the slope stability calculation, a safety factor is calculated for each of various sliding surfaces, and the lowest value, for example, is output as the final safety factor. Therefore, the slip surface candidate set determination unit 3 determines a set including a plurality of slip surfaces such that the safety factor is expected to be low.

  FIG. 2B shows an example of the slip surface 17 in the first embodiment. In the first embodiment, the slip surface 17 has an arc shape. In such a case, the candidate set of the slip surface 17 can be obtained by combining the center point coordinates and the radius values after the operator inputs the coordinate values of the plurality of center points and the plurality of radius values, for example. It is determined by forming arcs of various shapes. An arbitrary one is selected from the candidate set of the slip surface 17 determined in this way, and provided in the evaluation model 10. In the first embodiment, one end of the slip surface 17 is located on the upper surface 11c and the other end is located on the ground G in the water 12, and the entire water shield 15 is located above the slip surface 17. Is set.

  The strip dividing unit 4 divides the bank 11 and the ground G in the vertical direction at a plurality of horizontal positions to make them into pieces. More specifically, the part of the evaluation model 10 provided with the slip surface 17 as shown in FIG. 2B, which is located above the slip surface 17, extends in the vertical direction as shown by the broken line in FIG. It divides into a plurality of strips 18 (18A, 18B, 18C, 18D, 18E, 18F) at a plurality of positions with a plurality of lines.

  The water pressure calculation unit 5 calculates the water pressure on the slip surface 17 in each of the plurality of strips 18 divided by the strip division unit 4. In the present embodiment, the water pressure calculation unit 5 includes the water level surface 13, that is, the water surface 12 a and the water shield 15 of the water on the side where the water 12 of the bank 11 is stored at the horizontal center position of each strip 18. The water pressure is calculated based on the height positions of the surface 15a, the lower side infiltration line 16, and the slip surface 17.

Among the strips 18, for each strip 18 in which the surface 15a of the water shield 15 and the lower infiltration line 16 are not located at the central position in the horizontal direction, for example, the strips 18A and 18B in FIG. When the unit volume weight of water is γ _W , the portion 5 is based on the differences h _1A and h _1B in the height direction between the water surface 12a (water level surface 13) and the slip surface 17 at the central position in the horizontal direction. , The water pressure u _1A and u _1B corresponding to each strip 18A and 18B are calculated. Here, the difference in the height direction is obtained by subtracting the height position of the point at the lower position from the height position of the point at the higher position of the two points positioned at intervals in the vertical direction. Means the resulting value.

(Equation 1)
u _1A = h _1A × γ _W (1)
u _1B = h _1B × γ _W

Among the strips 18, with respect to the strip 18 in which the surface 15a of the water shield 15 and the lower infiltration line 16 are located at the central position in the horizontal direction, for example, the strips 18C and 18D in FIG. 5 is the difference in the height direction between the water level surface 13 of the bank 11 on the side where the water 12 is stored, that is, the water surface 12a and the water blocking surface 15a of the water blocking body 15 located below the water level surface 13. Based on the upper differences h _1C1 and h _1D1 , the hydraulic pressures u _1C and u _1D corresponding to the strips 18C and 18D on the slip surface 17 are calculated. In the strips 18C and 18D, the slip surface 17 is located below the lower infiltration line 16. In such a case, in particular, the water pressure calculation unit 5 adds the lower difference in addition to the upper differences h _1C1 and h _1D1. Based on the lower differences h _1C2 and h _1D2 which are the differences in the height direction between the side infiltration line 16 and the slip surface 17, more specifically, the lower differences h _1C2 and h _1D2 and the upper differences h _1C1 and h _1C1 and h _1C2 . _{Based on} the sum of _1D1, the water pressures u _1C and u _1D on the slip surface 17 are calculated. More specifically, the water pressure calculation unit 5 calculates the water pressure u _1C and u _1D by the following equation.

(Equation 2)
u _1C = (h _1C1 + h _1C2 ) × γ _W (2)
u _1D = (h _1D1 + h _1D2 ) × γ _W

As described above, in the strips 18C and 18D in which the sliding surface 17 is located below the lower infiltration line 16 at the central position in the horizontal direction, the water pressures u _1C and u _1D are calculated as described above, so that Differences h _1Cu and h _{1Du in} the height direction between the surface 15a of the water body 15 and the lower side infiltration line 16 are excluded from the difference in the height direction between the water level surface 13 and the slip surface 17, and are calculated.

The strips 18E and 18F are formed by the water surface 12a (water level surface 13), the lower side 15c of the water shield 15 and the lower infiltration line 16 above the slip surface 17 at the central position in each horizontal direction. Since the boundary line of water is not located, the water pressure u _1E and u _1F corresponding to each strip 18E and 18F is calculated as 0.

The safety factor calculation unit 6 calculates the safety factor based on the water pressures u _1A , u _1B , u _1C , u _1D , u _1E , u _1F calculated by the water pressure calculation unit 5. In the present embodiment, the safety factor F is derived by the Ferrenius equation or the modified Ferrenius equation. The Fellenius formula and the modified Ferrenius formula are: the adhesive force of the slip surface is c (kPa), the shear resistance angle of the slip surface is φ (°), the water pressure of each strip 18 is u (kPa), and the slip surface of each strip 18 is The length is 1 (m), the clod weight of each strip 18 is W (kN / m ³ ), the slip surface inclination angle of each strip 18 is α (°), and the width of each strip 18 is b (m). ) Are respectively expressed by the following formulas 3 and 4.

(Equation 3)
F = Σ {cl + (Wcosα-ul) tanφ} / ΣWsinα (3)

(Equation 4)
F = Σ {cl + (W-ub) cosαtanφ} / ΣWsinα (4)

In each of the mathematical expressions 3 and 4, the sum in the symbol Σ indicates the totalization for each strip 18, and the hydraulic pressures u _1A , u _1B , u _1C , u _1D , and u calculated by the hydraulic pressure calculation unit 5 are calculated. _1E and u _1F correspond to the water pressure u in Expressions 3 and 4, respectively. As can be seen from Equations 3 and 4, when the water pressure u is large, the safety factor F is calculated to be low.

  As described above, the slip surface candidate set determination unit 3 determines a set including a plurality of slip surfaces 17, and the safety factor calculation unit 6 derives a safety factor for each of the slip faces 17 in the set. .. The output unit 7 extracts, for example, the safety factor having the lowest value from the safety factors derived for each of the plurality of sliding faces 17, and extracts the value and the slip factor of the sliding face 17 corresponding to the safety factor. The shape is output to an output device such as a display.

(Slope stability calculation method)
Next, the processing procedure of the control unit 1 in the slope stability calculation device for a bank will be described with reference to the flowcharts shown in FIGS. 1 to 3 and 4.

  The process is started by the operator instructing the input device or the like to start calculation (step S1).

  First, an operator inputs an evaluation model 10 of a bank for which a safety factor is desired to be evaluated, as shown in FIG. 2A, for example, via an input device such as a keyboard and a mouse. At this time, the model input unit 2 supports the input of the evaluation model 10 by displaying an appropriate user interface or the like on an output device such as a display. The model input unit 2 receives the evaluation model 10 as described above and then saves it as data (step S2).

  When the input of the evaluation model 10 is completed, the slip surface candidate set determination unit 3 determines, for the input evaluation model 10, a set of slip surfaces 17 that is a target for deriving a safety factor. The candidate set of the slip surface 17 may be formed into various shapes of arcs by, for example, the operator inputting coordinate values of a plurality of center points and a plurality of radius values, and then combining these center point coordinates and radius values. It is determined by the formation (step S3).

  Next, the control unit 1 arbitrarily selects one slip surface 17 from the set of slip surfaces 17 determined by the slip surface candidate set determination unit 3 (step S4).

  With respect to the slip surface 17 selected in step S4, the strip dividing portion 4 shows a portion of the evaluation model 10 provided with the slip surface 17 as shown in FIG. As indicated by a broken line in FIG. 1, the line is divided at a plurality of positions by a plurality of lines extending in the vertical direction and divided into a plurality of strips 18 (18A, 18B, 18C, 18D, 18E, 18F) (step S5). ).

  As described above, the water pressure calculation unit 5 calculates the water pressure on the slip surface 17 in each of the plurality of strips 18 divided by the strip division unit 4 (step S6).

Among the strips 18, for each strip 18 in which the surface 15a of the water shield 15 and the lower infiltration line 16 are not located at the central position in the horizontal direction, for example, the strips 18A and 18B in FIG. The part 5 calculates the hydraulic pressures u _1A and u _1B corresponding to the strips 18A and 18B by using the above-described mathematical expression 1 as described above.

Among the strips 18, with respect to the strip 18 in which the surface 15a of the water shield 15 and the lower infiltration line 16 are located at the central position in the horizontal direction, for example, the strips 18C and 18D in FIG. 5 is the difference in the height direction between the water level surface 13 of the bank 11 on the side where the water 12 is stored, that is, the water surface 12a and the water blocking surface 15a of the water blocking body 15 located below the water level surface 13. Based on the upper differences h _1C1 and h _1D1 , the hydraulic pressures u _1C and u _1D corresponding to the strips 18C and 18D on the slip surface 17 are calculated. In the strips 18C and 18D, the slip surface 17 is located below the lower infiltration line 16. In such a case, in particular, the water pressure calculation unit 5 adds the lower difference in addition to the upper differences h _1C1 and h _1D1. Based on the lower differences h _1C2 and h _1D2 which are the differences in the height direction between the side infiltration line 16 and the slip surface 17, more specifically, the lower differences h _1C2 and h _1D2 and the upper differences h _1C1 and h _1C1 and h _1C2 . _{Based on} the sum of _1D1, the water pressures u _1C and u _1D on the slip surface 17 are calculated. The calculation is performed by the mathematical formula 2 as described above.

As described above, in the strips 18C and 18D in which the sliding surface 17 is located below the lower infiltration line 16 at the central position in the horizontal direction, the water pressures u _1C and u _1D are calculated as described above, so that Differences h _1Cu and h _{1Du in} the height direction between the surface 15a of the water body 15 and the lower side infiltration line 16 are excluded from the difference in the height direction between the water level surface 13 and the slip surface 17, and are calculated.

The strips 18E and 18F are formed by the water surface 12a (water level surface 13), the lower side 15c of the water shield 15 and the lower infiltration line 16 above the slip surface 17 at the central position in each horizontal direction. Since the boundary line of water is not located, the water pressure u _1E and u _1F corresponding to each strip 18E and 18F is calculated as 0.

After the water pressure calculator ₁ calculates the water pressure u _1A , u _1B , u _1C , u _1D , u _1E , u _1F , the safety factor calculator 6 calculates the calculated water pressure u _1A , u _1B , u _1C , u. _The safety factor is calculated based on _1D , u _1E , and u _1F . In the present embodiment, the safety factor F is derived by the Ferrenius equation or the modified Ferrenius equation shown as the equations 3 and 4 described above (step S7).

  From step S5 to step S7, the safety factor for one slip surface 17 selected in step S4 is derived. At this time, the safety factor is still included in the slip surface 17 candidate set selected in step S3. The control unit 1 determines whether or not there is an unprocessed slip surface 17 that has not been calculated (step S8). If there is an untreated slip surface 17, the process returns to step S4, one slip surface 17 is selected from the untreated slip surfaces 17, and the safety factor is derived for this slip surface 17.

  If it is determined in step S8 that there is no unprocessed slip surface 17, the output unit 7 extracts the lowest safety factor from the safety factors derived for the plurality of slip surfaces 17. , The value and the shape of the slip surface 17 corresponding to the safety factor are output to an output device such as a display (step S9), and then the control unit 1 ends the process (step S10).

  Next, effects of the above-mentioned bank slope stability calculation device, method, and program will be described.

According to the above-described configuration, the control unit 1 of the slope stability calculation device for the bank 11 has the water surface 13 of the water 12 on the side of the bank 11 where the water 12 is stored and the inclined surface 15a of the water shield 15. In the case where the continuous water boundary line formed by the lower wetting line 16 has a shape including folding back, such that the water level surface 13 is once folded back by the water shield 15 and continues to the lower wetting line 16, The water pressure on the slip surface 17, which is referred to in the calculation of the safety factor, is calculated by using the water level surface 13 of the water 12 on the side where the water 12 of the levee body 11 is stored and the inclined surface of the water shield 15 located below the water level surface 13. It is calculated based on the upper differences h _1C1 and h _1D1 which are the differences in the height direction from 15a. At this time, in the strips 18C and 18D of the first embodiment, the slip surface 17 is located below the lower infiltration line 16, but in such a case, the surface 15a of the water shield 15 and the lower surface Differences h _1Cu and h _1Du in the height direction from the infiltration line 16 are excluded from the difference in the height direction between the water surface 13 and the slip surface 17 for calculation. Since the differences h _1Cu and h _1Du calculated by excluding these correspond to the region where the stored water 12 does not infiltrate, this value is the difference in the height direction between the water level surface 13 and the slip surface 17. It becomes possible to calculate the water pressure value closer to the actual value by excluding it from the above. Especially, by deriving an appropriate safety factor from the conventional method of including these values in the water pressure calculation, the safety factor is too small. Can be prevented from being evaluated by.

Further, when the slip surface 17 is located below the lower infiltration line 16 like the strips 18C and 18D of the first embodiment, the difference in the height direction between the lower infiltration line 16 and the slip surface 17 is obtained. Based on the sum of certain lower differences h _1C2 , h _1D2 and upper differences h _1C1 , h _1D1 , the differences h _1Cu , h _1Du in the height direction between the surface 15a of the water shield 15 and the lower infiltration line 16, The water pressure on the slip surface 17 is calculated by excluding it from the difference in the height direction between the water level surface 13 and the slip surface 17. That is, even when the slip surface 17 is located below the lower infiltration line 16, it becomes possible to calculate water pressure values closer to actual values, and in particular, compared with the conventional method of including these values in water pressure calculation. Can derive an appropriate safety factor to prevent the safety factor from being underestimated.

  Further, even without using the permeation flow analysis, it is possible to derive an appropriate water pressure value that prevents the safety factor from being underestimated, so that the safety factor can be derived at high speed. This makes it possible to shorten the design period when it is desired to derive the safety factor many times for various models, for example, in the initial stage of the design of the bank.

(Second embodiment)
FIG. 5 is a diagram showing the evaluation model 20 shown as the second embodiment. In the present embodiment, except for the calculation of the water pressure, it can be carried out in the same manner as in the case of being applied to the first embodiment. Therefore, here, the calculation of the water pressure in the water pressure calculation unit 5 will be particularly described.

  In the evaluation model 20 of the second embodiment, similar to the evaluation model 10 of the first embodiment, the bank 11, the water shield 15, and the lower infiltration line 16 are formed. Have sliding surfaces 27 of different shapes. Since the slip surface 27 is different from the evaluation model 10, the strip 28 is also divided and provided so as to be different from the evaluation model 10.

  In the evaluation model 20, as in the evaluation model 10, the continuous water boundary line formed by the water surface 12a, that is, the water level surface 13, the lower side 15c of the water shield 15 and the lower side infiltration line 16 is the water surface 12a. It has a shape including a fold, which is once folded by the water shield 15 and continues to the lower infiltration line 16. One end of the slip surface 27 is located on the upper surface 11 c of the bank 11, and the other end is located on the water shield 15. The slip surface 27 is set above the lower infiltration line 16 as a whole.

  For such an evaluation model 20, the water pressure calculation unit 5 shown in FIG. 1 calculates the water pressure on the slip surface 27 in each of the plurality of strips 28. In the present embodiment, the water pressure calculation unit 5 includes the water level surface 13, that is, the water surface 12 a and the water shield 15 on the side where the water 12 of the bank 11 is stored at the horizontal center position of each strip 28. The water pressure is calculated based on the height positions of the surface 15a, the lower side infiltration line 16, and the slip surface 27.

More specifically, among the strips 28, for the strip 28 in which the surface 15a of the water shield 15 is located at the central position in the horizontal direction, for example, the strip 28A in FIG. An upper difference h which is a difference in the height direction between the water level surface 13 of the bank 11 on the side where the water 12 is stored, that is, the water surface 12a and the water blocking surface 15a of the water blocking body 15 located below the water level surface 13. _{Based on 2A1} , the hydraulic pressure u _2A corresponding to the strip 28A on the slip surface 27 is calculated. In the second embodiment, the slip surface 27 is located above the lower infiltration line 16, and the water pressure of water located below the lower infiltration line 16 does not act on the slip surface 27. The water pressure of the water located below is not considered when calculating the water pressure u _2A , unlike the first embodiment.

(Equation 5)
u _2A = h _2A1 × γ _W (5)

Thus, in the strip 28A in which the slip surface 27 is located above the lower infiltration line 16 at the central position in the horizontal direction, the surface pressure 15a of the water shield 15 is calculated by calculating the water pressure u _2A as described above. The difference h 2 _Au in the height direction between the slip surface 27 and the slip surface 27 is calculated by being excluded from the difference in the height direction between the water surface 13 and the slip surface 27.

The strips 28B, 28C, 28D are formed by the water surface 12a (water level surface 13), the lower side 15c of the water shield 15 and the lower side infiltration line 16 above the slip surface 27 at the central position in each horizontal direction. The water pressure u _2B , u _2C , u _2D corresponding to each of the strips 28B, 28C, 28D is calculated to be 0, because the boundary line of the spilled water is not located.

  The slope stability calculation device, method, and program of the bank according to the present embodiment, when deriving the safety factor by the evaluation model 20 in the second example, have the same effects as those described in the first example. Needless to say.

In the strip 28A of the second embodiment, the slip surface 27 is located above the lower infiltration line 16, but in such a case, the height between the surface 15a of the water shield 15 and the slip surface 27 is high. The difference h 2 _Au in the direction is calculated by excluding it from the difference in the height direction between the water level surface 13 and the slip surface 27. The difference _h2Au calculated by excluding it corresponds to a region where the stored water 12 does not infiltrate, so this value is excluded from the difference in the height direction between the water level surface 13 and the slip surface 27. This makes it possible to calculate water pressure values that are closer to the actual values, and even in such cases, therefore, it is possible to derive a more appropriate safety factor than the conventional method of including these values especially in water pressure calculation. Therefore, it is possible to prevent the safety factor from being underestimated.

(Third embodiment)
FIG. 6 is a diagram showing the evaluation model 30 shown as the third embodiment. In the present embodiment, except for the calculation of the water pressure, it can be carried out in the same manner as in the case of being applied to the first embodiment. Therefore, here, the calculation of the water pressure in the water pressure calculation unit 5 will be particularly described.

  The evaluation model 30 in the third embodiment includes a bank 31 having the same outer shape as the evaluation model 10 in the first embodiment, but the structure of the water shield 35 is different. That is, in the third embodiment, it is assumed that the dam body 31 is a reservoir dam body, and the water shield 35 is a water shield layer. Therefore, the water shield 35 is not embedded in the dam body 31. There is.

  More specifically, the water shield 35 has a shape in which two trapezoids are provided so as to be vertically connected to each other when their lower bases are aligned when viewed in cross section as shown in FIG. The water shield 35 has an outer shell formed by a shape formed by connecting each of the six points 35a, 35b, 35c, 35d, 35e, and 35f shown in FIG. 6 with a line, and each of these lines forms water lines. It has a water-blocking surface that blocks water. Of these lines, a water-impervious surface 35g connecting a point 35a located on the upper side of the bank 31 and on the water 12 side and a point 35b located on the lower side of the bank 31 and further to the water 12 side than the point 35a ( The surface) is inclined in substantially the same direction as the water-side slope 31a (slope) of the bank 31.

  The point 35a located on the upper side of the water shield 35 is provided at a height position substantially equal to or higher than the water surface 12a. The water level surface 33, which is the upper surface of the water on the side where the water 12 of the bank 31 is stored, is the upper side which is continuous from the water surface 12a of the stored water 12 to the surface 35g of the water shield 35 inside the bank 31. The wetting line 39 is provided, and the end point of the upper side wetting line 39 opposite to the water 12 side is provided so as to be located on the water-impervious surface 35g.

  The water-impervious surface 35h formed by connecting the point 35b, which is the lower end point of the water-impervious surface 35g of the water-impervious body 35, and the point 35c is positioned so as to be substantially perpendicular to the water-side slope 31a. ing. A water blocking surface 35i formed by connecting a point 35c of the water blocking surface 35h positioned away from the water-side slope 31a and a point 35d provided on the right side of the water blocking surface 35h extends substantially parallel to the ground G. Is provided.

  In the evaluation model 30, the area on the right side in FIG. 6, which is located on the side of the bank 31 opposite to the water 12 with respect to the water shield 35, is covered by the water shield 35 from the upper surface 31c to the ground G. Separated from water 12. Therefore, the water 12 does not infiltrate the region on the right side of the water shield 35 of the bank 31 and infiltrates the ground G located below the water shield 35 from the lower end of the water shield 35. There is. That is, the lower side infiltration line 36, which is a boundary between the portion infiltrated with the water 12 and the portion not infiltrated at a height lower than the inclined water-impervious surface 35 g of the water-impervious body 35, is below the water-impervious body 35. More specifically, starting from a point 35b that is the lower end of the water-impervious surface 35g, extending along the water-impervious surface 35h, and then bending at the point 35c that is the lower end of the water-impervious surface 35h, the water 12 Is provided in the ground G so as to extend substantially parallel to the ground G in the direction opposite to the side where the is stored. The continuous water boundary line formed by the water level surface 33 formed by the water surface 12a and the upper side infiltration line 39, the water blocking surface 35g of the water shield 35, and the lower side infiltration line 36 with the point 35b as the base point is The water level surface 33 is provided with a shape including a turn back such that the water level surface 33 is once turned back by the water shield 35 and continues to the lower infiltration line 36.

  The sliding surface 37 has one end located on the upper surface 31c of the dam body 31 and the other end located on the ground G in the water 12, and is set so that the entire water shield 35 is located above the sliding surface 37. Has been done. In such an evaluation model 30, a portion of the bank 31 above the slip surface 37 is divided into strips 38 (38A, 38B, 38C, 38D, 38E, 38F, 38G, 38H, 38I).

  For the evaluation model 30 as described above, the water pressure calculation unit 5 shown in FIG. 1 calculates the water pressure on the slip surface 37 in each of the plurality of strips 38. In the present embodiment, the water pressure calculation unit 5 has a water level surface 33 formed by the water surface 12a and the upper infiltration line 39, a water impervious surface 35g of the water impervious body 35, and a dot at the central position in the horizontal direction of each strip 38. The water pressure is calculated based on the lower infiltration line 36 having the base point 35b and the height position of the slip surface 37.

First, among the strips 38, each strip 38 in which the water-impervious surface 35g of the water shield 35 and the lower infiltration line 36 are not located at the central position in the horizontal direction, for example, the strips 38A, 38B in FIG. for the 38C, pressure calculating unit 5 of the central position in the horizontal direction, a water level surface 33 i.e. water 12a or upper infiltration lines 39, the difference _h 3A in the height direction of the sliding surface _37, h _3B, the _{h 3C} Based on this, the hydraulic pressures u _3A , u _3B and u _3C corresponding to the strips 38A, 38B and 38C are calculated by the following equation.

(Equation 6)
u _3A = h _3A × γ _W (6)
u _3B = h _3B × γ _W
u _3C = h _3C × γ _W

Among the strips 38, the strip 38 in which the water-impervious surface 35g of the water shield 35 and the lower infiltration line 36 are located at the central position in the horizontal direction, for example, strips 38D, 38E, 38F, 38G in FIG. , 38H, the water pressure calculation unit 5 determines the water level surface 33 of the levee body 31 on the side where the water 12 is stored, that is, the water surface 12a and the upper infiltration line 39, and the water shield 35 located below the water level surface 33. based on the above difference _{h 3D1, h 3E1, h 3F1} , h 3G1, h 3H1 is the height direction of the difference between the water shield surfaces 35 g, each strip 38D in the sliding surface 37, 38E, 38F, 38G, the 38H Calculate the corresponding water pressures u _3D , u _3E , u _3F , u _3G , u _3H .

Among these strips 38D, 38E, 38F, 38G, 38H, particularly with respect to the strips 38D, 38E, 38F in which the slip surface 37 is located below the lower infiltration line 36 at the central position in each horizontal direction. the water pressure calculation unit 5, in addition to the upper difference _{h 3D1, h 3E1, h 3F1} , lower difference _h 3D2 is the height direction of the difference between the sliding surface 37 lower infiltration lines _{36, h 3E2,} h _3F2 based on, and more particularly, a lower difference _{h 3D2,} h _{3E2, h 3F2,} based on the sum of the upper difference _{h 3D1, h 3E1, h 3F1} , each strip in the sliding surface 37 38D, 38E , 38F corresponding hydraulic pressures u _3D , u _3E , u _3F are calculated. More specifically, the water pressure calculation unit 5 calculates the water pressure u _3D , u _3E , u _3F by the following equation.

(Equation 7)
u _3D = (h _3D1 + h _3D2 ) × γ _W (7)
_{u 3E = (h 3E1 + h} 3E2) × γ W
u _3F = (h _3F1 + h _3F2 ) × γ _W

Thus, for the strips 38D, 38E, 38F in which the slip surface 37 is located below the lower infiltration line 36 at the central position in the horizontal direction, the hydraulic pressures u _3D , u _3E , u _3F are calculated as described above. By performing, the difference _h3Du , _h3Eu , _h3Fu in the height direction between the water-impervious surface 35g of the water-impervious body 35 and the lower infiltration line 36 is _calculated from the difference in the height direction between the water level surface 33 and the slip surface 37. It is excluded and calculated.

Further, among the strips 38D, 38E, 38F, 38G, and 38H, the strips 38G and 38H in which the slip surface 37 is located above the lower infiltration line 36 at the central position in each horizontal direction are described above. Similar to the strip 28A in the second embodiment, since the water pressure of the water located below the lower infiltration line 36 does not act on the slip surface 37, the water pressure u _3G corresponding to each strip 38G, 38H is calculated by the following equation. Calculate u _3H .

(Equation 8)
u _3G = h _{3G 1} × γ _W (8)
u _3H = h _3H1 × γ _W

Thus, in the strips 38G and 38H in which the slip surface 37 is located above the lower infiltration line 36 at the central position in the horizontal direction, the water pressure u _3G and u _3H are calculated as described above, so Differences h _3Gu and h _{3Hu in} the height direction between the water-impervious surface 35g of the water body 35 and the slip surface 37 are calculated by being excluded from the difference in the height direction between the water level surface 33 and the slip surface 37.

Regarding the strip 38I, at the central position in the horizontal direction, above the slip surface 37, the water level surface 33 formed by the water surface 12a and the upper wetting line 39, the water blocking surface 35g of the water blocking member 35, and the lower wetting line 36. The water pressure u _3I corresponding to the strip 38I is calculated to be 0 because the boundary of the water formed by is not located.

  The slope stability calculation device, method, and program of the embankment of the present embodiment have the same effects as those described in the first embodiment when deriving the safety factor by the evaluation model 30 in the third embodiment. Needless to say.

  Further, in the strips 38G and 38H of the third embodiment, the slip surface 37 is located above the lower infiltration line 36 at the central position in each horizontal direction, but it has been described in the second embodiment. As described above, even in such a case, it is possible to derive a more appropriate safety factor than the conventional method of including these values in the hydraulic pressure calculation, and prevent the safety factor from being underestimated.

(Fourth embodiment)
FIG. 7 is a diagram showing the evaluation model 40 shown as the fourth embodiment. In the present embodiment, except for the calculation of the water pressure, it can be carried out in the same manner as in the case of being applied to the first embodiment. Therefore, here, the calculation of the water pressure in the water pressure calculation unit 5 will be particularly described.

  The evaluation model 40 in the fourth embodiment includes a bank 41 having the same outer shape as the evaluation model 10 in the first embodiment, but the structure of the water shield 45 is different. That is, in the fourth embodiment, it is assumed that the dam body 41 is a fill dam and the water shield body 45 is the core of the fill dam. Therefore, the water shield body 45 is buried in the dam body 41.

  More specifically, the water shield 45 is formed in a trapezoidal shape when viewed in cross section as shown in FIG. 7. That is, the water shield 45 is formed in the vicinity of the upper surface 41c of the bank 41 and the ground G, respectively, and the upper bottom 45c and the lower bottom 45d located substantially parallel to the upper surface 41c and the ground G, and connecting the upper bottom 45c and the lower bottom 45d. It has two legs 45a, 45b of equal length. Each line that forms this trapezoidal outer shell is a water-impervious surface that blocks water. Of these lines, the water-impervious surface 45a (surface) corresponding to the leg 45a located on the water 12 side gradually moves toward the side where the water 12 of the bank 41 is stored, as it goes downward. It is inclined.

  The water level surface 43, which is the upper surface of the water on the side of the bank body 41 where the water 12 is stored, is the water surface 12a of the stored water 12 and the water surface 12a of the water shield body 45 inside the bank body 41 from the water surface 12a. The upper side infiltration line 49 is provided continuously to the surface 45a, and the end point of the upper side infiltration line 49 on the side opposite to the water 12 side is provided so as to be located on the water-impervious surface 45a.

  In the evaluation model 40, the area on the right side in FIG. 7 of the bank 41, which is located on the side opposite to the water 12 with respect to the water shield 45, is covered by the water shield 45 from the upper surface 41c to the ground G. Separated from water 12. Therefore, the water 12 does not infiltrate the region on the right side of the water shield 45 of the bank 41, but infiltrates the ground G located below the water shield 45 from the lower end of the water shield 45. There is. That is, the lower side infiltration line 46, which is a boundary between the portion infiltrated with the water 12 and the portion not infiltrated, at a height lower than the inclined water-impervious surface 45 a of the water-impervious body 45 is below the water-impervious body 45. More specifically, it is provided in the ground G so as to extend from the lower end 45e of the water-impervious surface 45a in a direction opposite to the side in which the water 12 is stored and substantially parallel to the ground G. There is. A continuous water boundary line formed by the water level surface 43 formed by the water surface 12a and the upper side infiltration line 49, the water blocking surface 45a of the water shield 45, and the lower side infiltration line 46 whose base point is the lower end 45e is: The water level surface 43 has a shape including a turn-back, which is once turned back by the water shield 45 and continues to the lower infiltration line 46.

  One end of the slip surface 47 is located on the slope 41b of the bank 41 opposite to the water 12, and the other end is located on the water side slope 41a (slope) of the water 12 side. It is provided to intersect with. In such an evaluation model 40, the part of the bank 41 above the slip surface 47 is divided into strips 48 (48A, 48B, 48C, 48D, 48E, 48F, 48G).

  For the evaluation model 40 as described above, the water pressure calculator 5 shown in FIG. 1 calculates the water pressure on the slip surface 47 in each of the plurality of strips 48. In the present embodiment, the water pressure calculation unit 5 includes the water level surface 43 formed by the water surface 12a and the upper infiltration line 49, the water impervious surface 45a of the impervious body 45, and the lower end at the central position in the horizontal direction of each strip 48. The water pressure is calculated based on the lower infiltration line 46 with 45e as the base point and the height position of the slip surface 47.

First, among the strips 48, each strip 48 in which the water-impervious surface 45a of the water shield 45 and the lower infiltration line 46 are not located at the central position in the horizontal direction, for example, the strips 48A, 48B in FIG. Regarding 48C, 48D, 48E, and 48F, the water pressure calculation unit 5 determines the difference h _4A in the height direction between the water level surface 43, that is, the water surface 12a or the upper infiltration line 49, and the sliding surface 47 at the central position in the horizontal direction, Based on h _4B , h _4C , h _4D , h _4E , h _4F , the hydraulic pressures u _4A , u _4B , u _4C , u _4D corresponding to the strips 48A, 48B, 48C, 48D, 48E, 48F by the following formula. , U _4E , u _4F are calculated.

(Equation 9)
u _4A = h _4A × γ _W (9)
u _4B = h _4B × γ _W
u _4C = h _4C × γ _W
u _4D = h _4D × γ _W
u _4E = h _4E × γ _W
u _4F = h _4F × γ _W

Of the strips 48, the strip 48 in which the water-impervious surface 45a of the water shield 45 and the lower infiltration line 46 are located at the central position in the horizontal direction, for example, the strip 48G in FIG. 5 is the height of the water level surface 43 of the bank 41 on the side where the water 12 is stored, that is, the water surface 12a and the upper infiltration line 49, and the water blocking surface 45a of the water blocking body 45 located below the water level surface 43. The water pressure u _4G corresponding to the strip 48G on the slip surface 47 is calculated based on the upper difference h _4G1 which is the difference in the direction.

  In the strip 48G, at the central position in the horizontal direction, the slip surface 47 is located above the lower infiltration line 46, and the water pressure of water located below the lower infiltration line 46 acts on the slip surface 47. Therefore, the water pressure is calculated by the following formula.

(Equation 10)
u _4G = h _4G1 × γ _W (10)

In this way, in the strip 48G in which the slip surface 47 is located above the lower side infiltration line 46 at the central position in the horizontal direction, the water pressure u _4G is calculated as described above, and thus the water shield of the water shield 45 is obtained. The difference _h4Gu in the height direction between the surface 45a and the slip surface 47 is calculated by being excluded from the difference in the height direction between the water level surface 43 and the slip surface 47.

  The slope stability calculation device, method, and program of the embankment of the present embodiment have the same effects as those described in the first embodiment when deriving the safety factor by the evaluation model 40 of the fourth embodiment. Needless to say.

  Further, in the strip 48G of the fourth embodiment, the slip surface 47 is located above the lower infiltration line 46 at the central position in the horizontal direction of the strip 48G, but it has been described in the second embodiment. As described above, even in such a case, it is possible to derive a more appropriate safety factor than the conventional method of including these values in the hydraulic pressure calculation, and prevent the safety factor from being underestimated.

The slope stability calculation device, method, and program for the bank of the present invention are not limited to the above-described embodiments described with reference to the drawings, and various other modified examples are conceivable within the technical scope thereof. Be done.
For example, in each of the above-described embodiments, the water shield is provided so that the lower end of the water-impervious surface is located at substantially the same height as the ground G, but the invention is not limited to this, and the lower end of the water-impervious surface is the ground. It may be provided at a position lower than G, or at a position higher than the ground G, that is, inside the levee, and the lower infiltration line is positioned inside the levee. It doesn't matter. In any case, it goes without saying that the water pressure value can be calculated according to the procedure described in the above embodiment.
Further, in the third and fourth embodiments, the upper infiltration lines 39 and 49 have the water surface 12a extending straight into the levee bodies 31 and 41 as shown in FIGS. It is needless to say that the water level, that is, the height, is not limited to this and the water level, that is, the height, may gradually decrease as the water enters the inside of the bank body 31, 41.

In addition, in each of the above-described embodiments, each slip surface has an arc shape, but the present invention is not limited to this and may have another shape. For example, a shape may be formed by an operator arbitrarily inputting a plurality of points on an evaluation model in a sectional view and connecting these points to each other.
Further, in each of the above-mentioned embodiments, the strip dividing portion 4 is illustrated in FIGS. 3, 5, 6 and 7 so that the strips have substantially the same width in the horizontal direction, but the present invention is not limited to this. I can't. For example, it may be divided into strips such that the slope of the ground or the slope of the dam body, the geology, or the like is divided at a point where it changes.

Further, in the above-described embodiment, the safety factor is derived by using the Ferrenius formula and the modified Ferrenius formula represented by Formula 3 and Formula 4, but the present invention is not limited to this, and is obtained by another formula using water pressure. It doesn't matter.
In the above embodiment, the height value of each strip is the height value of the strip at the central position in the horizontal direction, but is not limited to this. For example, the height may be measured at a plurality of horizontal positions in each strip, and this average value may be used as the height.

  Other than this, the configurations described in the above embodiments can be selected or changed to other configurations without departing from the spirit of the present invention.

1 Control Part 2 Model Input Part 3 Sliding Surface Candidate Set Determining Part 4 Strip Dividing Part 5 Water Pressure Calculating Part 6 Safety Factor Calculating Part 7 Output Part 10, 20, 30, 40 Evaluation Model 11, 31, 41 Dike 11a, 31a , 41a Water side slope (slope)
12 Water 12a Water surface (water level surface)
13, 33, 43 Water level surface 15, 35, 45 Water shield 15a, 35g, 45a Water shield surface (surface)
16, 36, 46 Lower infiltration line 17, 27, 37, 47 Sliding surface 18, 28, 38, 48 Strip 39, 49 Upper infiltration line (water level surface)
G Ground _{h 1C2, h 1D2, h 3D2} ~h 3F2 lower difference _{h 1C1, h 1D1, h 2A1} , h 3D1 ~h 3H1, h 4G1 upper difference _{h 1Cu, h 1Du, h 2Au} , h 3Du ~h 3Hu, h Difference calculated by excluding _4Gu

Claims (11)

A slope stability calculation device for a dam body for damming water, which is provided with an impermeable body having a sloped surface,
Below the water shield, a lower infiltration line extends in a direction opposite to the side where the water of the bank is stored, and when a slip surface is set for the bank,
Based on the upper difference which is the difference in the height direction between the water level surface of the bank body on the side where water is stored and the surface of the water shield located below the water level surface, the slip surface Calculate the water pressure,
And, in this case, when the slip surface is located below the lower infiltration line, the difference in the height direction between the surface of the water shield and the lower infiltration line is the slip surface When located above the side infiltration line, the difference in the height direction between the surface of the water shield and the slip surface is excluded from the difference in the height direction between the water level surface and the slip surface, respectively. Calculated,
An embankment slope stability calculation device comprising a control unit that calculates a safety factor based on the water pressure.   When the slip surface is located below the lower infiltration line, the control unit is a lower difference that is a difference in the height direction between the lower infiltration line and the slip surface, and the sum of the upper differences. The slope stability calculation device for a dam body according to claim 1, wherein the water pressure on the slip surface is calculated based on the above. The water shield, the surface is provided along the slope, in the vicinity of the surface layer of the slope of the bank,
The slope stability calculation device for a bank according to claim 1 or 2, wherein the water level surface is a water surface of stored water.   The slope stability calculation device for a bank according to claim 3, wherein the water shield is a water shield sheet. The water shield is embedded in the bank,
The slope of the dam body according to claim 1 or 2, wherein the water level surface includes a water surface of the stored water and an upper infiltration line continuous from the water surface to the surface of the water shield inside the dam body. Stable calculator.   The slope stability calculation device for a bank according to claim 5, wherein the bank is a fill dam, and the water shield is a core of the fill dam.   The slope stability calculation device for a dam body according to claim 5, wherein the dam body is a reservoir dam body, and the water shield body is a water shield layer. A slope stability calculation method for a dam body for damming water, which is provided with an impervious body whose surface is inclined,
Below the water shield, a lower infiltration line extends in a direction opposite to the side where the water of the bank is stored, and when a slip surface is set for the bank,
Based on the upper difference which is the difference in the height direction between the water level surface of the bank body on the side where water is stored and the surface of the water shield located below the water level surface, the slip surface Calculate the water pressure,
And, in this case, when the slip surface is located below the lower infiltration line, the difference in the height direction between the surface of the water shield and the lower infiltration line is the slip surface When located above the side infiltration line, the difference in the height direction between the surface of the water shield and the slip surface is excluded from the difference in the height direction between the water level surface and the slip surface, respectively. Calculated,
A slope stability calculation method for a bank, which calculates a safety factor based on the water pressure.   When the slip surface is located below the lower infiltration line, a lower difference that is a difference in the height direction between the lower infiltration line and the slip surface, and based on the sum of the upper differences, the The slope stability calculation method for a bank according to claim 8, wherein the water pressure on the slip surface is calculated. A slope stability calculation program for a dam body that dams water, provided with an impervious surface.
Below the water shield, a lower infiltration line extends in a direction opposite to the side where the water of the bank is stored, and when a slip surface is set for the bank,
Based on the upper difference which is the difference in the height direction between the water level surface of the bank body on the side where water is stored and the surface of the water shield located below the water level surface, the slip surface Calculate the water pressure,
And, in this case, when the slip surface is located below the lower infiltration line, the difference in the height direction between the surface of the water shield and the lower infiltration line is the slip surface When located above the side infiltration line, the difference in the height direction between the surface of the water shield and the slip surface is excluded from the difference in the height direction between the water level surface and the slip surface, respectively. Calculated,
A levee slope stability calculation program that calculates a safety factor based on the water pressure.   When the slip surface is located below the lower infiltration line, a lower difference that is a difference in the height direction between the lower infiltration line and the slip surface, and based on the sum of the upper differences, the The slope stability calculation program for a levee body according to claim 10, which calculates the water pressure on a slip surface.

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