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過給荷重による側方土圧

Calculating Lateral Earth Pressure due to Surcharge Loads on Retaining Wall

追加荷重による側方土圧の計算擁壁の両側の土壌ゾーンには、通常、いくつかの追加の外部荷重が適用されます. Those can be live surcharge loads on the retaining wall such as vehicular traffic, pedestrian traffic, and parking, or permanent loads such as protection systems against slope erosion, and adjacent structures. 記事上で, we will focus on how to calculate the lateral earth pressure acting on the backface of a Retaining Wall due to three types of superimposed or surcharge loads:

  • 追加荷重による側方土圧の計算 3種類の重ね荷重により擁壁の背面に作用する側方土圧の計算方法に焦点を当てます。
  • 3種類の重ね荷重により擁壁の背面に作用する側方土圧の計算方法に焦点を当てます。 3種類の重ね荷重により擁壁の背面に作用する側方土圧の計算方法に焦点を当てます。
  • 3種類の重ね荷重により擁壁の背面に作用する側方土圧の計算方法に焦点を当てます。 3種類の重ね荷重により擁壁の背面に作用する側方土圧の計算方法に焦点を当てます。

追加荷重による側方土圧の計算擁壁の両側の土壌ゾーンには、通常、いくつかの追加の外部荷重が適用されます

追加荷重による側方土圧の計算擁壁の両側の土壌ゾーンには、通常、いくつかの追加の外部荷重が適用されます

When the applied permanent or live surcharge load on the retaining wall is uniform and can be assumed that it is an infinite distributed load, 追加荷重による側方土圧の計算擁壁の両側の土壌ゾーンには、通常、いくつかの追加の外部荷重が適用されます. For that reason, the location of the resultant is in the middle of the wall’s total height. In the case of a sloped backfill, the pressure distribution skews an angle equal to the backfill inclination. この場合, the calculation of the resultant goes as follows:

  • For soil in at-rest condition:

\(P_{dist, \; at-rest} = K_{0} \cdot q \cdot H_{土}\)

  • cdot q cdot H_soil :

\(P_{dist, \; 下部構造土} = K_{a} \cdot q \cdot H_{土}\)

  • cdot q cdot H_soil :

\(P_{dist, \; passive} = K_{p} \cdot q \cdot H_{土}\)

前に述べたように, since the distribution is uniform, the location of the resultant is located right in the middle of the soil height.

Cantilever Concrete Retaining Wall showing Lateral Earth Pressure due to Uniform Load

Adapted from: それか, B. M. (2010). 基礎工学の原則, SI Edition. 章 7 Lateral Earth Pressure. Cengage Learning. 図 7.3

Patch Load

For the case of a patch or strip surcharge load on a retaining wall, the total force per unit length may be expressed as:

\(P_{パッチ} = frac{q}{90} [H(\theta_2-\theta_1)]\)

どこ,

\(\theta_1 = tan^{-1}(\フラク{b’}{H}) (君は)\)

\(\theta_2 = tan^{-1}(\フラク{a’ + b’}{H}) (君は)\)

This resultant force from the lateral earth pressure due to a patch or strip load is located at \(\バー{と}\) measured from the bottom of the pressure distribution, \(\バー{と}\) may be estimated using the following expression:

\(\バー{と} = H – [\フラク{H^2(\theta_2-\theta_1) + (R-Q) – 57.3a’H}{2H(\theta_2-\theta_1)}]\)

どこ \(R = (a’+b’)^2\cdot(90 – \theta_2)\) そして \(Q = b’^2(90-\theta_1)\)

Cantilever Concrete Retaining Wall showing Lateral Earth Pressure due to Strip or Patch Load

Taken from: それか, B. M. (2010). 基礎工学の原則, SI Edition. 章 7 Lateral Earth Pressure. Cengage Learning. 図 7.14

Line Load

最後に, for the case of a line surcharge load on a retaining wall, the stress on a retaining wall backface at any depth \(z\), can be expressed as:

\(\sigma = \frac{4q}{\pi H} \フラク{a^2 b}{(a^2 + b^2)^ 2}\) ために \(a > 0.4\)

\(\sigma = \frac{q}{H} \フラク{0.203 b}{(0.16+ b^2)^ 2}\) ために \(a \leq 0.4\)

Cantilever Concrete Retaining Wall showing Lateral Earth Pressure due to Line Load

Taken from: それか, B. M. (2010). 基礎工学の原則, SI Edition. 章 7 Lateral Earth Pressure. Cengage Learning. 図 7.14

Integrating the expressions above from \(b = 0\) に \(b = 1\), it is possible to get the value of the resultant force due to the stress distributions of the applied line load:

\(P_{line} = \int_{0}^{H}\sigma \,dz = – \フラク{4 H^2 a^{2} q}{2 H^2 a^{2} \パイ + 2 H^2 \pi} + \フラク{2 q}{\パイ} = frac{2 q}{\pi \left(a^{2} + 1\正しい)}\) ために \(a > 0.4\)

\(P_{line} = \int_{0}^{H}\sigma \,dz = 0.546875 q \) ために \(a \leq 0.4\)

For calculating the location of the resultant force, the initial expressions for the stress at any depth are integrated over two intervals, one from \(b = 0\) に \(b = b_r\) and the other from \(b = b_r\) に \(b = 1\), after that, both expressions are plugged into an equation and its solution is the location of the resultant force from the lateral pressure distribution:

\(\バー{と} = H \left(1 – a \sqrt{\フラク{1}{2 a^{2} + 1}}\正しい)\) ために \(a > 0.4\)

\(\バー{と} = H (1- 0.348155311911396) \) ために \(a \leq 0.4\)

結論

Correctly estimating the lateral earth pressure resultant force due to superimposed loads and its location is a crucial step in the Retaining Wall Design Process. For more information about how this lateral earth pressure is included in the Retaining Wall Design Process, refer to the article ここに.

Apart from the lateral earth pressure due to surcharge loads, the self-weight of the soil also exerts pressure on the Retaining Wall’s backface, the details of how to calculate this pressure for different soil conditions like at-rest, 下部構造土, and passive are discussed in another article ここに.

参考文献

それか, B. M. (2010). 基礎工学の原則, SI Edition. 章 7 Lateral Earth Pressure. Cengage Learning.

擁壁計算機

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