JP2018123544A - Method of evaluating safety of retaining wall, safety assessment program of retaining wall and safety evaluation system of retaining wall - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method of evaluating the safety of a retaining wall which evaluates the safety of the retaining wall with high accuracy in the case where a ground surface shape of a back face of the retaining wall is of a complicated shape or when considering the adhesive force to the soil of the back face of the retaining wall, and a safety assessment program of a retaining wall and a safety evaluation system of a retaining wall.SOLUTION: A method of evaluating the safety of a retaining wall for evaluating the safety of a retaining wall, comprises the steps of: determining a slip form occurring on a back face of the retaining wall; deciding the calculation method of earth pressure according to the determined slip form; calculating an earth pressure received from the back face of the retaining wall by using an iterative algorithm of the present invention by a different approach from the conventional calculation method (trial wedge method and improved trial wedge method); evaluating the safety of a retaining wall using earth pressure; and graphically showing change of earth pressure over the entire calculation range.SELECTED DRAWING: Figure 3

Description

  The present invention obtains the earth pressure received from the back of the retaining wall by an approach different from the conventional calculation method, and uses the earth pressure to evaluate the safety of the retaining wall, and the safety of the retaining wall. The present invention relates to an evaluation program and a retaining wall safety evaluation system.

A retaining wall is a structure for effectively using land. Currently, retaining walls are being constructed in construction work in the construction field and road improvement work in the civil engineering field. In the design of the retaining wall, the shape, location and weight of the retaining wall are determined by calculation so that the retaining wall can be kept stable against the invisible force of earth pressure due to earth. This calculation is called retaining wall stability calculation.
The earth pressure is calculated using the earth pressure calculation formula under conditions where the earth pressure calculation formula can be applied, and conditions where the earth pressure calculation formula cannot be applied (for example, when considering adhesive force or When the shape of the ground surface changes in various ways, when using the cantilever type retaining wall described later in the case of two-side slip), the earth pressure using the trial wedge method based on the Coulomb earth pressure theory or the improved trial wedge method Is calculated.
In the trial wedge method, the maximum working earth pressure is experimentally increased while increasing the angle of the R surface described later at a certain angular interval (a discrete angle such as 1 degree interval or 0.1 degree interval). It is a method to ask for. In the trial wedge method, the slip surface for performing trial calculation is only the R plane, and the slip mode at the time of ultimate equilibrium (see later) corresponds to “one-plane linear slip” described later.
The improved trial wedge method is a method in which the maximum working earth pressure is determined on a trial basis while increasing the angles of the R surface and L surface described later at a certain angular interval. The number of examinations is obtained by multiplying the number of examinations on the R plane by the number of examinations on the L plane. In the improved trial wedge method, the slip surfaces to be trial-calculated are the R plane and the L plane, and the slip mode at the ultimate equilibrium corresponds to the “two-plane linear slip” described later.

JP 2012-197604 A JP 2005-83066 A

The problems to be solved by the present invention are the following four.
The first is a method for determining the slip form on the back surface of the retaining wall at the time of earth pressure calculation. In the current calculation method of earth pressure considered at the time of retaining wall stability calculation, the slip form generated on the back surface of the retaining wall depends on the structure type of the retaining wall. More specifically, a structure such as a gravitational retaining wall with a slanted shape on the back surface of the structure body is assumed to generate a “one-sided linear slip” on the back surface of the retaining wall, and is L-shaped. In the case of a cantilever retaining wall having a heel plate such as a retaining wall or an inverted T-shaped retaining wall, “two-sided linear sliding” is assumed to occur. However, even when the shape of the back of the structure body, such as a gravity retaining wall, is inclined, a “two-sided linear slip” may occur. It is unclear.
The second is the calculation method of the improved trial wedge method. As described above, in the calculation of the cantilever retaining wall, it is necessary to obtain the maximum working earth pressure with the slip configuration as “two-sided linear slip”, but the current earth pressure of “two-sided linear slip” is required. The improved trial wedge method, which is a calculation method, has two sliding surfaces to be trial-calculated. Therefore, a large number of trial calculations (for example, trial calculation within the range of calculation of the angle of the L-plane between 30 degrees and 80 degrees) If the interval is 0.1 degree, the angle of the R plane is within a calculation range of 30 to 80 degrees, and the trial calculation interval is 0.1 degree, 500 × 500 calculations are required. . Therefore, the solution cannot be calculated instantaneously, and it takes several minutes to obtain a highly accurate solution. For this reason, in the calculation of earth pressure of cantilever type retaining walls, in order to simplify the calculation, the slip surface is assumed to be one surface (only the R surface), and the earth pressure is assumed to be “one surface linear slip”. It is now mainstream to calculate
Third, the trial wedge method and the improved trial wedge method have a problem that affects the accuracy of the solution depending on the calculation interval of the slip surface angle that is increased during the trial calculation. (For example, the solution obtained when the trial calculation interval is calculated at intervals of 0.1 degrees is different from the solution obtained when the trial calculation interval is calculated at intervals of 1 degree.)
The fourth is a method for expressing the maximum earth pressure graph. The output of the trial calculation by the trial wedge method and the improved trial wedge method is near the maximum earth pressure (for example, when the trial calculation interval is set to 1 degree interval, about 5 degrees at intervals of 1 degree before and after the maximum value) The value related to the angle of the sliding surface and the value related to the earth pressure are graphed and displayed. This is because of the nature of the trial wedge method and the improved trial wedge method, it is necessary to show the basis for selecting the maximum earth pressure, but the values related to the angle of the slip surface and the values related to the earth pressure are However, there is a drawback that it is not possible to visually recognize what kind of change will occur.

A retaining wall safety evaluation method comprising at least one of a one-sided linear sliding mode or a two-sided linear sliding mode, an obtaining step for obtaining data relating to a retaining wall constant, a soil constant, a load constant, and the like; The calculation step of calculating the load including earth pressure acting on the retaining wall based on the data acquired in the step, and the safety of the retaining wall based on the load including earth pressure acting on the retaining wall calculated in the calculation step. It is composed of an evaluation step for evaluating at least one and a display step for displaying a result evaluated in the evaluation step. Data acquired in the acquisition step includes retaining wall shape information, retaining wall material information, retaining wall back surface. Soil information, supporting ground information, terrain information behind the retaining wall, load information acting on the terrain behind the retaining wall, and other load information, and the calculating step includes Obtained based acquired data and the inclination angle of the back side of the computed seismic compound angle θ and the calculated retaining wall α in step, calculation conditions (constant phi _ShitabetaL, constant phi _{Shitabetaaru,} criteria L side vertical load p _{0 L} , R-side reference load p _0R , L-side reference adhesive strength c _0L , R-side reference adhesive force c _0R , L-side reference horizontal load t _0L , R-side reference horizontal load t _0R , Constant horizontal load t _0A and constant vertical load W _A ), and in the two-plane linear sliding mode, based on the above calculation conditions, extreme main earth pressure P _a0 and L-plane fixed extreme main _earth pressure P _a0L and R Calculates the earth pressure including at least one of the fixed surface extreme extreme earth pressures _Pa0R or the angle of the sliding surface. In the one-surface linear sliding mode, the one-surface linear sliding mode is based on the above calculation conditions. earth pressure containing L plane fixed extreme main働土pressure _{P a0L,} Others are intended to calculate the angle of the sliding surface, for the number 1, obtained from the number 2 omega _{[beta] R,} or the initial value of omega _{[beta] R} or formula from omega _{[beta] R} of the fixed value (42), equation (55), formula ( 56), Expression (57), Expression (71), and Expression (161) are calculated, and using the obtained μ _L , t _2L , t _2R , t _2A , k, and ξ _L , Expression (68), Expression ( 163) is calculated, which acquires the omega _.beta.L, for the number 2, obtained from the number 1 omega _.beta.L or initial value of omega _.beta.L or expression from omega _.beta.L fixed value (41), equation (28), Expressions (29), (30), and (162) are calculated, and Expressions (52) and (164) are calculated using the obtained μ _R , t _1L , t _1R , t _1A and ξ _R. is intended to obtain the omega _{[beta] R,} in the calculation of the extreme main働土pressure P _a0 in two planes straight shear mode, Define any number in omega _.beta.L or omega _{[beta] R} as an initial value in the later iteration, the number 1 and so repetition calculated alternately number 2 to a predetermined accuracy, alternately repeatedly calculated omega _.beta.L or omega until predetermined accuracy is intended to calculate the extremum main働土pressure P _a0 with _{[beta] R,} the L plane calculation of the fixed extreme main働土pressure P _A0L in dihedral straight shear mode, giving omega _.beta.L fixed value of the number 2, The obtained ω _βR is used to calculate the L-plane fixed extreme value main _earth pressure P _a0L . In the calculation of the R-plane fixed extreme value main _earth pressure P _{a0R in} the two-plane linear sliding mode, the fixed value ω _βR is given in _Formula 1, and the obtained ω _βL is used to calculate the R-plane fixed extreme _earth pressure P _a0R , and the L-plane fixed extreme _earth pressure P _{a0L in} the 1-plane linear sliding mode in the calculation, beta define any number _{L, and} the fixed value _{ω βL = π / 2-α} + _L applied to the number 2, and calculates the L plane fixed extreme main働土pressure P _A0L at one side straight shear mode using the obtained omega _{[beta] R.}

An outline of the algorithm of the iterative method of the present invention used for calculation of the extreme main earth pressure P _{a0 in} the two-plane linear sliding mode will be described.
To determine the maximum value of the main働土pressure acting on retaining wall may be determined a maximum value of hereinafter described basic main働土pressure P _a. The basic main働土pressure P _a is a variable angle omega _L angle omega _R and L side of the R-plane. Using this, you obtain the angle omega _L of L faces basic main働土pressure P _a becomes a maximum by fixing the angle omega _R any R surfaces, or to fix the angle omega _L of any L surface obtains an angle omega _R the R plane basic main働土pressure P _a is the maximum Te, the angle omega _R the angle omega _L or R faces of the obtained L face again, fixed and basic main働土pressure P _a is the maximum become sought angle omega _L angle omega _R or L plane of the R plane, by repeating this, basic main働土pressure P _a maximum value and a basic main働土pressure P _a is maximized L face angle omega _L And the angle ω _{R of the} R plane can be obtained. Therefore, the iterative algorithm of the present invention drastically reduces the number of calculations compared to the conventional improved trial wedge method (for example, the number of calculations when the slope change point is 10 is about 10 × 10 = Therefore, the solution can be calculated instantaneously and a highly accurate solution can be obtained. In addition, by repeating repeated calculations, the error with respect to the true solution can be approximated to zero.

  In the evaluation step, the vertical load and the resistance moment and the horizontal load and the falling moment acting on the retaining wall are calculated with respect to the weight of the retaining wall and the external force acting on the retaining wall obtained in the calculation step. .

  Slip surfaces generated from the back side of the retaining wall bottom surface toward the ground surface include an L surface described later and an R surface described later. In the calculation step, it is determined whether the L surface occurs along the retaining wall or appears in the ground, and when the L surface occurs along the retaining wall, “one-plane straight slip” When it appears in the ground, it is referred to as “two-plane linear slip”, and the earth pressure or the angle of the slip surface according to the form of the slip is calculated.

  For the earth pressure calculated in the calculation step, not only the vicinity of the maximum earth pressure but also the value relating to the angle of the slip surface and the value relating to the earth pressure in the entire calculation range or the entire topography of the retaining wall are displayed in a graph. A display step is included. It is good also as a graph showing the relation between the point where a slip surface and the ground surface intersect, and the earth pressure calculated from the angle of the slip surface at that point. A configuration may be adopted in which any one of the retaining wall shape, the ground surface shape, the action state of the load, or the slope cross-sectional view showing the sliding surface and the above graph are displayed in an overlapping manner.

A retaining wall safety evaluation program, comprising: a computer for obtaining data relating to a retaining wall constant, a soil constant, a load constant, and the like; and a soil acting on the retaining wall based on the data obtained by the obtaining means. Calculation means for calculating a load including pressure, evaluation means for evaluating at least one of the safety of the retaining wall based on the load including earth pressure acting on the retaining wall calculated by the calculating means; and It is a program that functions as a display unit that displays an evaluation result, and the acquisition unit, the calculation unit, and the evaluation step for the acquisition step, the calculation step, the evaluation step, and the display step in the retaining wall safety evaluation method Each calculation process is executed by the means and the display means.
According to the retaining wall safety evaluation program, by causing the computer to execute the program, the retaining wall safety evaluation method operates in the same manner as the retaining wall safety evaluation method, and has the same effect.

Retaining wall safety evaluation system (retaining wall safety evaluation device), wherein the computer acquires data relating to the retaining wall constant, soil constant, load constant, and the like, and the data acquired by the acquiring means Calculating means including a load including earth pressure acting on the retaining wall based on the calculation means, and evaluating at least one of the safety of the retaining wall based on the load including the earth pressure acting on the retaining wall calculated by the calculating means. And a display unit for displaying the result of the evaluation in the evaluation step. The system includes a retaining wall safety evaluation program, the acquisition unit, the calculation unit, the evaluation unit, and the display unit. However, each calculation process is performed by the command of the retaining wall safety evaluation program.
This retaining wall safety evaluation system operates in the same manner as the retaining wall safety evaluation method and has the same effect.

  The present invention is an approach different from the trial wedge method and the improved trial wedge method for calculating the earth pressure received from the back surface of the retaining wall used in the conventional calculation program. The earth pressure acting on the retaining wall can be calculated quickly and with high accuracy in accordance with the load condition acting on the ground surface. As a result, the work is facilitated, and the effective determination of the cross section of the retaining wall can be supported. In addition, the earth wall pressure is used to determine the safety of the retaining wall (for example, overturning, sliding, supporting force, necessary reinforcing bar amount, cross-sectional force, etc.) as safety evaluation items for the retaining wall described in various standards. be able to.

It is possible to determine the slip form ("1-sided linear slip" described later, "2-sided linear slip" described later), and to evaluate the safety of the retaining wall with the earth pressure according to the slip form.
In addition, since the relationship between the angle of the sliding surface and the earth pressure acting on the retaining wall is graphed on the entire slope, the change in earth pressure on the entire slope can be seen visually, so the optimum retaining wall cross section can be selected and retained. In addition to supporting the determination of the wall arrangement, it is possible to support the determination of the optimum ground surface shape and the load application position on the back surface of the retaining wall that minimizes the earth pressure acting on the retaining wall.

  The retaining wall calculation processing program of the present invention can be provided by being stored in a storage medium such as a flexible disk or a CD-ROM, or can be provided by downloading from the Internet or the like. A sex evaluation device can be realized.

It is explanatory drawing which showed an example of arrangement | positioning of a retaining wall. It is a block diagram of a retaining wall safety evaluation system (retaining wall safety evaluation device) equipped with a retaining wall safety evaluation program according to the present embodiment. It is a flowchart which shows the flow of operation | movement of the retaining wall safety evaluation program which concerns on this Embodiment. It explains the situation of the ground surface on the back of the retaining wall, the load situation that acts on the ground surface, and the load situation that acts on the wedge-shaped slip soil mass when “two-sided linear slip” occurs. It is explanatory drawing for calculating the load which acts on the weight of a wedge-shaped slip soil lump when a "two-surface straight slip" generate | occur | produces, and a slip soil lump. It is a power diagram at the time of limit equilibrium in a rotating coordinate system. It is an action | operation direction figure of the main earth pressure which acts on the L surface in a rotation coordinate system. It is an action | operation direction figure of the main earth pressure which acts on the L surface in an actual coordinate system. It is a flowchart which shows the flow for selection of the slip form which generate | occur | produces on a retaining wall back surface. It is a figure showing the limit state where "one-sided linear slip" and "two-sided linear slip" occur simultaneously on the back of a trapezoidal structure, (a) is an explanatory view of the action state of force, (b ) Is a linkage diagram showing balance of forces. It is explanatory drawing for changing a calculation formula. It is an input screen of Example 1, (a) is an input screen of the shape information of a retaining wall, (b) is the figure which showed the input result of the shape information of a retaining wall. It is an input screen of Example 1, It is an input screen of the material information of a retaining wall, the soil information of a retaining wall back surface, and the information of a support ground. It is the figure which showed the caution point at the time of the input of the topographical information on the back of a retaining wall. It is an input screen of Example 1, It is an input screen of the terrain information on the back surface of a retaining wall, and the load information which acts on the terrain on the back surface of a retaining wall. It is an input screen of Example 1, and is an input screen of other load information. It is an output screen of Example 1, and is a calculation result of basic conditions. Constant is an explanatory view of a vertical load _{W Ai} 'and constant horizontal load _{t 0Ai'.} It is an output screen in the 2-plane linear sliding mode of Example 1, and is a calculation result of each main earth pressure in Li = 1. It is an output screen in the 2-plane linear sliding mode of Example 1, and it is the figure which put together the parameter used in order to calculate each main earth pressure and each main earth pressure. It is an output screen in the 2-plane linear sliding mode of Example 1, (a) The main earth pressure which acts on the L surface when the basic main earth pressure becomes the maximum and the basic main earth pressure becomes the maximum. it is also the data summarized related, (b) are those showed safety evaluation results of retaining wall, a graph (c) showed the relationship between the basic main働土pressure P _a and the sliding surface. An output screen when computed by subdividing the terrain data at the same input data used in Example 1 is a graph showing the relationship between the basic main働土pressure P _a and the sliding surface. It is an input screen of Example 2 and Example 3, (a) is an input screen of the shape information of a retaining wall, (b) is the figure which showed the input result of the shape information of a retaining wall. It is an input screen of Example 2, and is an input screen of the material information of a retaining wall, the soil information of a retaining wall back surface, and the information of a support ground. It is an input screen of Example 2 and Example 3, and is an input screen of the terrain information on the back surface of a retaining wall, and the load information which acts on the terrain on the back surface of a retaining wall. It is an input screen of Example 2 and Example 3, and is an input screen of other load information. It is an output screen of Example 2 and Example 3, and is a calculation result of a basic condition. It is an output screen in the 2-plane linear sliding mode of Example 2 and Example 3, and is a calculation result of each main earth pressure in Li = 2. It is an output screen in the 2-plane linear sliding mode of Example 2 and Example 3, and is the figure which put together the parameter used in order to calculate each main earth pressure and each main earth pressure. It is an output screen of Example 2, (a) summarizes the data regarding the main earth pressure which acts on the L surface when the basic main earth pressure becomes the maximum and the basic main earth pressure becomes the maximum. Yes, (b) are those showed safety evaluation results of retaining wall, a graph (c) showed the relationship between the basic main働土pressure P _a and the sliding surface. It is an input screen of Example 3, and is an input screen of the material information of a retaining wall, the soil information of a retaining wall back surface, and the information of a support ground. It is an output screen in 1 surface linear sliding mode of Example 3, and is a calculation result of each main earth pressure. It is the output screen in the 1-plane linear sliding mode of Example 3, and it is the figure which put together the parameter used in order to calculate each main earth pressure and each main earth pressure. It is an output screen in the 1-plane linear sliding mode of Example 3, and (a) is the main earth pressure acting on the L surface when the basic main earth pressure becomes maximum and the basic main earth pressure becomes maximum. it is also the data summarized related, (b) are those showed safety evaluation results of retaining wall, a graph (c) showed the relationship between the basic main働土pressure P _a and the sliding surface.

Hereinafter, embodiments of a retaining wall safety evaluation method, a retaining wall safety evaluation program, and a retaining wall safety evaluation system according to the present invention will be described with reference to the drawings. In addition, the same code | symbol is attached | subjected about the element which is the same or it corresponds in each figure and each formula, and the overlapping description is abbreviate | omitted.
In the present embodiment, the present invention is applied to a retaining wall safety evaluation system (retaining wall safety evaluation apparatus) configured in a personal computer or the like equipped with a retaining wall safety evaluation application program. The retaining wall safety evaluation system according to the present embodiment evaluates the retaining wall safety against a newly installed retaining wall or an existing retaining wall.

In FIG. 1, the ground surface on the back side of the retaining wall is indicated by reference numeral GL ₁ , the ground surface on the front side of the retaining wall is indicated by reference numeral GL ₂ , and the retaining wall is indicated by reference numeral RW.

The retaining wall safety evaluation system according to the present embodiment will be described in detail with reference to FIGS.
The safety evaluation system (retaining wall safety evaluation device) 1 can be used quickly and accurately according to the shape of the ground surface on the back of the retaining wall, the soil condition on the back of the retaining wall, and the action state of the load. Calculate the earth pressure acting on the wall and evaluate the safety of the retaining wall.
The safety evaluation system 1 is configured by a computer and includes an input unit 2, a storage unit 3, a calculation unit 4, an evaluation unit 5, and a display unit 6. In the present embodiment, the input unit 2 corresponds to the acquisition unit described in the claims, the calculation unit 4 and the evaluation unit 5 correspond to the calculation unit and the evaluation unit described in the claims, and the display unit 6 Corresponds to the display means described in the claims.

The input unit 2 includes an input device such as a mouse keyboard of a computer as an input unit and a computer display for displaying an input screen so that the user can input various data related to the retaining wall.
As input data, retaining wall shape information (for example, retaining wall height and width dimension information, etc.), retaining wall material information (for example, retaining wall unit volume weight γ _C , wall surface friction on the back surface of retaining wall) Angle δ, concrete strength, allowable cross-sectional force, amount of necessary reinforcing bars, etc.), soil information on the back of retaining wall (eg, back soil unit volume weight γ _S , internal friction angle φ, adhesive force c, etc.), information on supporting ground (eg, , Friction coefficient μ between the retaining wall bottom surface and the supporting ground, allowable bearing strength qa, etc., topographic information on the back surface of the retaining wall, and load information acting on the topography on the back surface of the retaining wall (for example, topographic dimension information, ground surface on the back surface of the retaining wall, or Horizontal force and vertical force acting on the retaining wall) and other load information (for example, horizontal seismic intensity k _V , horizontal seismic intensity k _H , load acting directly on the retaining wall) and the like.
Data to be input (for example, soil information on the back of the retaining wall) is input from the input unit 2 using an input device such as a mouse keyboard. For example, viscous soil, sandy soil, gravelly soil Extracting (selecting) a value stored in advance in the back surface degree data table stored in the storage unit 3 corresponding to the value of the soil constant of the back soil, as in the form of selecting from the pull-down menu as the value of the designation such as The structure to do may be sufficient.

The storage unit 3 is configured in a part of the memory of the computer in order to store various data relating to the retaining wall necessary for evaluation and data input from the input unit 2. The data stored in advance in the storage unit 3 includes, for example, concrete table data (for example, the unit volume weight γ _{C of} the retaining wall, the wall friction angle δ on the rear surface of the retaining wall, the concrete strength, the allowable cross-sectional force, the amount of necessary reinforcing bars). , Table data on the back soil (for example, soil quality of the back soil (for example, clay soil, sandy soil, gravel soil), back soil unit volume weight γ _S , internal friction angle φ, adhesive force c), support ground table There are data (for example, friction coefficient μ between the retaining wall bottom and supporting ground, allowable bearing capacity qa), and table data of seismic force (for example, horizontal seismic intensity k _V , horizontal seismic intensity k _H ).

  The calculation unit 4 is configured by a CPU of a computer executing calculation processing according to a command from an application program for retaining wall safety evaluation. According to the input data at the input unit 2, the earth pressure received by the retaining wall from the rear surface of the retaining wall and the angle of the sliding surface are calculated.

  The evaluation unit 5 is configured by the CPU of the computer executing arithmetic processing according to a command from an application program for safety evaluation of the retaining wall. In accordance with the determination result in the evaluation unit 5, the load and moment force generated in the retaining wall are calculated using the calculation result in the calculation unit 4. Further, the evaluation unit 5 evaluates the safety of the retaining wall from the load and moment force generated on the retaining wall.

The display unit 6 is configured by a display such as a computer in order to display the calculation result of the calculation unit 4 and the evaluation result of the evaluation unit 5.

Next, the flow of operations by the safety evaluation application program in the retaining wall safety evaluation system 1 will be described with reference to the flowchart of FIG.
In S1, the person performing the evaluation inputs the shape information of the retaining wall using an input device such as a mouse keyboard while looking at the input screen displayed on the display (for example, the input screen of FIG. 12A). While viewing the input screen displayed on the display (for example, the input screen of FIG. 13), input the material information of the retaining wall, the soil information on the back of the retaining wall, and the information of the supporting ground using an input device such as a mouse keyboard. While viewing the input screen displayed on the display (for example, the input screen of FIG. 15), input the terrain information on the back of the retaining wall and the load information acting on the terrain on the back of the retaining wall using an input device such as a mouse keyboard. While viewing the input screen displayed on the display (for example, the input screen of FIG. 16), other load information is input. The input data is received by the input unit 2 and is used for retaining wall shape information, retaining wall material information, soil texture information on the back of the retaining wall, support ground information, topographic information on the back of the retaining wall, and topography on the back of the retaining wall. The acting load information and other load information are stored in the storage unit 3.
In S2, the calculation unit 4 of the safety evaluation system 1 calculates the basic conditions described later according to the stored (input) data in S1.
In S3, the calculation unit 4 of the safety evaluation system 1 executes the calculation in the later-described two-plane linear sliding mode based on the storage (input) data in S1 and the calculation result in S2.
In S4, the calculation unit 4 of the safety evaluation system 1 determines the slip type based on the storage (input) data in S1 and the calculation results in S2 and S3. In S4, when the slip form is “two-plane straight slip”, the process proceeds to the process of the arrow direction of YES, and when the slip form is “one-plane straight slip", the process of the NO arrow direction is performed. Proceed with
In S5, the calculation unit 4 of the safety evaluation system 1 uses the stored (input) data in S1 and the calculation result in S2 to perform calculation in the single-plane linear sliding mode described later.
In S6, the operation unit 4 of the safety evaluation system 1 calculates the earth pressure acting on the L surface (for example, the main earth pressure P _aY acting on the L surface) described later based on the operation result in S3 or S5. Is done.
In S7, the evaluation unit 5 of the safety evaluation system 1 calculates the vertical load, horizontal load, resistance moment and tipping moment acting on the retaining wall according to the storage (input) data in S1 and the calculation result in S6. To do.
In S8, the evaluation unit 5 of the safety evaluation system 1 evaluates the safety of the retaining wall using the vertical load, horizontal load, resistance moment, and tipping moment calculated in S7.
In S9, on the display unit 6 of the safety evaluation system 1, the storage (input) data of S1, the calculation results of S2, S3, S5, and S6, the determination result of S4, and the evaluation results of S7 and S8 (for example, FIG. 21). Output screen) on the display. Further, based on the calculation result, the value relating to the earth pressure is graphed (for example, FIG. 22) and displayed on the display.

  Although not shown in the flowchart of FIG. 3, the slip mode determination in S4 is based on the determination based on the retaining wall structure type described later and the determination based on the slip type determination formula described later. It is also possible to adopt a configuration in which any one of the “one-plane straight slip” and “two-plane straight slip” slip modes can be selected. In the case where the slip mode can be selected in the input unit 2, when “one-side straight slip” is selected in the input unit 2, the process of S 3 and S 4 is omitted after the process of S 2 and the process proceeds to S 5. When “two-plane straight slip” is selected in the input unit 2, the process of S4 and S5 is omitted after the process of S3, and the process proceeds to S6.

Before specifically explaining the retaining wall safety evaluation system according to the present embodiment,
Explain the technical terms used.
The cantilever type retaining wall is a retaining wall made of reinforced concrete composed of a ridge wall RW _a and a bottom slab (heel plate) RW _b as shown in FIG. 1, and an inverted T type retaining wall depending on the position of the ridge wall RW _a . It is a structure called an L-shaped retaining wall or an inverted L-shaped retaining wall.
In the case of extreme equilibrium, a slip surface is assumed on the back of the retaining wall, the block of soil blocks separated by the slip surface is regarded as a rigid body, the soil mass and the load acting on the soil mass weight balance, and the soil block does not slip Indicates the limit state.
The L plane is the left slip plane of the two slip planes shown in FIG. 4 and refers to a slip plane generated on the retaining wall side during ultimate equilibrium.
The R plane is the right slip plane of the two slip planes shown in FIG. 4 and refers to a slip plane that is generated on the side opposite to the retaining wall side during ultimate equilibrium.
The virtual back surface is an apparent surface (line) that is created when a line is drawn in the vertical direction from the slip surface base point SP to the ground surface as described later. In the current simple calculation method for the L-shaped retaining wall, The safety of the retaining wall is evaluated by applying earth pressure to the surface.
The “one-plane linear slip” refers to a slip form in which the L plane occurs along the boundary between the soil and the structure on the back side of the retaining wall, and the R plane occurs in the ground.
“Two-plane linear slip” refers to a slip mode in which the L plane and the R plane occur in the ground.
The one-plane linear slip mode is an operation format related to “one-plane linear slip”, and the calculation is performed using the formulas shown in Equations 44 and 45. In addition, the conventional simple calculation method of the cantilever type retaining wall in which the virtual back surface is set and the maximum earth pressure is calculated only by the R surface can be calculated in the single surface linear sliding mode.
The 2-sided linear sliding mode is a calculation format related to “2-sided linear sliding”, and the calculation is performed using the calculation formulas shown in Equations 3 to 38. For example, in the short cantilever type retaining wall of the heel plate RW _b , the L surface may not intersect the ground surface GL ₁ but may intersect the back side of the wall RW _a. during safety assessment of wall, it is given to the safety evaluation system horizontal force and the vertical force sliding clods receives from vertical wall RW _a as input data, is calculated as dihedral straight shear mode.

Before specifically explaining the retaining wall safety evaluation system according to the present embodiment,
With reference to FIGS. 4 to 8, a method for deriving each calculation formula regarding “two-sided linear slip” will be described.
It should be noted that in the determination formulas for the 2-plane linear sliding mode, the 1-plane linear sliding mode, and the slip form described later, the horizontal force T acting on the sliding mass is taken into account, but the horizontal force T acting on the sliding mass is taken into consideration. In the case of not _performing the calculation, t _0L = 0, t _0R = 0, and t _0A = 0 (T = 0) are substituted into those equations.

First, with reference to FIG. 4 and FIG. 5, the sliding soil mass weight at the time of the extreme equilibrium and the load acting on the sliding soil mass will be described.
When the shape of the ground surface GL ₁ on the back surface of the retaining wall has a shape as shown in FIG. 4, when the “two-sided linear slip” occurs, how to determine the weight of the sliding mud and the load acting on the sliding mud , area _{a L} as shown in FIG. 5, the area _{a M,} determined by dividing the portion of the area _{a R.}
Area A _L represents the area of the portion of the triangle surrounded by omega _0L is the boundary angle omega _L and part of the area A _L is the angle L surface, the area A _R is angle omega _R the area of the L surface represents the area of the portion of the triangle surrounded boundary angle portion of a _R in omega _0R, area a _M represents the area of the L rest.
Total W _L vertical force acting on the sliding soil mass parts of the sliding clod weight and area A _L of the portion of the area A _L becomes Equation (1).
Here, the unit volume weight of the soil behind the retaining wall is γ _S.
Further, the angle of the L face omega _{L, (a} positive slope soaring) area A _L of the portion of the boundary angle a is omega _0L, the area A _L portions inclination angle beta _L of the ground surface of, The friction angle (internal friction angle) on the L plane is φ _L , and the L plane side ground surface orthogonal height, which is the length of the orthogonal line from the intersection of the L plane and the R plane to the ground surface of the area A _L , is H _L ′. the vertical, etc. distributed load acting on the portion of the area a _L and q _VL.
Further, horizontal force T _L acts on the sliding soil mass parts of the area A _L becomes Equation (2).
Here, the horizontal direction, etc. distributed load acting on the portion of the area A _L and q _HL.

The total W _R vertical force acting on the sliding soil mass parts of the sliding clod weight and area A _R of the portion of the area A _R is the formula (3).
Here, the angle of the R-plane omega _{R, (the} slope of soaring positive) _0R boundary angle portion of the area A _{R omega,} the inclination angle beta _R of the ground surface of the portion of the area A _R, R the friction angle (angle of internal friction) of phi _R, L side and R side ground surface perpendicular height indicating the length of the orthogonal line from the intersection of the R-plane to the ground surface of the portion of the area a _R of the plane H _R ', _Let q _VR be the vertical uniform load acting on the area AR.
Further, horizontal force T _R acting on the sliding soil mass parts of the area A _R is the formula (4).
Here, the horizontal direction, etc. distributed load acting on the portion of the area A _R and q _HR.

The total W _M vertical force acting on the sliding soil mass parts of the sliding clod weight and area A _M of the portion of the area A _M is the formula (5).
Here, the aggregate value of the vertical force acting on the portion of the area A _M and .SIGMA.P _V.
Further, the horizontal force T _M acting on the sliding soil block of the area A _M is expressed by Equation (6).
Here, the aggregate value of the horizontal force acting on the portion of the area A _M and .SIGMA.P _H.

Therefore, the total weight W of the sliding soil mass and the vertical force acting on the sliding soil mass at the extreme equilibrium is expressed by Equation (7), and the horizontal force T acting on the sliding soil mass is expressed by Equation (8).

Next, an effective weight W ′ (see below) is obtained from FIG.
Here, the target retaining wall, the ground surface behind the retaining wall, and the entire support ground are tilted and rotated so that the direction of the resultant inertial force, which is the combination of gravity and the inertial force of the seismic force, becomes vertical. This coordinate system is called a rotational coordinate system. Moreover, the figure which showed the balance of the force containing a sliding clump weight is called a connection figure.
FIG. 6 is an interaction diagram at the time of extreme equilibrium in the rotating coordinate system.
Here, if Formula (9) and Formula (10) are utilized, Formula (11)-Formula (13) will be materialized from FIG.
Here, let c be the adhesive force per unit area of the soil on the back of the retaining wall.
Further, the adhesive force on the R plane is C _R , the adhesive force on the L plane is C _L , and the resultant force of the vertical stress and the frictional force on the L plane is R _L. Here, among _RL , the effective force remaining after the offsetting of the force with the adhesive force is referred to as _RL ′ and is referred to as an effective reaction force. In addition, the seismic composite angle is θ, the horizontal seismic intensity is k _H , and the vertical seismic intensity is k _V. Further, _'the active component of the force remaining after offsetting the force of adhesion of the ÷ cosθ W' W × k _V and referred to as effective weight.

Here, if Expressions (1) to (8) and Expressions (13) to (30) are used, Expression (12) becomes Expression (31).

Here, if Expression (32) and Expression (33) are used, Expression (31) becomes Expression (34).

Next, the horizontal component of the main earth pressure in the rotating coordinate system is obtained. Here, the horizontal component of the main働土pressure at the rotating coordinate system and P _a, referred to as basic main働土pressure. For equal basic main働土pressure P _a is the horizontal component of the effective reaction force R _{L ',} equation (35) holds.

Here, if Expression (11) and Expression (36) are used, Expression (35) becomes Expression (37) or Expression (38).

Conditions for obtaining the basic main働土pressure P _a is maximum in "dihedral linear sliding" when x and y are simultaneously satisfy ∂P _a ÷ ∂x = 0 and ∂P _a ÷ ∂y = 0, or, x Is when only satisfying an expression of ∂P _a ÷ ∂x = 0, or when y satisfies only an expression of ∂P _a ÷ ∂y = 0. However, conditions for basic main働土pressure P _a to obtain the maximum value is not a condition that basic main働土pressure P _a to obtain the maximum value.
The x in the case of satisfying ∂P _a ÷ ∂x = 0 and ∂P _a ÷ ∂y = 0 at the same time called extreme points _{X R,} the ∂P _a ÷ ∂x = 0 and ∂P _a ÷ ∂y = 0 When y is simultaneously satisfied, y is referred to as an extreme point Y _L , and the basic main earth pressure obtained from the extreme point X _R or the extreme point Y _L is referred to as an extreme main earth pressure Pa _0, and ∂P _a ÷ ＝ x = 0 referred to x when satisfying only L plane fixed extreme points x _R, referred to basic main働土pressure obtained from L plane fixed extreme point x _R and L side fixed extreme main働土pressure _P a0L, ∂P _a the y when ÷ ∂y = 0 satisfies only referred to as R-plane fixed extreme points y _L, the basic main働土pressure obtained from the R-plane fixed extreme point y _L and R face fixed extreme main働土pressure P _A0R Call it. Further, the extreme main earth pressure P _a0 , the L-plane fixed extreme _earth pressure P _a0L , the R-plane fixed extreme _earth pressure P _a0R , and the double-side fixed main _earth pressure P _a0LR described later are collectively referred to as each main _earth pressure. Called. The extreme point X _R , the extreme point Y _L , the L plane fixed extreme point x _R , and the R plane fixed extreme point y _L are collectively referred to as each extreme point.
Incidentally, the basic main働土pressure P _a is included each major働土pressure.

The R-plane fixed extreme points y _L, when seeking basic main働土pressure P _a fixed angle omega _R the R-plane to the boundary angle omega _0R, points basic main働土pressure P _a is the maximum say, the L face fixed extreme points x _R, when seeking basic main働土pressure P _a fixed angle omega _L of L surface to the boundary angle omega _0L, the basic main働土pressure P _a is the maximum Say point.

Then, obtained from ∂P _a ÷ ∂x = 0 to L side fixed extreme point _{x R.}
Expression (38) becomes Expression (40) when Expression (39) is used to transform into a function of x.

Furthermore, if Formula (41)-Formula (46) is utilized, Formula (40) will become Formula (47).

To determine the L plane fixed extreme points _{x R,} since the may be obtained the x contained in the formula _{(47) (cotφ θβR -x)} × (x + cotξ R) ÷ (x + cotμ R) becomes maximal,
if _{f (x) = (cotφ θβR} -x) × (x + cotξ R) ÷ (x + cotμ R), ∂f (x) ÷ ∂x becomes equation (48).

Therefore, if equation (48) is solved for x from ∂f (x) ÷ ∂x = 0, the solution of equation (49) is obtained.

Here, if the expression (50) and the expression (51) are used to delete the addition / subtraction code “±” of the expression (49) and x is returned to _cotωβR , the expression (49) becomes the expression (52). .

Then, obtained from ∂P _a ÷ ∂y = 0 R-plane fixed extreme point _{y L.}
First, equation (37) is transformed into equation (53) by adding T cos θ to both sides of equation (37) and transforming it into a function of y.

Here, if Expressions (54) to (58) are used, Expression (53) becomes Expression (59).

Furthermore, if Expression (60) is used, Expression (59) becomes Expression (61).

To determine the R plane fixed extreme points _{y L,} it may be determined a y _{where P a} of formula (61) is maximized. Similarly to the partial differential solution of equation (48), P _a is partially differentiated with respect to y, and if equation (62) is used, the solution of equation (63) is obtained.

Therefore, if the equation (64) is used and the equation (63) is solved for y from ∂P _a ÷ ∂y = 0, the solution of the equation (65) is obtained.

Here, using equation (66) and (67) to remove the subtraction sign "±" in equation (65), by returning the y in Cotomega _.beta.L, equation (65) becomes equation (68) .

In addition, here, using Equation (69), Equation (55), and Equation (70) and arranging k, Equation (64) becomes Equation (71).

To determine the extreme main働土pressure _{P a0} is, x that satisfies the equation (52) Equation (68) at the same time, it finds the y. Therefore, x and y are converged to a true solution and calculated using an algorithm of the iterative method of the present invention described later.

Next, a calculation formula for the R-plane fixed extreme _earth pressure _Pa0R is derived.
First, transform a included in the formula _{(61) (cotφ θβL + cotμ} L) × (y + cotξ L) ÷ (y + cotμ L) and using the equation (64) and (65) Formula (72).

Here, since Expression (60) becomes Expression (73), Expression (72) becomes Expression (74) when Expression (28), Expression (55), and Expression (73) are used.

Therefore, y = a cotω βL = _{y L,} by substituting the equation (74) into equation (61), calculation of the R-plane fixed extreme main働土pressure _{P A0R} can be derived in equation (75).

Next, a formula for calculating the L-plane fixed extreme _earth pressure _Pa0L is derived.
First, if (cot _φθβR + cot μ _R ) × (x + cot ξ _R ) / (x + cot μ _R ) included in the equation (47) is modified similarly to the equation (72), the equation (76) is obtained.

Therefore, x = a cotω βR = _{x R,} by substituting the equation (76) into equation (47), calculation of the L face fixed extreme main働土pressure _{P A0L} can be derived in equation (77).

Next, the extreme value main earth pressure _Pa0 will be described.
The x obtained by the algorithm of the present invention as extreme points X _R, the y obtained by the algorithm of the present invention the extreme point Y _{L. Here, x = cotω βR = x R} = X R, since it is _{y = cotω βL = y L =} Y L, formula extreme main働土pressure _{P a0,} from equation (75) and (77) Equations (78) and (79) are obtained.

Next, the double-sided fixed primary _earth pressure _Pa0LR will be described.
Double-sided fixed _earth pressure P _a0LR is a boundary angle (ω _0L or ω _0R ) or an arbitrary angle (ω _L or ω) at the change point of the topography on the back surface of the retaining wall or the change point of the load loaded on the ground surface on the back surface of the retaining wall. _R ) is a basic main earth pressure obtained by substituting ω _L or ω _R in formula (40) or formula (59).
Therefore, the formula for calculating the double-sided fixed main _earth pressure _Pa0LR is formula (80) or formula (81).

Next, the maximum value _PaMAX of the basic main _earth pressure will be described.
The maximum value _PaMAX of the basic main _earth pressure is expressed by the formula (82).

Next, the main _earth pressure _PaY acting on the L surface will be described.
The use of tilt delta _L by L surface adhesion as shown in FIG. 7, equation (83) holds.

The acting direction of the main _earth pressure _PaY acting on the L plane in the rotating coordinate system is inclined clockwise by _{ΔPaY with} respect to the vertical direction of the rotating coordinate system as shown in FIG. Δ _PaY is _referred to as the _PaY rotational coordinate system direction angle.
Further, the inclination angle delta _L by L surface adhesion becomes equation (84). Further, if Expression (84) is used and Expression (83) is modified, Expression (85) is obtained. Therefore, the main _earth pressure _PaY acting on the L surface is expressed by Expression (86).

In addition, if the rotational coordinate system is returned to the actual coordinate system with reference to FIG. 8, the horizontal component P _aYH (the horizontal level of the main _earth pressure acting on the L plane) in the actual coordinate system of the main _earth pressure acting on the L plane will be described. referred to as directional component P _AYH.) is referred to as a vertical component P _AYV main働土pressure acting on the vertical component _P aYV _(L plane in and the actual coordinate system of the main働土pressure acting on L side.) is From FIG. 8, equations (87) and (88) are obtained.

Next, before specifically explaining the retaining wall safety evaluation system according to the embodiment,
The iterative algorithm of the present invention will be described.
The algorithm of iterative method of the present invention, basic main働土pressure _{P a} is the maximum value _{ω βL (ω βL = arccot (} Y L)) and _{ω βR (ω βR = arccot (} X R)) is obtained.
The iterative algorithm of the present invention consists of stages 1 to 4.
In phase 1, define any number in omega _.beta.L or omega _{[beta] R} as an initial value of the iterative method.
In step 2, omega _.beta.L the initial value of the iterative method or the formula from omega _.beta.L obtained from step 3 (41), equation (28), equation (29), equation (30), equation (162) is calculated, Using the obtained μ _R , t _1L , t _1R , t _1A and ξ _R , the _values are substituted into the equations (52) and (164) to obtain ω _βR .
In stage 3, the initial value ω _βR of the iterative method or ω _βR obtained in stage 2 is _used to formula (42), formula (55), formula (56), formula (57), formula (71), formula (161). ) Is calculated, and the obtained μ _L , t _2L , t _2R , t _2A , k, and ξ _L are substituted into the equations (68) and (163) to obtain ω _βL .
In step _{4, μ L, μ R,} t 1L, t 1R, t 1A, t 2L, t 2R, t 2A, k, ξ L, ξ R, y L, x R, either omega _.beta.L and omega _{[beta] R} Steps 2 and 3 are alternately repeated until the value of becomes a predetermined accuracy.

Next, before specifically explaining the retaining wall safety evaluation system according to the embodiment,
With reference to FIGS. 9 to 11, a method for determining a slip mode and a method for deriving the determination formula will be described.
First, the flow of the slip type determination method will be described with reference to the flowchart of FIG.
In F1, the slip form is determined according to the structural form of the retaining wall. For example, in the case of a retaining wall whose back surface is inclined at a constant gradient, such as a gravity retaining wall, “one-sided linear slip” occurs, but “two-sided linear slip” occurs under certain conditions described later. May occur. Further, in the case of a cantilever retaining wall having a heel plate such as an L-shaped retaining wall or an inverted T-shaped retaining wall, “two-sided linear sliding” occurs. Therefore, when the retaining wall structural type is determined to be a cantilever retaining wall, the slip mode is determined to be “two-sided linear sliding”, and the process proceeds to the arrow direction of YES, and the retaining wall structural type If it is not determined as a cantilever retaining wall, the process proceeds to a process indicated by an arrow NO.
In F1, the data table of the slip form according to the structure type of the retaining wall is set in advance, the structure type of the retaining wall is determined from the input shape information of the retaining wall, and the slip according to the structure type of the retaining wall is determined. Although the configuration is such that the form is extracted from the data table, it is possible to adopt a configuration in which an arbitrary slip form (“1-plane straight slip” or “2-plane straight slide”) can be selected.
In F2, it determines with the determination formula of a slip form mentioned later. In F2, although it is set as the structure determined by the judgment formula of a slip form mentioned later, it is good also as a structure which can select arbitrary slip forms ("1-surface straight slip""2-surface straight slip"). In F2, if the slip type determination formula described later is satisfied or if the “two-sided linear slip” slip type is selected, the process proceeds to the processing in the arrow direction of YES, and the slip type determination formula described later is satisfied. If not, or if the slip form of “one-plane linear slip” is selected, the process proceeds to the process in the direction of the arrow of NO.

Next, a method for deriving the slip type determination formula will be described.
Even in the back surface of the trapezoidal structure having the inclination gradient α on the back surface of the retaining wall as shown in FIG. 10A, the L surface does not occur along the back surface of the retaining wall but occurs in the ground. There is a case.
Since L surface generated in the surface resistance is small slip, when the sliding resistance force f _S in the ground becomes less slip resistance force f _C in a retaining wall back, L plane is generated in the ground. Therefore, in order for the slip mode to be “two-plane linear slip”, it is necessary to satisfy Expression (89).
Further, the slip resistance force fc on the back surface of the retaining wall and the slip resistance force fs in the ground satisfy Expression (90) and Expression (91). Here, Rc is the reaction force from the retaining wall, R _L is the resultant of the normal stress and the frictional force in the L plane, C _L is the adhesive strength in the L plane, [delta] is the wall friction angle of the retaining wall back, phi is back The internal friction angle of the soil.

FIG. 10B is a force diagram relating to the portion A shown in FIG. 10A in a limit state where “one-plane linear slip” and “two-plane linear slip” occur simultaneously.
Equation (92) is established from FIG.
Here, ω _L is the angle of the L surface, α is the inclination angle of the back surface of the retaining wall, β _L is the inclination angle of the ground surface on the L surface side, θ is the earthquake synthesis angle of equation (9), and ω _βL is ω _L + β represents the calculated value of _L.
Further, when formula (92) is arranged, formula (93) is obtained.

Moreover, Formula (94) and Formula (95) are formed from FIG.
Here, delta _L represents a tilt due to adhesion of formula (84).

Therefore, Expression (90) becomes Expression (96) from Expression (93) and Expression (94), and Expression (91) becomes Expression (97) from Expression (95).

Therefore, Formula (89) becomes Formula (98) or Formula (99) from Formula (96) and Formula (97). At this time, it is necessary to satisfy Expression (100) as a necessary condition.

  That is, the determination of the slip mode is executed by Expression (89) or Expression 43. Equation (89) and Equation 43 are referred to as slip type determination equations. That is, when the slip type determination formula is not satisfied, it is determined as “one-plane linear slip”, and when the slip type determination formula is satisfied, it is determined as “two-plane straight slip”.

Next, before specifically explaining the retaining wall safety evaluation system according to the embodiment,
A method of deriving each calculation formula regarding “one-plane linear slip” will be described.
“One-sided linear slip” is a slip form in which the L-plane is fixed to a surface along the back surface of the retaining wall, so that the main _earth pressure P _aY acting on the L-plane in the one-sided linear slip mode is maximized. The L-plane fixed extreme value P _{a0L in} the one-plane linear sliding mode and the L-plane fixed extreme point x _R in the one-plane linear sliding mode at that time may be obtained.
Also, the derivation method of each calculation formula regarding “one-plane linear slip” is to convert ω _L to π / 2-α from each calculation formula related to “two-plane linear slip” and convert ω _0L to π / 2-α. Then, φ _L may be converted to δ. Note that in the slip mode of “one-plane linear slip”, the L plane angle ω _L = the boundary angle ω _0L of the L plane, and as can be seen from the fact that the solution of W _{L in} equation (1) is zero, FIG. The 5 A _L portion does not exist, and β _L does not exist accordingly. Therefore, each calculation expression for "1 plane linear sliding" is provided from becoming independent of the beta _L of formula, beta is no problem even if converted to an arbitrary value of _L a (beta any value to _L Therefore, β _L is converted to α, and the conversion to each calculation formula relating to “one-plane linear slip” is simplified.
These transformations, omega _.beta.L is π / 2-α + α = π / 2 becomes, y is cot (π / 2) = 0, and the next phi _ShitabetaL is δ + θ + α, μ _R is a _π / _2-φ θβL -φ θβR Become.

Therefore, if converting a formula on "dihedral linear sliding" by the methods of conversion, the constant vertical load W _A in one plane linear sliding mode is converted from the equation (24) into equation (101), one side linear The constant horizontal load t _0A in the sliding mode is converted from Expression (27) to Expression (102), and T cos θ in the one-plane linear sliding mode is converted from Expression (62) to Expression (103). The constant horizontal load t _1R in the sliding mode is converted from Expression (29) to Expression (104), and the constant horizontal load t _1A in the one-plane linear sliding mode is converted from Expression (30) to Expression (105). The cot ξ _R in the one-plane linear sliding mode is converted from the equation (39) to the equation (106), and the L-plane fixed extreme point x _R in the one-surface linear sliding mode is calculated from the equations (52) to (107 ), And in one-plane linear sliding mode The L-plane fixed extreme _earth pressure P _a0L of Equation (108) is the same as the equation (77), and the double-side fixed main _earth pressure P _a0LR in the one-surface linear sliding mode is _calculated from the equation (80) to the equation ( 109) and the maximum value _{Pa MAX} of the basic main _earth pressure in the one-plane linear sliding mode is converted from the equation (82) to the equation (110), and the _{Pa Y} rotational coordinate system direction in the one-surface linear sliding mode is converted. angle delta _PAY, since it becomes _{π / 2-φ θβL -Δ L} , equation (85) is converted to equation (111), the main働土pressure _{P aY} acting on L surface in one plane linear sliding mode The horizontal component P _aYH of the main _earth pressure acting on the L plane in the one-plane linear sliding mode is converted from the expression (86) to the expression (112), and is converted from the expression (87) to the expression (113). vertical component P _a main働土pressure acting on L surface in one plane linear shear mode _V is converted from equation (88) into equation (114).

Next, before specifically explaining the retaining wall safety evaluation system according to the present embodiment,
Describe how to evaluate the safety of retaining walls.
The retaining wall safety evaluation method is determined according to the retaining wall safety evaluation method according to various guidelines (such as earthwork guidelines and residential land development regulations). This evaluation method is the same as the conventional safety evaluation method for retaining walls. This can be confirmed by a known calculation.

Example 1 will be described with reference to FIGS.
In the first embodiment, a calculation example in the case where the shape of the retaining wall is a cantilever structure as shown in FIG. 12B will be described.
Each calculation in the embodiment is a real number calculation without rounding with a certain number of significant digits. Also, in the description of the embodiment, i is added to the end of the symbol as an expression indicating the calculated value in the section number i. For example, ΔX in the section number i is expressed as ΔX _i, and ΔX when the section number i = 1 is expressed as ΔX ₁ for explanation.

** (Acquisition means) **
An input screen according to the first embodiment will be described.
First, on the input screen for the retaining wall shape information, the retaining wall shape information is input to the computer using an input device such as a mouse keyboard. The shape of the retaining wall is an arbitrary shape, and each change point of the retaining wall is input as a coordinate value. Alternatively, as shown in FIG. 12A, on the input screen for the cross-sectional dimensions of the retaining wall, the horizontal dimensions (H1, H2, H3, H4, H5) and the vertical dimensions (B1, B2, B3). , B4, B5, B6, B7).
In the first embodiment, the retaining wall shape information shown in FIG. Therefore, the shape of the retaining wall of Example 1 is a cantilever L-shape as shown in FIG. For the retaining wall height H, H = 4.00 (m) is displayed on the screen of the display as the calculation result of H1 + H2 + H3. As for the bottom surface width B, B = 2.00 (m) is displayed on the display screen as a calculation result of B1 + B2 + B3 + B4 + B5. For the X coordinate X _SP of the slip surface base point, X _SP = B1 + B3 + B5 = 2.00 (m) is displayed on the display screen, and for the Y coordinate Y _SP of the slip surface base point SP, Y _SP = 0.00 (M) is displayed on the screen of the display.
The X coordinate X _SP of the slip surface base point and the Y coordinate Y _SP of the slip surface base point SP represent relative coordinate values from the base point P shown in FIG.

Next, in the input screen for the retaining wall material information, the soil information on the back surface of the retaining wall, and the information on the supporting ground, the material information on the retaining wall (for example, the unit volume weight γ _{C of} the retaining wall, the wall friction angle δ on the back surface of the retaining wall) ) And soil information on the back of the retaining wall (for example, back soil unit volume weight γ _S , internal friction angle φ, adhesive force c) and supporting ground information (for example, friction coefficient μ between retaining wall bottom and supporting ground, allowable bearing capacity) q _a ) is input using an input device such as a mouse keyboard.
In Example 1, the material information of the retaining wall, the soil information on the back surface of the retaining wall, and the information on the supporting ground shown in FIG. 13 are input.

The data to be input (for example, the unit volume weight γ _{C of} the retaining wall, the wall friction angle δ of the rear surface of the retaining wall, the back soil unit volume weight γ _S , the internal friction angle φ, the adhesive force c, the horizontal seismic intensity k _V , and the horizontal seismic intensity. k _H , friction coefficient μ of retaining wall bottom surface and supporting ground μ, allowable bearing force q _a ) are preset in default values and can be selected from pull-down menu candidates, and the computer refers to the data table, It is also possible to input.

Next, on the input screen for the terrain information on the back of the retaining wall, the load information acting on the terrain on the back of the retaining wall, and other load information, In addition, for each change point of the load information acting on the terrain on the back surface of the retaining wall, in order from the section number i = 1, the horizontal distance ΔX _i and the vertical distance for each change point of the terrain information from the top of the retaining wall to the back surface of the retaining wall. The value of the additional distance from the previous point of ΔY _i is input using an input device such as a mouse keyboard, and load information that acts on the terrain on the back surface of the retaining wall for each input terrain information (for example, vertical equally distributed load) q _Vi , horizontal _equally distributed load q _Hi , vertical concentrated load P _Vi , and horizontal concentrated load P _Hi ) are input using an input device such as a mouse keyboard.
The topographic shape information on the back surface of the retaining wall may be configured such that the relative coordinate value X _i and the relative coordinate value Y _i can be input.

Note that the horizontal distance ΔX _i and the vertical distance ΔY _i in the section number i to which the concentrated load is input are set to 0 when the CPU of the computer executes arithmetic processing according to a command from the application program for retaining wall safety evaluation. The value of is entered.
Further, the angle of the sliding surface obtained by the calculation as shown in FIG. 14, one time fit into consideration the interval (omega between _0i-1 of omega _0i) within basic main働土pressure P _a in the study interval and maximum However, even if the slip surface is within the examination section, as shown by the circle A shown in FIG. 14, a part of the slip surface is removed from the ground surface GL _1. A slip surface that goes out cannot occur physically. Therefore, when the shape of the ground surface GL ₁ as shown in FIG. 14 is exhibited, the CPU of the computer executes a calculation process in accordance with a command of the application program for safety evaluation of the retaining wall, so that a circle B The point of change is set at the intersection of the slip surface indicated by (the slip surface where the slip surface passes all through the ground) and the ground surface GL ₁ , and each calculation in the section where the slip surface does not pass through the ground is Omitted. This process is executed on both the R surface side and the L surface side.

In the first embodiment, the terrain information on the back surface of the retaining wall and the load information acting on the terrain on the back surface of the retaining wall shown in FIG. 15 are input. As for the X coordinate X _GP of the contact point between the retaining wall and the ground surface, as shown in FIG. 15, X _GP = B1 + B2 + B4 = 0.40 (using the values of B1, B2, and B4 in FIG. 12A). m) is displayed on the screen of the display, and for the Y coordinate Y _GP of the contact point between the retaining wall and the ground surface, Y _GP = 4.00 (m) is displayed using the value of H in FIG. Displayed on the screen.
The X coordinate X _GP of the contact point between the retaining wall and the ground surface and the Y coordinate Y _GP of the contact point between the retaining wall and the ground surface represent relative coordinate values from the base point P shown in FIG.
As the X coordinate X _GP of the contact point between the retaining wall and the ground surface and the Y coordinate Y _GP of the contact point between the retaining wall and the ground surface, a coordinate value of an arbitrary point in contact with the retaining wall may be input.

Next, on the input screen for other load information, other load information (for example, horizontal seismic intensity k _V , horizontal seismic intensity k _H , load acting directly on the retaining wall) is input using an input device such as a mouse keyboard.
In Example 1, other load information shown in FIG. 16 is input. As for the vertical load reduction coefficient k _V ′, k _V ′ = 1 is displayed on the display screen as a calculation result of 1-k _V. As for the seismic force composite angle θ, θ = 0.04996 (rad) is displayed on the display screen as a calculation result of arctan (k _H ÷ k _V ′).

* * (Calculation means-Calculation of basic conditions) * *
Subsequently, in order to calculate the earth pressure from the back soil acting on the retaining wall, the basic condition is calculated by a known calculation method based on the input data.
Here, the basic conditions are: relative coordinate value X _i , relative coordinate value Y _i , slope gradient β _i , boundary angle ω _0i , ground surface orthogonal height H _i ′, constant φ _θβLi , constant φ _θβRi , reference vertical load p _0i, reference adhesive force _{c 0Li} the L side, the reference adhesion _{c 0Ri} the R side, the reference horizontal load _{t 0i, W AMi ', W} AEi, ΣP Vi', the constant vertical load _{W Ai ', t AMi',} t _AEi , ΣP _Hi ′, constant horizontal load t _0Ai ′.
Incidentally, the constant vertical load W _{Ai 'and} constant horizontal load t _0Ai' is intended to be pre-calculated in order to calculate the constant vertical load W _A and the constant horizontal load t _0A. Without calculation of constant vertical load W _{Ai 'and} constant horizontal load t _0Ai', directly, directly by the constant vertical load W _A and the constant horizontal load t _0A known calculation method may be configured to computed.
The calculation result of Example 1 is the result shown in FIG.

The relative coordinate value X _i and the relative coordinate value Y _i represent the relative coordinate value from the base point P shown in FIG.
From Equation 46, the relative coordinate value X _i and the relative coordinate value Y _i are calculated.

Formula 47 shows a calculation example of the relative coordinate value X ₃ and the relative coordinate value Y ₃ when i = 3.

Further, the slope slope β _i is calculated from Equation 48.

Formula 49 shows a calculation example of the slope gradient β ₃ at i = 3.

Further, the boundary angle ω _0i is calculated from _Equation 50.

Formula 51 shows a calculation example of the boundary angle ω ₀₃ when i = 3.

Further, the ground surface orthogonal height H _i ′ is calculated from Equation 52.

Formula 53 shows a calculation example of the slope gradient H ₃ ′ at i = 3.

_Further , the constant φ _θβLi and the constant φ _θβRi are calculated from _Equation 54.

The number 55, i = 3 constant at _φ θβL3, showing an example of calculation of constants _φ θβR3.

Further, from _Formula 56, the reference vertical load p _0i , the L-side reference adhesive force c _0Li , the R-side reference adhesive force c _0Ri , and the reference horizontal load t _0i are calculated.

_{Formula 57} shows a calculation example of the reference vertical load p ₀₃ at i = 3, the reference adhesive force c _0L3 on the L surface side, the reference adhesive force c _{0R3 on} the R surface side, and the reference horizontal load t ₀₃ .

Since the constant vertical load W _Ai ′ is calculated, W _AMi ′ is calculated from _Equation 58.
W _AMi ′ represents the total weight of the mass of the mass of A _M ′ shown in FIG. 18 and the total value of the vertical loads due to the vertically distributed load acting on A _M ′ and the earthquake inertia force with respect to the total value. That is, W _AMi 'represents the vertical force in the rotating coordinate system.

Equation 59 shows a calculation example of W _AM3 ′ when i = 3.

In addition, since the constant vertical load W _Ai ′ is calculated, W _AEi is calculated from _Equation 60.
W _AEi represents the total weight of the mass of _AE shown in FIG. 18 and the total value of the vertical forces acting on A _E and the resultant force of the seismic inertia force with respect to the total value. That is, W _AEi represents the vertical force in the rotating coordinate system. Note that ΔX _Ei shown in FIG. 18 is an additional distance in the horizontal direction from the ground surface orthogonal point X coordinate X _Ci to the relative coordinate value X _i−1 , and is an operation value of X _Ci −X _i−1 .

_Formula 61 shows an example of calculating _WAE3 when i = 3.

In addition, since the constant vertical load W _Ai ′ is calculated, ΣP _Vi ′ is calculated from Equation 61.
ΣP _Vi ′ represents the resultant force of the total value of the vertical force acting on the part A _M ′ shown in FIG. 18 and the seismic inertia force with respect to the total value. That is, ΣP _Vi represents the vertical force in the rotating coordinate system.

Formula 63 shows a calculation example of the additional deduction load ΣP _V3 at i = 3.

Further, the constant vertical load W _Ai ′ is calculated from _Equation 64.

Formula 65 shows a calculation example of the constant vertical load W _A3 ′ at i = 3.

In addition, since the constant horizontal load t _0Ai ′ is calculated, t _AMi ′ is calculated from _Equation 66.
t _AMi ′ represents a result of converting a horizontal load due to a horizontally distributed load acting on a portion A _M ′ shown in FIG. 18 into a horizontal component in the rotating coordinate system.

Formula 67 shows a calculation example of t _AM5 ′ when i = 5.

In addition, since the constant horizontal load t _0Ai ′ is calculated, t _AEi is calculated from _Equation 68.
t _AEi represents a result of converting a horizontal load due to a horizontally distributed load acting on a portion _AE shown in FIG. 18 into a horizontal direction component in the rotating coordinate system.

_Formula 69 shows a calculation example of the constant horizontal load t _AE5 at i = 5.

Further, since the constant horizontal load t _0Ai ′ is calculated, ΣP _Hi ′ is calculated from Equation 70.
ΣP _Hi ′ represents a value obtained by converting the total value of the horizontal force acting on the portion A _M ′ shown in FIG. 18 into a horizontal component in the rotating coordinate system.

Number 71 shows an example of calculating the additional net load .SIGMA.P _H5 at i = 5.

Further, the constant horizontal load t _0Ai ′ is calculated from _Equation 72.

_Formula 73 shows a calculation example of the constant horizontal load t _0A5 ′ at i = 5.

* * (Calculation means-Calculation of each main earth pressure and each extreme point by combination with each section) * *
Subsequently, based on the input data and the calculation result of the basic condition, the calculation of each main earth pressure and each extreme point by the combination with each section is executed.
In the calculation, the section number i on the L plane side is set to the section number Li (Li = 1, 2, 3,... N), and the section number i on the R plane side is set to the section number Ri (Ri = 1, 2, 3,. .., N), the constant vertical load W _A , the constant horizontal load t _0A , and the extreme point X are combined by combining the basic condition in the section number Li and the basic condition in the section number Ri, respectively. _R , extreme point Y _L , extreme main earth pressure P _a0 , R plane fixed extreme point y _L , R plane fixed extreme _earth pressure P _a0R , L plane fixed extreme point x _R , L plane fixed extreme value The main _earth pressure P _a0L and the double-side fixed main _earth pressure P _a0LR are calculated. However, the combination is calculated in the range of Li ≦ Ri in order to omit redundant calculation. In the embodiment, description will be made by adding (Li, Ri) to the end of the symbol as an expression of the combination of the section number Li on the L plane side and the section number Ri on the R plane side. For example, _{W W} A (Li, Ri) for _A and to express, in the _{W A} in the case of the section number of the L side Li = 1, the R side section number Ri = _3, W A (1, 3 ) And explain.
The calculation result when Li = 1 in Example 1 is the result shown in FIG.

※※ (calculation means - calculating constants vertical load _{W A} and the constant horizontal load _{t 0A)} ※※
Number 74 constant vertical load _{W A} and the constant horizontal load _{t 0A} is calculated from.
It is a constant vertical load _{W A} represents a solution obtained from the equation (24), a constant horizontal load _{t 0A} represents a solution obtained from equation (27).

Formula 75 shows a calculation example of the constant vertical load W _A (1, 3) and the constant horizontal load t _0A (1, 3) at Li = 1 and Ri = 3.

※※ (calculation means - calculation of the extreme points _{X R} and extreme point _{Y L)} ※※
Next, using the algorithm of iterative method of the invention described above, from equations 1 and _{2 ω βL (ω βL = arccot} (Y L)) and _{ω βR (ω βR = arccot (} X R)) is calculated The
In the embodiment, in order to explain the calculation process, description will be made using Equation 76.

In the embodiment, the initial value of ω _βR = ω _0βRi = ω _0R −β _Ri is given in _Equation 1.
The number 77 shows a calculation example of Li = 1, Ri = 3 in the _ω βL (1,3) and _ω βR (1,3).

In Example 1, the solution of the iterations omega was displayed after the decimal point 5 digits obtained in _βL or the calculation at point omega _{[beta] R} of displaying up to 5 digits obtained, respectively twice the same numerical value at iteration When is obtained, the iterative calculation stops.
Therefore, the result of the iterative calculation, 1.40206 to _{ω βL (1,3) (rad)} , obtain .81811 (rad) in _ω βR (1,3).

The conditional expression of for angle omega _R the angle omega _L and R face of L faces are present in the investigated interval represented by the number 78. When Formula 78 is not satisfied at the same time, a maximum value appears in a combination other than the examination section. Therefore, it is determined that there is no solution in that combination, and the extreme main earth pressure P _a0 described later is not calculated.

Formula 79 shows a calculation example of the determination formula when Li = 1 and Ri = 3.

※※ (calculation means - calculation of the extreme main働土pressure P _a0) ※※
Next, an extreme value main earth pressure _Pa0 is calculated from the equation (79). Note that t _1R is calculated from Equation (29). Further, X _R = cot (ω _βR ).
The number 80 shows a calculation example of the extreme main働土pressure _{P a0} in Li = 1, Ri = 3.

* * (Calculation means-Calculation of R-plane fixed extreme _earth pressure _Pa0R ) * *
Next, in order to calculate the R plane fixed extreme main働土pressure P _A0R, the number 1 from the R-plane fixed extreme point y _L is calculated. Ω _βR given to _Equation 1 is ω _βR = ω _0βRi = ω _0Ri −β _Ri .
Further, using the calculated ω _βL = arccot (y _L ), it is determined whether the angle ω _L = ω _βL −β _{Li of the} L plane is within the range of the equation (187). If the equation (187) is not satisfied, it is determined that there is no solution, and the R-plane fixed extreme value main _earth pressure _Pa0R described later in that combination is not calculated.
Formula 81 shows an example of determination when Li = 1 and Ri = 3.
Since in the embodiment that an initial value _{ω βR = ω 0βRi = ω 0Ri} -β Ri upon analysis of extreme points _{X R} and extreme point _{Y L,} R plane fixed extreme point _{y L} and omega _.beta.L = arccot ( Since y _L ) has already been calculated in Expression (173) and Expression (174) in the 1/2 cycle of the cycle, the determination in Expression (187) is executed using the value of Expression (174).

Next, the R plane fixed extreme value main _earth pressure _Pa0R is calculated from the equation (75). Note that t _1L is calculated from Equation (28). Further, T cos θ is calculated from the equation (62). Further, x = cot (ω _βR ) and y _L = y = cot (ω _βL ).
_{Formula 82} shows a calculation example of the R-plane fixed extreme _earth pressure _Pa0R when Li = 1 and Ri = 3.

* * (Calculation means-Calculation of L surface fixed extreme value main _earth pressure _Pa0L ) * *
Next, in order to calculate the L plane fixed extreme main働土pressure P _A0L, number 2 from L plane fixed extreme point x _R is calculated. _Ω βL be given to the number 2, and _{ω βL = π-ω 0βLi-} 1 = π-ω 0Li-1 + β Li.
_Formula 83 shows a calculation example of ω _βR = _arccot (x _R ) when Li = 1 and Ri = 3.

_Further , using the calculated ω _βR , it is determined whether the angle ω _R = ω _βR + β _{Ri of} the R plane is within the applicable range of the equation (188). When the expression (188) is not satisfied, it is determined that there is no solution, and the L-plane fixed extreme value main _earth pressure _Pa0L described later in that combination is not calculated.
Formula 84 shows an example of determination when Li = 1 and Ri = 3.

Next, the L-plane fixed extreme _earth pressure _Pa0L is calculated from the equation (77). Note that x _R = x = cot (ω _βR ).

_{Formula 85} shows an example of calculation of the L-plane fixed extreme _earth pressure _Pa0L with Li = 1 and Ri = 3.

* * (Calculation means-Calculation of double-sided fixed primary _earth pressure _Pa0LR ) * *
Next, the double-side fixed main _earth pressure _Pa0LR is calculated from the equation (80).
_{Formula 86} shows a calculation example of the double-side fixed main _earth pressure _Pa0LR when Li = 1 and Ri = 3. _{Incidentally, t 1R} and Cotkushi _R utilize _{t 1R} and Cotkushi _R computed in the calculation of the L face fixed extreme point _{x R.} In addition, ω _βR = ω _{0β Ri} = ω _{0 Ri−} β _Ri .

* * (Calculation means-Calculation of the maximum value _PaMAX of basic main _earth pressure) * *
Next, based on the calculation result of each main earth pressure by the combination with each section, the maximum value _PaMAX of the basic main _earth pressure is calculated, and the result is displayed on the screen of the display.
Maximum value P _Amax of basic main働土pressure, the maximum value of the extreme main働土pressure P _a0 which is calculated by each combination, with the maximum value of L faces the fixed extremes main働土pressure P _aL which is calculated by each combination, the maximum value of the R plane fixed extreme main働土pressure P _aR, which is calculated by each combination is calculated as the maximum of these three values. That is, the maximum value _PaMAX of the basic main _earth pressure is calculated from _Equation 87.
Furthermore, parameters used for calculating the respective main働土pressure _{(e.g., ω βL, ω βR, Tcosθ} , reference adhesive force _{c 0L} the L side, constant phi _ShitabetaLi, reference horizontal load _t 0L the L side, R The surface side reference horizontal load t _0R and constant horizontal load t _0A ) are extracted, and the result is displayed on the display screen. If T cos θ is not calculated at the time of calculating each main earth pressure, T cos θ is calculated from equation (62).

The calculation results of Example 1 are displayed on the display screen as shown in FIG.
_Formula 88 shows a calculation example of the maximum value _PaMAX of the basic main _earth pressure.

※ (calculated inclination angle delta _L by calculating means _{-P aY} rotating coordinate system direction angle delta _PAY and L surface adhesion) ※
Further, the _PaY rotational coordinate system direction angle Δ _PaY is calculated from the equation (85), and the inclination angle Δ _L due to the L surface adhesive force is calculated from the equation (84), and the result is displayed on the display screen.
P _aY rotational coordinate system direction angle Δ _PaY and inclination angle Δ _L due to L surface adhesive force and main _earth pressure _{Pa aY} acting on L surface described below are _used to calculate the basic main _earth pressure maximum value _{Pa MAX} and basic main _earth pressure. the maximum value _P parameters used _{for aMAX} calculating the _{(ω βL, ω βR, Tcosθ} , reference adhesive force _{c 0Li} the L side, a constant _φ θβLi) is calculated using the.
In Example 1, the inclination angle delta _L by P _aY rotating coordinate system direction angle delta _PAY and L surface adhesion, the results shown in FIG. 21 (a) is displayed on the screen of the display.
Number 89 _shows an example of calculation of the inclination angle delta _L by calculation examples and L surface adhesion of _{P aY} rotating coordinate system direction angle delta _PAY.

* * (Slip type judgment) * *
Next, the slip form is determined according to the flow of FIG. 9, and the result is displayed on the screen of the display.
In Example 1, since the structure type of the retaining wall is a cantilever retaining wall, the result of the sliding form shown in FIG. 21A is displayed on the display screen.

* * (Calculation means-Calculation of main _earth pressure P _aY acting on L surface) * *
Next, the main _earth pressure P _aY acting on the L surface is calculated from the equation (86), and the horizontal component P _aYH of the main _earth pressure acting on the L surface is calculated from the equation (87). From the equation (88) The vertical component _PaYV of the main _earth pressure acting on the L plane is calculated, and the result is displayed on the screen of the display.
In Example 1, the result shown in FIG. 21A is displayed on the screen of the display.
_Formula 90 shows calculation examples of the main _earth pressure P _aY acting on the L plane, the horizontal component P _{aYH of} the main _earth pressure acting on the L plane, and the vertical direction component P _aYV of the main _earth pressure acting on the L plane.

※※ (Evaluation means) ※※
Next, the safety of the retaining wall is determined based on the above result. This calculation method is the same as the conventional calculation method for stable calculation. This can be confirmed by a known calculation.
If the criterion is satisfied, “OK” is displayed on the display screen. If the criterion is not satisfied, “NG” is displayed on the display screen.

In Example 1, the result shown in FIG. In the first embodiment, “falling”, “sliding”, and “ground support” are checked. In other words, the examination of “falling” is determined based on whether or not the eccentric distance e is within the allowable range (B / 6 in the first embodiment), and “OK” is displayed on the display screen to satisfy the standard. Is done. Study on "sliding" is (in Example 1, 1.5) value F _S is the allowable value is determined by whether or not more than, to meet the criteria of "OK" is displayed on the screen of the display. The examination for “ground support” is determined by whether or not the values q ₁ and q ₂ are less than the allowable bearing capacity (200 kN / m _{2 in} Example 1), and “OK” is displayed on the display screen to satisfy the standard. Is displayed. From these results, it is determined that the retaining wall of Example 1 can secure safety because it satisfies the standards for “falling”, “sliding”, and “ground support”, and “OK” is displayed in the comprehensive evaluation column. Displayed on the screen.

Further, the display screen of the calculation results, the graph showing the angular relationship of surfaces sliding with basic main働土pressure P _a is displayed. The graph may be a graph showing the angular relationship of the basic main働土pressure P _a and the sliding surface which acts on the L side. It is good also as a graph showing the relation between the point where a slip surface and the ground surface intersect, and the earth pressure calculated from the angle of the slip surface at that point. It is good also as a structure which piles up and displays the slope sectional view which showed the retaining wall shape, the ground surface shape, the load condition, and the sliding surface, and the said graph.

In Example 1, the graph shown in FIG. 21C is displayed on the display screen.
Graph of FIG. 21 (c) in the graph showing the relationship between the basic main働土pressure P _a to R surface and the ground surface is calculated from the angle of the sliding surface at the point and its point of intersection, the ground surface of the current state shape (the ground line) basic main働土pressure P _a is obtained by displaying superimposed sliding surface when the maximum.
If the change point of the slope is made finer in the graph, the curve showing the relationship between earth pressure and slip angle can be expressed as a smooth curve. For example, the topographic dimension of the slope is 0.5 m under exactly the same input conditions as in Example 1. If it is subdivided into intervals, the graph shown in FIG. 21 (c) can be expressed as a smooth curve like the graph shown in FIG. 22, so that the CPU of the computer executes arithmetic processing according to the command of the application program for safety evaluation of the retaining wall By doing so, it is good also as a structure which subdivides the topographical dimension of the input back surface of a retaining wall, calculates earth pressure, and draws a smooth curve on a graph.

Example 2 will be described with reference to FIGS.
In the second embodiment, a calculation example in the case where the shape of the retaining wall is a gravitational structure as shown in FIG. 14 will be described.

** (Acquisition means) **
An input screen according to the second embodiment will be described.
First, in the retaining wall shape information input screen, retaining wall shape information is input to the computer using an input device such as a mouse keyboard in the same manner as in the first embodiment.
In Example 2, the retaining wall shape information shown in FIG. 23A is input. Therefore, the shape of the retaining wall of Example 2 is a trapezoidal shape as shown in FIG. For the retaining wall height H, H = 4.00 (m) is displayed on the screen of the display as the calculation result of H1 + H2 + H3. As for the bottom surface width B, B = 2.40 (m) is displayed on the display screen as a calculation result of B1 + B2 + B3 + B4 + B5. For the X coordinate X _SP of the slip surface base point SP, X _SP = B1 + B3 + B5 = 2.40 (m) is displayed on the display screen, and for the Y coordinate Y _SP of the slip surface base point SP, Y _SP = 0. 00 (m) is displayed on the display screen. As for the inclination angle α on the back side of the retaining wall, α = 0.46365 (rad) is displayed on the display screen as a calculation result of arctan (B3 ÷ H).

Next, in the input screen for retaining wall material information, retaining wall back soil information and supporting ground information, retaining wall material information, retaining wall back soil information and supporting ground information are the same as in the first embodiment. It is input using an input device such as a mouse keyboard.
In Example 2, the material information of the retaining wall, the soil information on the back surface of the retaining wall, and the information on the supporting ground shown in FIG. 24 are input.

Next, in the input screen of the terrain information on the back surface of the retaining wall and the load information that acts on the terrain on the back surface of the retaining wall, the terrain information on the back surface of the retaining wall and the load information that acts on the terrain on the back surface of the retaining wall are the same as in the first embodiment. It is input using an input device such as a mouse keyboard.
In Example 2, the terrain information on the back surface of the retaining wall and the load information acting on the terrain on the back surface of the retaining wall shown in FIG. 25 are input. As for the X coordinate X _GP of the contact point between the retaining wall and the ground surface, X _GP = B1 + B2 + B4 = 0.40 (m) is obtained by using the values of B1, B2, and B4 in FIG. As for the Y coordinate Y _GP of the contact point between the retaining wall and the ground surface, Y _GP = 4.00 (m) is displayed on the display screen by using the value of H in FIG. .

Next, on the other load information input screen, the other load information is input using an input device such as a mouse keyboard in the same manner as in the first embodiment.
In Example 2, other load information shown in FIG. 26 is input.
As for the vertical load reduction coefficient k _V ′, k _V ′ = 1 is displayed on the display screen as a calculation result of 1-k _V. For the seismic force composite angle θ, θ = 0.252607 (rad) is displayed on the display screen as the calculation result of arctan (k _H ÷ k _V ′).

* * (Calculation means-arrangement of basic conditions in each section) * *
Subsequently, in order to calculate the earth pressure from the back soil acting on the retaining wall, the calculation of the basic condition is executed in the same manner as in the first embodiment based on the input data.
The calculation result of Example 2 is the result shown in FIG.
In _Equation 91, the relative coordinate value X ₅ , the relative coordinate value Y ₅ , the slope gradient β ₅ , the boundary angle ω ₀₅ , the slope slope H ₅ ′, the constant φ _θβL5 , the constant φ _θβR5 , the reference vertical load p ₀₅ at i = 5. the reference adhesive force _{c 0L5,} R side of the reference adhesive force _{c 0R5} of L side, the reference horizontal load _{t 05, W AM5 ', W} AE5, ΣP V5', constant vertical load _{W A5 ', t AM5',} t Calculation examples of _AE5 , ΣP _H5 ′, and constant horizontal load t _0A5 ′ are shown.

* * (Calculation means-Calculation of each main earth pressure and each extreme point by combination with each section) * *
Subsequently, based on the input data and the calculation result of the basic condition, the calculation of each main earth pressure and each extreme point by the combination with each section is executed in the same manner as in the first embodiment.
The calculation result when Li = 2 in Example 2 is the result shown in FIG.

※※ (calculation means - calculating constants vertical load _{W A} and the constant horizontal load _{t 0A)} ※※
Constant vertical load W _A and the constant horizontal load t _0A is calculated in the same manner as in Example 1.
Formula 92 shows a calculation example of the constant vertical load W _A (2, 5) and the constant horizontal load t _0A (2, 5) at Li = 2 and Ri = 5.

※※ (calculation means - calculation of the extreme points _{X R} and extreme point _{Y L)} ※※
Next, using the algorithm of iterative method of the invention described above, from equations 1 and _{2 ω βL (ω βL = arccot} (Y L)) and _{ω βR (ω βR = arccot (} X R)) is Example Calculation is performed in the same manner as 1.
In the embodiment, the initial value of ω _βR = ω _0βRi = ω _0R −β _Ri is given in _Equation 1.
The number 93 and number 94 shows a calculation example of Li = 2, Ri = 5 in the _ω βL (2,5) and _ω βR (2,5).

In Example 2, the solutions of the iterations omega was displayed after the decimal point 5 digits obtained in _βL or the calculation at point omega _{[beta] R} of displaying up to 5 digits obtained, respectively twice the same numerical value at iteration When is obtained, the iterative calculation stops.
Therefore, 2.22138 to _{ω βL (2,5) (rad)} , to obtain a 0.52267 (rad) in _ω βR (2,5).

The angle omega _L and R face angle omega _R the L plane is determined in the same manner as or Example 1 present in the studied section.
Formula 95 shows a calculation example of the judgment formula when Li = 2 and Ri = 5.

※※ (calculation means - calculation of the extreme main働土pressure P _a0) ※※
Next, the extreme value main earth pressure _Pa0 is calculated in the same manner as in the first embodiment.
Formula 96 shows a calculation example of the extreme main earth pressure P _a0 when Li = 2 and Ri = 5.

* * (Calculation means-Calculation of R-plane fixed extreme _earth pressure _Pa0R ) * *
Next, in order to calculate the R plane fixed extreme main働土pressure P _A0R, R plane fixed extreme point y _L is computed in the same manner as in Example 1.
Further, using the calculated ω _βL = arccot (y _L ), it is determined in the same manner as in the first embodiment whether the angle ω _L = ω _βL -β _{Li of the} L plane is within a predetermined range.
In the second embodiment, as in the first embodiment, the initial value is set to ω _βR = ω _0βRi = ω _0Ri −β _{Ri in} the analysis of the extreme value point X _R and the extreme value point Y _L. Since y _L and ω _βL = arccot (y _L ) have already been calculated in Formula (251) and Formula (252) in the 1/2 cycle of the cycle, the value of Formula (252) is used in Formula (187). This determination is executed.
Formula 97 shows an example of determination when Li = 2 and Ri = 5.

Next, the R-plane fixed extreme _earth pressure _Pa0R is calculated in the same manner as in the first embodiment.
_{Formula 98} shows an example of calculating the R-plane fixed extreme _earth pressure _Pa0R when Li = 2 and Ri = 5.

* * (Calculation means-Calculation of L surface fixed extreme value main _earth pressure _Pa0L ) * *
Next, in order to calculate the L plane fixed extreme main働土pressure P _A0L, number 2 from L plane fixed extreme point x _R is calculated in the same manner as in Example 1.
_Formula 99 shows a calculation example of ω _βR = _arccot (x _R ) when Li = 2 and Ri = 5.

_Further , using the calculated ω _βR , it is determined in the same manner as in the first embodiment whether the angle ω _R = ω _βR + β _{Ri of} the R plane is within a predetermined range.
Formula 100 shows an example of determination when Li = 2 and R _i = 5.

Next, an L-plane fixed extreme _earth pressure _Pa0L is calculated in the same manner as in the first embodiment.
_{Formula 101} shows a calculation example of the L-plane fixed extreme _earth pressure _Pa0L with Li = 2 and Ri = 5.

* * (Calculation means-Calculation of double-sided fixed primary _earth pressure _Pa0LR ) * *
Next, the double-side fixed main _earth pressure _Pa0LR is calculated in the same manner as in the first embodiment.
_{Formula 102} shows a calculation example of the double-side fixed main _earth pressure _Pa0LR when Li = 2 and Ri = 5. _{Incidentally, t 1R} and Cotkushi _R utilize _{t 1R} and Cotkushi _R computed in the calculation of the L face fixed extreme point _{x R.} In addition, ω _βR = ω _{0β Ri} = ω _{0 Ri−} β _Ri .

* * (Calculation means-Calculation of the maximum value _PaMAX of basic main _earth pressure) * *
Next, based on the calculation result of each main earth pressure by the combination with each section, the maximum value _PaMAX of the basic main _earth pressure is calculated in the same manner as in the first embodiment, and the result is displayed on the display screen. .
Further, the parameters used for calculating each main earth pressure are displayed on the display screen in the same manner as in the first embodiment.
The calculation results of Example 2 are displayed on the display screen as shown in FIG.
_Formula 103 shows a calculation example of the maximum value _PaMAX of the basic main _earth pressure.

* * (Calculation means-Calculating the tilt angle by the _PaY rotational coordinate system direction angle Δ _PaY and L surface adhesive force) * *
Also, P _aY rotating coordinate system direction angle delta _PAY and inclination delta _L by L surface adhesion is calculated in the same manner as in Example 1, the result is displayed on the screen of the display.
In Example 2, the inclination angle delta _L by P _aY rotating coordinate system direction angle delta _PAY and L surface adhesion, the results shown in FIG. 30 (a) is displayed on the screen of the display.
_Formula 104 _shows a calculation example of the _PaY rotational coordinate system direction angle Δ _{PaY and} a calculation example of the tilt angle Δ _L due to the L-plane adhesive force.

* * (Slip type judgment) * *
Next, the slip mode is determined in the same manner as in the first embodiment, and the result is displayed on the screen of the display.
In the second embodiment, the retaining wall structure is a gravity retaining wall. Therefore, according to the flow of FIG. 9, it is determined by the equation shown in Equation 43, and the result of the slip form shown in FIG. 30A is displayed on the display screen. Is done.
Formula 105 shows a calculation example in the second embodiment.

* * (Calculation means-Calculation of main _earth pressure P _aY acting on L surface) * *
Next, the main _soil pressure P _aY acting on the L surface, the horizontal component P _{aYH of} the main _soil pressure acting on the L surface, and the vertical component P _aYV of the main _soil pressure acting on the L surface are the same as in the first embodiment. And the result is displayed on the display screen.
In Example 2, the result shown in FIG. 30A is displayed on the display screen.
_Formula 106 shows a calculation example of the main _earth pressure P _aY acting on the L plane, the horizontal component P _{aYH of} the main _earth pressure acting on the L plane, and the vertical direction component P _aYV of the main _earth pressure acting on the L plane.

※※ (Evaluation means) ※※
Next, the safety of the retaining wall is determined based on the above result. This calculation method is the same as the conventional calculation method for stable calculation. This can be confirmed by a known calculation.
If the criterion is satisfied, “OK” is displayed on the display screen. If the criterion is not satisfied, “NG” is displayed on the display screen.
In Example 2, the result shown in FIG. In the second embodiment, “falling”, “sliding”, and “ground support” are checked. In other words, the examination of “falling” is determined by whether or not the eccentric distance e is within the allowable range (B / 3 in the second embodiment), and “OK” is displayed on the display screen to satisfy the standard. Is done. The examination with respect to “sliding” is determined based on whether or not the value F _S is equal to or greater than the allowable value (1.2 in the second embodiment), and “NG” is displayed on the display screen because the criterion is not satisfied. The examination for “ground support” is determined by whether or not the values q ₁ and q ₂ are less than the allowable bearing capacity (450 kN / m 2 in Example 2), and “OK” is displayed on the display screen to satisfy the standard. Is displayed. From these results, it is determined that the retaining wall of Example 2 cannot secure safety because any of “falling”, “sliding”, and “ground support” does not satisfy the standard, and “NG” is displayed in the comprehensive evaluation column. Displayed on the screen. Therefore, change the retaining wall to a safer side (for example, change the top wall thickness of the retaining wall to be thicker and place it by excavating the ground surface behind the retaining wall to reduce the effective weight W ') and evaluate again. There is a need to do.

Further, the display screen of the calculation results, the graph showing the angular relationship of the basic main働土pressure P _a and the sliding surface is displayed in the same manner as in Example 1.
In Example 2, the graph shown in FIG. 30C is displayed on the display screen.

A third embodiment will be described with reference to FIGS. 23, 25 to 29, and 31 to 34.
In the third embodiment, a calculation example will be described in the case where “single-surface linear slip” occurs on the rear surface of the retaining wall under the same input conditions as in the second embodiment (excluding the wall friction angle δ on the rear surface of the retaining wall).

** (Acquisition means) **
An input screen according to the third embodiment will be described.
First, on the retaining wall shape information input screen, retaining wall shape information is input to a computer using an input device such as a mouse keyboard in the same manner as in the second embodiment.
In the third embodiment, the same retaining wall shape information as that of the second embodiment shown in FIG.
Next, in the input screen for retaining wall material information, retaining wall back soil information and supporting ground information, retaining wall material information, retaining wall back soil information and supporting ground information are the same as in the second embodiment. It is input using an input device such as a mouse keyboard.
In Example 3, the material information of the retaining wall, the soil information on the back surface of the retaining wall, and the information of the supporting ground shown in FIG. 31 are input. In addition, the input information of FIG. 31 is the same value as the input information shown in FIG.
Next, in the input screen for the terrain information on the back surface of the retaining wall and the load information that acts on the terrain on the back surface of the retaining wall, the terrain information on the back surface of the retaining wall and the load information that acts on the topography on the back surface of the retaining wall are the same as in the second embodiment. It is input using an input device such as a mouse keyboard.
In the third embodiment, the same terrain information on the back surface of the retaining wall and the load information acting on the terrain on the back surface of the retaining wall are input as in the second embodiment shown in FIG.
Next, on the input screen for other load information, the other load information is input using an input device such as a mouse keyboard in the same manner as in the second embodiment.
In the third embodiment, the same other load information as that of the second embodiment shown in FIG. 26 is input.

* * (Calculation means-arrangement of basic conditions in each section) * *
Subsequently, in order to calculate the earth pressure from the back soil acting on the retaining wall, the calculation of the basic condition is executed in the same manner as in the second embodiment based on the input data.
The calculation result of the third embodiment is the same as that of the second embodiment shown in FIG.
* * (Calculation means-Calculation of each main earth pressure and each extreme point by combination with each section) * *
Subsequently, based on the input data and the calculation result of the basic condition, the calculation of each main earth pressure and each extreme point by the combination with each section is executed in the same manner as in the second embodiment.
The calculation result when Li = 2 in Example 3 is the same as that in Example 2 shown in FIG.
* * (Calculation means-Calculation of the maximum value _PaMAX of basic main _earth pressure) * *
Next, based on the calculation result of each main earth pressure by the combination with each section, the maximum value _{Pa MAX} of the basic main _earth pressure is calculated in the same manner as in the second embodiment.
The calculation result of the third embodiment is the same as that of the second embodiment shown in FIG.
* * (Calculation means-Calculating the tilt angle by the _PaY rotational coordinate system direction angle Δ _PaY and L surface adhesive force) * *
Further, the _PaY rotational coordinate system direction angle Δ _PaY and the inclination angle Δ _L due to the L surface adhesive force are calculated in the same manner as in the second embodiment.
In Example 3, the P _aY rotational coordinate system direction angle Δ _PaY and the inclination angle Δ _L due to the L-surface adhesive force are the same as those in Example 2 shown in FIG.

* * (Slip type judgment) * *
Next, the slip mode is determined in the same manner as in the second embodiment, and the result is displayed on the screen of the display.
In the third embodiment, since the retaining wall structure is a gravity retaining wall, according to the flow of FIG. 9, it is determined by the equation shown in Equation 43, and the result of the slip form shown in FIG. 34 (a) is displayed on the display screen. Is done.
Formula 107 shows a calculation example in the third embodiment.

* * (Calculation means-calculation of each main earth pressure and each extreme point) * *
According to the determination result, the calculation in the 1-plane linear sliding mode is executed.
First, according to the result of the input data and the basic condition, L the constant horizontal load t _{0A, one} face straight shear mode at a constant vertical load W _A, one side straight shear mode in one plane linear shear mode surface fixed extreme point x _R, L plane fixed extremes main in one plane linear sliding mode働土pressure _{P a0L, 1} surface sided fixed main働土pressure P _A0LR in straight shear mode is calculated. Here, the L-plane fixed extreme _earth pressure P _{a0L in} the one-surface linear sliding mode and the double-surface fixed main _earth pressure P _a0LR in the one-surface linear sliding mode are referred to as respective main _earth pressures in the one-surface linear sliding mode.
In addition, since the L plane is fixed in “one-plane linear slip”, the extreme point X _R , the extreme point Y _L , the extreme active earth pressure P _a0 , the R plane fixed extreme point y _L , and the R plane fixed The extreme main _earth pressure _Pa0R does not need to be calculated.
The calculation result in Example 3 is the result shown in FIG.
In Example 3, a constant vertical load W _A in one plane linear sliding mode has already been calculated as a constant vertical load W _{A 'when} the calculation of the basic condition, also, a constant horizontal load at one side straight shear mode Since t _0A has already been calculated as a constant vertical load t _0A ′ at the time of calculation of the basic condition, those calculations can be omitted.

* * (Calculation means-Calculation of L-plane fixed extreme _earth pressure _Pa0L in one-plane linear sliding mode) * *
First, in order to L surface fixed extreme main働土pressure P _A0L in one plane linear sliding mode is calculated, L plane fixed extreme point x _R in than the number 108 first surface linear sliding mode is calculated.

_Formula 109 shows a calculation example of ω _βR = _arccot (x _R ) when i = 5.

_Further , using the calculated ω _βR , it is determined whether or not the angle ω _R = ω _βR + β _{i of} the R plane is within the applicable range of the equation (309). When the expression (309) is not satisfied, it is determined that there is no solution, and the L-plane fixed extreme value main _earth pressure P _a0L ′ in the one-plane linear sliding mode described later is not calculated.

Formula 111 shows a determination example when i = 5.

Next, the L-plane fixed extreme value _earth pressure _{Pa0L in the} one-plane linear sliding mode is calculated from the equation (311).

Formula (312) shows a calculation example of the L-plane fixed extreme value primary _earth pressure _Pa0L in the one-plane linear sliding mode at i = 5.

* * (Calculation means-Calculation of double-sided fixed primary _earth pressure _Pa0LR ) * *
Next, the double-side fixed main _earth pressure _{Pa0LR in the} single-sided linear sliding mode is calculated from the equation (313).

Formula (314) shows a calculation example of the double-side fixed main _earth pressure P _a0LR in the one-plane linear sliding mode at i = 5. _{Incidentally, t 1RI} and Cotkushi _Ri utilize _{t 1RI} and Cotkushi _Ri computed during the calculation of L faces the fixed extreme point _{x R} at one side straight shear mode. Further, ω _βR = ω _0βRi = ω _0i -β _i is set.

* * (Calculation means-Calculation of the maximum value _PaMAX of basic main _earth pressure) * *
Next, based on the calculation results of each main earth pressure in the one-sided linear sliding mode, the maximum value _PaMAX of the basic main _earth pressure in the one-sided linear sliding mode is calculated, and the result is displayed on the display screen. The
The maximum value P _aMAX of the “one-sided linear sliding” basic main _earth pressure is the maximum value of the L-plane fixed extreme value main _earth pressure _Pa0L in the one-sided linear sliding mode in each section number and one side in each section number. The maximum value of the two-side fixed main _earth pressure _{Pa0LR in} the linear sliding mode is calculated as the maximum value of these two values. That is, the maximum value _PaMAX of the “one-sided linear slip” basic main _earth pressure is calculated from the equation (116).
Parameters used for calculating each main earth pressure in the one-plane linear sliding mode (for example, ω _βR , Tcos θ, L-side reference adhesive force c _0Li , constant φ _θβLi , reference horizontal load t _0i , constant The horizontal load t _0Ai ′) is extracted and the result is displayed on the display screen. If T cos θ is not calculated at the time of calculating each main earth pressure, T cos θ is calculated from equation (62).

The calculation results of Example 3 are displayed on the display screen as shown in FIG.
_{Formula 117} shows a calculation example of the maximum value _PaMAX of the basic main _earth pressure in the one-plane linear sliding mode.

* (Calculation means- _{Pay Y} rotation coordinate system direction angle (φ _θβL '+ Δ _L ) and calculation of tilt angle Δ _L by L surface adhesive force) *
Further, the _PaY rotational coordinate system direction angle (φ _θβL ′ + Δ _L ) in the one-plane linear sliding mode is calculated from the equation (111), and the inclination angle Δ _L due to the L-plane adhesive force in the one-plane linear sliding mode is (φ _{[theta] [beta] L} '+ [Delta] _L )-[ _{phi] [theta] [beta]} ' and the result is displayed on the display screen.
For the calculation of the _PaY rotational coordinate system direction angle (φ _θβL '+ Δ _L ) in the 1-plane linear sliding mode and the main _earth pressure _PaY acting on the L-plane in the 1-plane linear sliding mode described later, the 1-surface linear sliding The calculation is performed using the maximum value _{Pa MAX} of the basic main _earth pressure in the mode and the parameters (ω _βR , T _cos θ, reference adhesive force c _0Li on the L plane side, constant φ _θβLi ) used to calculate the value.
In Example 3, the inclination angle delta _L by P _aY rotating coordinate system direction angle _(φ θβL '+ Δ _L) and L surface adhesion at one surface straight shear mode in one plane linear sliding mode, in FIG. 34 (a) The result shown is displayed on the display screen.
Number 118 indicates an example of calculating the inclination angle delta _L by L-coated adhesive force at P _aY calculation example of the rotating coordinate system direction angle _(φ θβL '+ Δ _L), and one side straight shear mode in one plane linear sliding mode.

* * (Calculation means-Calculation of main _earth pressure P _aY acting on L surface) * *
Next, the main _earth pressure _PaY acting on the L surface in the one-surface linear sliding mode is calculated from the equation (112), and the main _earth pressure acting on the L surface in the one-surface linear sliding mode is calculated from the equation (113). The horizontal component P _aYH is calculated, and the vertical component P _aYV of the main _earth pressure acting on the L plane in the one-plane linear sliding mode is calculated from the equation (114), and the result is displayed on the display screen.
In Example 3, the result shown in FIG. 34A is displayed on the screen of the display.
In _Equation 119, the main _earth pressure P _aY acting on the L plane in the one-plane linear sliding mode and the horizontal component P _aYH of the main _earth pressure acting on the L plane in the one-plane linear sliding mode and the one-plane linear sliding mode The calculation example of the vertical direction component _PaYV of the main _earth pressure which acts on the L surface of this is shown.

※※ (Evaluation means) ※※
Next, the safety of the retaining wall is determined based on the above result. This calculation method is the same as the conventional calculation method for stable calculation. This can be confirmed by a known calculation.
If the criterion is satisfied, “OK” is displayed on the display screen. If the criterion is not satisfied, “NG” is displayed on the display screen.
In Example 3, the result shown in FIG. 34B is obtained. In Example 3, “falling”, “sliding”, and “ground support” are checked. In other words, the examination of “falling” is determined based on whether or not the eccentric distance e is within the allowable range (B / 3 in the third embodiment), and “NG” is displayed on the display screen because the criterion is not satisfied. Is displayed. The examination for “sliding” is determined based on whether or not the value F _S is equal to or greater than the allowable value (1.2 in the third embodiment), and “NG” is displayed on the display screen because the criterion is not satisfied. The examination for “ground support” is determined based on whether or not the values q ₁ and q ₂ are equal to or less than the allowable bearing capacity (450 kN / m _{2 in the} third embodiment). Is displayed. From these results, it is determined that the retaining wall of Example 3 cannot secure safety because any of “falling”, “sliding”, and “ground support” does not satisfy the standard, and “NG” is displayed in the comprehensive evaluation column. Displayed on the screen. Therefore, change the retaining wall to a safer side (for example, adjust the position (separation) between the retaining wall and the building (mounted load)) An evaluation is necessary.

Further, the display screen of the calculation results, the graph showing the angular relationship of the basic main働土pressure P _a and the sliding surface is displayed in the same manner as in Example 2.
In Example 2, the graph shown in FIG. 34C is displayed on the display screen.

The present invention is an approach different from the trial wedge method and the improved trial wedge method for calculating the earth pressure received from the back surface of the retaining wall used in the conventional calculation program. It is possible to calculate the earth pressure acting on the retaining wall quickly and with high accuracy according to the load condition acting on the ground surface. This facilitates the work and supports the effective determination of the cross section of the retaining wall. Further, since it is possible to evaluate the safety instantly, there is no waiting time for the calculation result, so that there is an advantage that the user of the retaining wall safety evaluation system is not stressed. In addition, the earth wall pressure is used to determine the safety of the retaining wall (for example, overturning, sliding, supporting force, necessary reinforcing bar amount, cross-sectional force, etc.) as safety evaluation items for the retaining wall described in various standards. .
Slip forms (“one-sided linear slip”, “two-sided linear slip”) are determined, and the safety of the retaining wall is evaluated by earth pressure according to the slip form.
In addition, by graphing the relationship between the magnitude of earth pressure acting on the retaining wall and the angle of the slip surface due to changes in the angle of the slip surface, it is possible to visually recognize the change in earth pressure on the entire slope, so Accordingly, it is possible to select the optimum cross section of the retaining wall and to arrange the retaining wall so that the earth pressure acting on the retaining wall is minimized.

DESCRIPTION OF SYMBOLS 1 ... Safety evaluation system (safety evaluation apparatus), 2 ... Input part, 3 ... Memory | storage part, 4 ... Determination part,
5 ... Evaluation part, 6 ... Display part.

Claims (6)

A retaining wall safety evaluation method comprising at least one of a one-sided linear sliding mode or a two-sided linear sliding mode,
An acquisition step of acquiring data relating to the retaining wall constant, soil constant, load constant, etc .;
A calculation step of calculating a load including earth pressure acting on the retaining wall based on the data acquired in the acquisition step;
An evaluation step for evaluating at least one of the safety of the retaining wall based on a load including earth pressure acting on the retaining wall calculated in the calculating step;
It comprises a display step for displaying the result of evaluation in the evaluation step,
The data acquired in the acquisition step includes retaining wall shape information, retaining wall material information, retaining wall back soil information, supporting ground information, retaining wall back terrain information, and load information acting on the retaining wall back terrain. And other load information,
The calculation step is based on the data obtained in the acquisition step and the calculated earthquake composite angle θ and the calculated inclination angle α on the back side of the retaining wall,
Calculation conditions (constant φ _θβL , constant φ _θβR , L-side reference vertical load p _0L , R-side reference load p _0R , L-side reference adhesive force c _0L , R-side reference adhesive force c _0R , reference horizontal load _{t 0L} the L side, the reference of the R plane side horizontal load _{t 0R,} a constant horizontal load _{t 0A} and constant vertical load _{W a)} calculated,
In the two-plane linear sliding mode, the earth pressure including at least one of the extreme value main earth pressure P _a0 , the L-plane fixed extreme _earth pressure _{Pa a0L,} and the R-plane fixed extreme earth pressure _{Pa aR} based on the calculation condition. Or to calculate the angle of the sliding surface,
In the 1-plane linear sliding mode, the earth pressure including the L-plane fixed extreme value main earth pressure _Pa0L in the 1-plane linear sliding mode or the angle of the sliding surface is calculated based on the above calculation conditions.
The number 1, obtained from the number 2 omega _{[beta] R,} or the initial value of omega _{[beta] R} or formula from omega _{[beta] R} of the fixed value (42), equation (55), equation (56), equation (57), equation (71) and Equation (161) is calculated, and using the obtained μ _L , t _2L , t _2R , t _2A , k and ξ _L , Equation (68) and Equation (163) are calculated to obtain ω _βL. Yes,
For Equation ₂ , Equation (41), Equation (28), Equation (29), Equation (30), and Equation (162) are obtained from ω _βL obtained from Equation 1, ω _{βL of the} initial value, or ω _{βL of the} fixed value. The equations (52) and (164) are calculated using μ _R , t _1L , t _1R , t _1A and ξ _R that are calculated and obtained to obtain ω _βR .
In calculating the extremum main働土pressure P _a0 in two planes straight shear mode, set to any number in omega _.beta.L or omega _{[beta] R} as an initial value in the later iteration, alternately number 1 and number 2 to a predetermined accuracy is repeatedly calculated, which calculates the extreme main働土pressure P _a0 using an iterative computed omega _.beta.L or omega _{[beta] R} alternately until a predetermined accuracy,
The L plane calculation of the fixed extreme main働土pressure P _A0L in dihedral straight shear mode, giving omega _.beta.L fixed value of the number 2, L plane fixed extrema using the resulting omega _{[beta] R} main働土pressure P _A0L Is to calculate
In calculating the R plane fixed extreme main働土pressure P _A0R of two-plane linear sliding mode, giving omega _{[beta] R} of the fixed value of the number 1, R plane fixed extrema using the resulting omega _.beta.L main働土pressure P _A0R Is to calculate
In the calculation of the L-plane fixed extreme value primary _earth pressure P _{a0L in} the 1-plane linear sliding mode, an arbitrary value is determined for β _L , and a fixed value ω _βL = π / 2−α + β _L is given in _Equation 2, and obtained. A retaining wall safety evaluation method characterized by calculating an L-plane fixed extreme _earth pressure _Pa0L in a one-plane linear sliding mode using _ωβR .

In the evaluation step, the vertical load and the resistance moment and the horizontal load and the falling moment acting on the retaining wall are calculated with respect to the weight of the retaining wall and the external force acting on the retaining wall obtained in the calculation step. The retaining wall safety evaluation method according to claim 1.
The step of calculating includes determining a slip form of “one-sided linear slip” and “two-sided linear slip”, and calculating an earth pressure or an angle of the slipping surface according to the slip form. The retaining wall safety evaluation method according to claim 1.
For the earth pressure calculated in the calculation step, not only the vicinity of the maximum earth pressure but also the value relating to the angle of the slip surface and the value relating to the earth pressure in the entire calculation range or the entire topography of the retaining wall are displayed in a graph. The retaining wall safety evaluation method according to claim 1, further comprising a display step.
Retaining wall safety assessment program, computer
An acquisition means for acquiring data on retaining wall constants, soil constants, load constants, etc .;
Calculation means for calculating a load including earth pressure acting on the retaining wall based on the data acquired by the acquisition means;
An evaluation means for evaluating at least one of the safety of the retaining wall based on a load including earth pressure acting on the retaining wall calculated by the calculating means;
A program that functions as display means for displaying the result of the evaluation in the evaluation step;
The said acquisition means, the said calculation means, and the said evaluation about the said acquisition step, the said calculation step, the said evaluation step, and the said display step in the safety evaluation method of the retaining wall of any one of Claims 1-4. Retaining wall safety evaluation program characterized in that each calculation process is executed by the means and the display means.
Retaining wall safety evaluation system, computer
An acquisition means for acquiring data on retaining wall constants, soil constants, load constants, etc .;
Calculation means for calculating a load including earth pressure acting on the retaining wall based on the data acquired by the acquisition means;
An evaluation means for evaluating at least one of the safety of the retaining wall based on a load including earth pressure acting on the retaining wall calculated by the calculating means;
A system that functions as a display unit that displays a result of the evaluation performed in the evaluation step;
The retaining wall safety evaluation program according to claim 5 is installed,
The retaining wall safety evaluation system, wherein the acquisition means, the calculation means, the evaluation means, and the display means execute respective calculation processes according to a command of the retaining wall safety evaluation program.

Images