JP4924819B2 - Evaluation method for bearing capacity of direct foundation on slope - Google Patents

Description

  The present invention relates to a method for evaluating the compressive bearing force of a direct foundation installed in the vicinity of a slope such as cut soil, taking a three-dimensional effect into consideration, based on a velocity field method.

  It has been found that the bearing capacity of the direct foundation installed in the vicinity of the slope, such as cut, is significantly lower than the bearing capacity of the direct foundation installed on the horizontal ground due to the influence of the slope. The influence of the slope is the slope angle, the distance to the shoulder, the height of the slope, etc. The conventional methods for evaluating the influence of these parameters are (1) limit balance method, (2) slip analysis. And (3) analysis methods such as limit analysis are used. The limit balance method is a method of formulating as a static force balance problem assuming a rigid body slip, changing the slip shape and position, and obtaining the minimum support force value. Belongs. The slip analysis method is a method of solving the plastic equilibrium stress satisfying both the force balance and the fracture criterion defined by continuum mechanics from the simultaneous ordinary differential equations along the slip line under given boundary conditions. The Meyerhof method belongs to this. The limit analysis method is a method that can clarify the relationship with the correct answer in handling fracture problems in continuum mechanics. For the correct values satisfying the three, set the allowable velocity field to set the upper bound value that satisfies only the strain fit and the compositional relationship, and set the allowable velocity field to set the lower bound value that satisfies the force balance and the constituent relationship. It is what you want.

  The above-described method for obtaining the upper bound value is a method called “velocity field method”. In Non-Patent Document 1 below, as shown in FIG. Is a logarithmic spiral with E as the pole, CD is a straight line that reaches the slope slope, and this is assumed to be a discontinuous field of velocity. It has been proposed. In this document, the calculation result of the velocity field method is summarized as a reduction rate μ with respect to the support force of the horizontal ground, and the support force of the direct foundation on the inclined ground is calculated by calculating the reduction rate μ on the horizontal ground A method for obtaining by multiplying by is proposed.

On the other hand, with respect to the reduction rate μ, a graph of the reduction rate of the supporting force with respect to the horizontal ground with the distance to the shoulder as a parameter is shown in Non-Patent Document 2 below. In this graph, as shown in FIG. 12, the horizontal axis is the distance ratio α _{S to the} shoulder (separation distance to the shoulder / base width), and the vertical axis is the bearing capacity decrease rate ζ _S0 with respect to the horizontal ground. In addition to the analysis results by the velocity field method, other analysis methods and experimental values are listed.
Osamu Kusakabe, “Calculation on bearing capacity evaluation of direct foundation on slope”, “Soil and foundation”, vol33, No2,1985, p.7-12 Architectural Institute of Japan, “Basic Design Guidelines for Architectural Buildings”, 2001, p119

From the graph of the distance ratio α _S (separation distance to the shoulder / base width) -bearing force decrease rate ζ _{S0 to} the horizontal ground shown in FIG. 12, the analysis result by the velocity field method is the other analysis. The rate of decrease is lower than the method (Meyerhof method, Bishop method, Gemperline equation) and experimental values, indicating that the influence of the slope is overestimated.

  This is because the analysis by the velocity field method is handled as a two-dimensional plane strain model, and the increase in bearing force due to the so-called three-dimensional effect is not taken into consideration. The increase in the bearing force due to the three-dimensional effect includes an increase in bearing force in consideration of the side resistance in addition to the fracture surface of the ground drawn by a two-dimensional model. Furthermore, it is mentioned as a cause that the foundation penetration resistance etc. are not considered.

  Accordingly, the main problem of the present invention is to provide a method for evaluating the support force of a foundation directly on a slope, considering the three-dimensional effect based on the fact that the support force decrease rate due to the influence of the slope is obtained by the velocity field method. There is.

In order to solve the above-mentioned problem, the present invention according to claim 1 is a method for evaluating the compression support force of a direct foundation installed in the vicinity of a slope,
Calculating a bearing force ratio (ζ ₁ ) to the horizontal ground of the direct foundation based on a velocity field method;
Using the direct foundation as a two-dimensional model, the horizontal ground model produced under the condition that the surrounding ground is horizontal ground, and the slope ground model produced under the ground conditions reproducing the slope, respectively, were subjected to a centrifugal model experiment, respectively. Determining a bearing capacity ratio (ζ ₂ ) for the horizontal ground in the model;
Using the 3D model for the direct foundation and the horizontal ground model with the surrounding ground as the horizontal ground, and the slope ground model manufactured with the ground conditions reproducing the slope, respectively, we performed a centrifugal model experiment, Determining a bearing capacity ratio (ζ ₃ ) for the horizontal ground in the model;
A ratio (ζ ₃ / ζ ₂ ) between the bearing force ratio ζ ₂ for the horizontal ground in the two-dimensional model and the bearing force ratio ζ ₃ for the horizontal ground in the three-dimensional model is obtained, and this ratio (ζ ₃ / ζ ₂ ) is obtained. Bearing capacity ratio for direct foundation horizontal ground taking into account the three-dimensional effect by setting as a three-dimensional correction coefficient (β _C ) and multiplying the bearing capacity ratio ζ ₁ for the direct foundation horizontal ground obtained by the velocity field method There is provided a method for evaluating a bearing capacity of a foundation directly on a slope, comprising the step of obtaining (β _C · ζ ₁ ).

In the first aspect of the present invention, the bearing force ratio (ζ ₁ ) for the horizontal foundation of the direct foundation obtained by the velocity field method is to obtain the bearing force using a model treated as a two-dimensional plane strain problem. It has been confirmed from previous model experiments that it matches well with the bearing capacity problem. Therefore, in order to evaluate the three-dimensional effect appropriately based on the determination of the bearing force decrease rate due to the influence of the slope by the velocity field method, a correction coefficient (β _C ) based on the centrifugal model experiment is used. Is multiplied by the bearing capacity ratio (ζ ₁ ) of the direct foundation with respect to the horizontal ground obtained by the velocity field method, thereby appropriately evaluating the bearing capacity of the foundation directly on the slope.

The calculation of the three-dimensional correction coefficient (β _C ) is based on a two-dimensional model based on the direct basis of the object and a horizontal ground model prepared on the condition that the surrounding ground is a horizontal ground, and a slope prepared on the ground conditions reproducing the slope. A centrifugal model experiment was conducted for each of the ground models, and the bearing force ratio (ζ ₂ ) for the horizontal ground in the two-dimensional model was determined, and the direct foundation was used as the three-dimensional model, and the surrounding ground was prepared under the conditions of the horizontal ground. Centrifugal model experiments were performed on the horizontal ground model and the slope ground model produced under the ground conditions that reproduced the slope, respectively, and the bearing force ratio (ζ ₃ ) to the horizontal ground in the three-dimensional model was obtained, and the ratio between the two (ζ _{If 3} / ζ ₂ ) is obtained, the rate of increase due to the three-dimensional effect can be evaluated appropriately in a form close to reality.

  As a second aspect of the present invention according to claim 2, there is provided a method for evaluating a bearing capacity of a direct foundation on a slope according to claim 1, wherein the two-dimensional model of the direct foundation is a model produced by using a depth width of the direct foundation as a model width. .

  As a third aspect of the present invention according to claim 3, the three-dimensional model of the direct foundation is a similar model that reproduces the direct foundation installed in the vicinity of the slope in the depth width of the direct foundation. A bearing capacity evaluation method is provided.

  As described above in detail, according to the present invention, it is possible to appropriately consider the three-dimensional effect on the basis of obtaining the rate of decrease in bearing force due to the influence of the slope by the velocity field method.

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

[Calculation of bearing capacity by speed field method]
The procedure for calculating the bearing capacity of the slope direct foundation by the velocity field method proposed in Non-Patent Document 1 will be described below.

1. Horizontal ground bearing capacity
The work formed by the external force (q) acting on the foundation width (B) gives motion to a mass of unit volume weight (γ), the work component that the mass makes against the earth's gravity, and each element of the mass that moves Is equal to the sum of the components of the internal dissipation dissipated inside the mass by the relative speed difference between them and the adhesive force (c) there. That is, if L, M, and N are expressed as equations, the following equation (1) is obtained.

If the above equation (1) is arranged for the external force q, the following equation (2) is obtained.

The above formula (2) is a well-known formula for supporting Tertzagi. In the above equation (2), Nc and Nγ are expressed as a function including a geometric parameter that mathematically expresses the mechanism of the fracture and the material property value φ of the soil, and the following equations (3), ( It can be obtained by 4).

2. Bearing capacity calculation by the velocity field method According to the upper bound theorem, since it is guaranteed that the minimum q is closest to the correct value, q should be minimized with respect to the geometric parameter. A schematic diagram of the destruction mechanism by the velocity field method is shown in FIG. Triangle ABE is the main working rust, BC is a logarithmic spiral with E as the pole, and CD is a straight line reaching the slope slope. Assuming that the main working rust base angle ω is 45 ° + π / 2, the bearing force q is the slope θ, the distance to the shoulder (α · B), and the foundation width (B ) And the ratio α (hereinafter referred to as the separation distance ratio), and is expressed by the following equation (5).

Where l _CD : Length of straight line CD
S _CDEF : The area of quadrilateral CDEF From the above, to calculate the bearing capacity ratio (ζ ₁ ) of the direct foundation to the horizontal ground based on the velocity field method, the foundation on the slope is assumed to be horizontal ground. The support force q is obtained, the support force qs in the case of the slope ground is obtained by the velocity field method, and the ratio of both is obtained by the following equation (6).

Assuming that the foundation conditions are foundation width B: 2.4 m, foundation penetration depth Df: 3.7 m, ground conditions are c = 0, φ = 40.6 degrees, γ = 15.7 kN / m ³ , Under the condition that the slope angle is 35 °, the horizontal axis is the separation distance ratio α and the vertical axis is Drawing a graph with the bearing force ratio ζ ₁ against the ground gives the result shown in FIG.

[Centrifuge model experiment]
Centrifugal model experiment is a model experiment conducted using a 1 / N model in which centrifugal acceleration ((1 × N) G) N times the gravitational acceleration (1G) is applied by a centrifugal loading device. By acting on the model, the stress state generated in the model is equivalent to the actual state.

In the centrifuge model experiment, the direct foundation is made as a two-dimensional model by making the depth width of the direct foundation as a model width, and the horizontal ground model produced under the condition that the surrounding ground is horizontal ground, and the ground reproducing the slope. Centrifugal model experiments are performed on the slope ground model produced under the conditions, and the bearing force ratio (ζ ₂ ) for the horizontal ground in the two-dimensional model is obtained.

Further, the depth width of the direct foundation is a three-dimensional model by reproducing the direct foundation installed in the vicinity of the slope, and a horizontal ground model produced on the condition that the surrounding ground is horizontal ground, and the slope A centrifugal model experiment is performed for each of the slope ground models produced under the ground conditions that reproduce the above, and the bearing force ratio (ζ ₃ ) to the horizontal ground in the three-dimensional model is obtained.

[Calculation of bearing capacity considering three-dimensional effects]
If the ratio (ζ ₃ / ζ ₂ ) between the bearing force ratio ζ ₂ for the horizontal ground in the two-dimensional model and the bearing force ratio ζ ₃ for the horizontal ground in the three-dimensional model is obtained by the centrifugal model experiment, The ratio (ζ ₃ / ζ ₂ ) was set as a three-dimensional correction coefficient (β _C ), and the three-dimensional effect was taken into account by multiplying the bearing capacity ratio ζ ₁ for the direct horizontal ground obtained by the velocity field method. The bearing force ratio (β _C · ζ ₁ ) for the horizontal ground of the direct foundation is obtained.

1. Two-dimensional centrifugal model model The basic conditions (foundation width B: 2.4 m, foundation penetration depth Df: 3.7 m) for determining the bearing capacity ratio ζ ₁ for horizontal ground by the velocity field method shown in Fig. 2 A two-dimensional centrifuge model was prepared under ground conditions (c = 0, φ = 40.6 degrees, γ = 15.7 kN / m ³ ) and slope conditions (slope angle = 35 °). The scale of the centrifuge model is a 1/40 model, and the depth of the foundation is directly used as the model width in order to obtain a two-dimensional model. As shown in FIG. As shown in the model (Case-1) and Fig. 4, the distance b to the shoulder is 180mm as the slope condition and the separation ratio α is α = 3 (b / B = 180mm / 60mm)) Two centrifugal model models with the slope model (Case-2) were prepared (see Table 1 below).

2. Three-dimensional Centrifuge Model model also shown in FIG. 2, basal conditions (basal width determined bearing capacity ratio zeta ₁ relative to the horizontal ground the speed field method B: 2.4 m, embedment depth of the foundation Df: 3.7 m ), Ground conditions (c = 0, φ = 40.6 degrees, γ = 15.7 kN / m ³ ) and slope conditions (slope angle = 35 °), a three-dimensional centrifuge model was prepared. The scale of the centrifuge model is a 1/40 model, and in order to make a three-dimensional model, the depth width of the direct foundation is a half-section similar model that reproduces the direct foundation, and as shown in FIG. As shown in FIG. 6, the horizontal ground model (Case-3) produced on the condition that the surrounding ground is horizontal ground, and as shown in FIG. 6, the distance b to the shoulder is 90 mm and the separation distance ratio α is α = 1. 5 (b / B = 90mm / 60mm)) and the slope condition model (Case-4), and as shown in Fig. 7, the distance b to the shoulder is 180mm and the separation ratio α Is a slope ground model (Case-5) in which α = 3.0 (b / B = 180mm / 60mm)), and as shown in Fig. 8, the distance b to the shoulder is 270mm as the slope condition. Four centrifugal model models with a slope ground model (Case-6) with a separation distance ratio α = 4.5 (b / B = 270mm / 60mm)) (See Table 2 below).

3. Results of centrifugal model experiment
(1) Two-dimensional model Fig. 9 shows the results of a two-dimensional model centrifuge model experiment. In the case of a two-dimensional model, when the model is observed, slip lines are clearly formed, indicating a failure mode close to general failure. The inflection point appears clearly also in the graph of FIG. 9, and the bearing force ratio ζ _{2 with} respect to the horizontal ground was ζ ₂ = 0.65 (26.0 kN / 40.0 kN). The strain level is about 12 to 17% within a range where an inflection point (break point) is observed.

(2) Three-dimensional model Fig. 10 shows the results of a three-dimensional model centrifuge model experiment. In the case of a three-dimensional model, a clear inflection point of load displacement does not appear and a curve that rises slowly is drawn. That is, in the case of the three-dimensional mode, it is presumed that the inflection point did not appear because the local fracture mode in which the fracture progresses locally is shown.

The support force ratio ζ ₃ is obtained for Case-5 having a separation distance ratio (b / B) of 3.0 that can be compared with the two-dimensional mode. In the three-dimensional mode, since the inflection point does not appear, the bearing force ratio ζ ₃ is obtained for the position of the strain level 10% and the position of 30%. The bearing force ratio ζ _{3 (10)} for the horizontal ground at a strain level of 10% is ζ _{3 (10)} = 0.85 (7.0 kN / 8.2 kN), and the bearing force ratio ζ ₃ for the horizontal ground at a strain level of 30%. ₍₃₀₎ was ζ _{3 (30)} = 0.75 (12.2 kN / 16.2 kN).

4). Calculation of correction coefficient for three-dimensional effect Ratio (ζ ₃ / ζ ₂ ) (bearing force ratio ζ ₂ for horizontal ground in the two-dimensional model and bearing force ratio ζ ₃ for horizontal ground in the three-dimensional model (three-dimensional correction coefficient) β _C ) is summarized as shown in Table 3 below.

As shown in Table 3 above, when the distortion level of the three-dimensional model is 10%, the three-dimensional correction coefficient β _C is β _C = 1.30, and when the distortion level of the three-dimensional model is 30%, the three-dimensional correction coefficient β _C is β _C = 1.15. In this embodiment, the three-dimensional correction coefficient β _C is calculated for the strain levels of 10% and 30%, but the strain level is determined appropriately by the designer in consideration of the importance of the target structure and the allowable displacement amount. A proper distortion level may be set.

5. Application to the velocity field method Once the three-dimensional correction coefficient β _C is calculated, the horizontal ground of the direct foundation considering the three-dimensional effect by multiplying the bearing capacity ratio ζ ₁ for the horizontal ground of the direct foundation obtained by the velocity field method. The bearing force ratio (β _C · ζ ₁ ) can be obtained. Specifically, as shown in FIG. 11, if a straight line obtained by multiplying the linear gradient of the bearing force ratio ζ _{1 with} respect to the horizontal ground obtained by the velocity field method 1.30 times and 1.15 times is drawn, the three-dimensional effect is obtained. It becomes a linear gradient of the bearing capacity ratio considered.

[Other examples]
(1) In the above embodiment, the bearing capacity ratio (β _C · ζ for the direct foundation horizontal ground considering the three-dimensional effect by multiplying the bearing capacity ratio ζ ₁ for the foundation foundation horizontal ground obtained by the velocity field method. ₁ ). However, the support force directly obtained by the analysis by the velocity field method may be multiplied by the three-dimensional correction coefficient β _C to obtain the support force on the slope base. .

It is a schematic diagram of the destruction mechanism by a velocity field method. It is the graph of the bearing force ratio (zeta) ₁ calculated | required by the velocity field method with respect to a separation distance ratio-horizontal ground. A horizontal ground model (Case-1) produced under the two-dimensional model condition is shown, (A) is a model plan view, and (B) is a model side view. A slope ground model (Case-2) produced under the two-dimensional model conditions is shown, (A) is a model plan view, and (B) is a model side view. A horizontal ground model (Case-3) produced under three-dimensional model conditions is shown, (A) is a model plan view, and (B) is a model side view. A slope ground model (Case-4) produced under three-dimensional model conditions is shown, (A) is a model plan view, and (B) is a model side view. A slope ground model (Case-5) produced under three-dimensional model conditions is shown, (A) is a model plan view, and (B) is a model side view. A slope ground model (Case-6) produced under three-dimensional model conditions is shown, (A) is a model plan view, and (B) is a model side view. It is a graph which shows the centrifuge model experiment result of a two-dimensional model. It is a graph which shows the centrifuge model experiment result of a three-dimensional model. It is the graph which correct | amended the bearing force ratio (zeta) ₁ with respect to the horizontal ground by the speed field method in consideration of the three-dimensional effect. It is a bearing capacity fall rate graph with respect to the horizontal ground which contrasted the solution result by the speed field method, and other analysis methods.

Claims (3)

A method for evaluating the compressive bearing capacity of a direct foundation installed near a slope,
Calculating a bearing force ratio (ζ ₁ ) to the horizontal ground of the direct foundation based on a velocity field method;
Using the direct foundation as a two-dimensional model, the horizontal ground model produced under the condition that the surrounding ground is horizontal ground, and the slope ground model produced under the ground conditions reproducing the slope, respectively, were subjected to a centrifugal model experiment, respectively. Determining a bearing capacity ratio (ζ ₂ ) for the horizontal ground in the model;
Using the 3D model for the direct foundation and the horizontal ground model with the surrounding ground as the horizontal ground, and the slope ground model manufactured with the ground conditions reproducing the slope, respectively, we performed a centrifugal model experiment, Determining a bearing capacity ratio (ζ ₃ ) for the horizontal ground in the model;
A ratio (ζ ₃ / ζ ₂ ) between the bearing force ratio ζ ₂ for the horizontal ground in the two-dimensional model and the bearing force ratio ζ ₃ for the horizontal ground in the three-dimensional model is obtained, and this ratio (ζ ₃ / ζ ₂ ) is obtained. Bearing capacity ratio for direct foundation horizontal ground taking into account the three-dimensional effect by setting as a three-dimensional correction coefficient (β _C ) and multiplying the bearing capacity ratio ζ ₁ for the direct foundation horizontal ground obtained by the velocity field method And (β _C · ζ ₁ ). A method for evaluating a bearing capacity of a direct foundation on a slope.   2. The method for evaluating the bearing capacity of a direct foundation on a slope according to claim 1, wherein the two-dimensional model of the direct foundation is a model produced by using the depth width of the direct foundation as a model width.   The method for evaluating the bearing capacity of a direct foundation on a slope according to claim 1, wherein the three-dimensional model of the direct foundation is a similar model that reproduces the direct foundation installed in the vicinity of the slope with the depth width of the direct foundation.

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