# Method and assumptions

How Rischio calculates a retaining wall: units and conventions, the key assumptions, and the method from earth pressure to bearing capacity.

How Rischio calculates a retaining wall: the units and conventions, the key assumptions and, in order, the method, with a page for each of its parts. The [overview](https://rischio.io/docs/retaining-wall/) shows how a model is built.

## Units and conventions

-   SI units: m, kN, kPa, kN/m³ and degrees, for a section one metre long: forces in kN/m, moments in kN·m/m.
-   $x$ runs from the toe, the front edge of the base ($x = 0$), towards the backfill; heights, up from the bottom of the base. Moments are taken about the toe.
-   Behind the wall, depths are measured down from the crest; in front, down from the ground at the toe, so water standing above that ground has a negative depth.
-   $\beta$ is the slope of the backfill. $\phi$, $c$, $\gamma$ and $\gamma_{sat}$ are a stratum’s friction angle, cohesion, unit weight and saturated unit weight, and $\gamma' = \gamma_{sat} - \gamma_w$. The studio’s form writes $\varphi'$ and $c'$; the equations in these pages and in the report write $\phi$ and $c$.
-   $q$ is the surcharge in the earth pressure and the overburden at the base in the bearing capacity, as in the report.
-   The unit weight of water is $\gamma_w = 9.81$ kN/m³.

## Key assumptions

-   A two-dimensional section under static loads.
-   The soil between the wall and the [virtual back](https://rischio.io/docs/retaining-wall/theory/earth-pressure/#active-thrust) moves with the wall: it adds its weight, and the earth pressure acts on the virtual back.
-   The soil above the toe adds no weight.
-   A surcharge pushes the wall, but its weight over the heel doesn’t resist, as usual for variable loads.
-   Soil carries no tension: a negative active pressure is taken as zero.
-   Water is hydrostatic on each side of the wall, with no seepage.
-   If the wall is embedded, the passive resistance counts in full, against sliding only.

## The method

Each part of the method has its own page, in this order. [Earth pressure](https://rischio.io/docs/retaining-wall/theory/earth-pressure/) covers the thrusts on the wall: Rankine’s active thrust on the virtual back, the water and the surcharge behind the wall and, if the wall is embedded, the passive resistance in front. With the weights and the uplift, those thrusts give the [stability](https://rischio.io/docs/retaining-wall/theory/stability/) checks: overturning about the toe, sliding on the base and the eccentricity of the resultant. The base is then checked as a strip footing for [bearing capacity](https://rischio.io/docs/retaining-wall/theory/bearing-capacity/). A [gabion wall](https://rischio.io/docs/retaining-wall/theory/gabions/) goes through all of this whole, and then level by level. [Equations](https://rischio.io/docs/retaining-wall/equations/) has every step, in the order of the calculation report.

## References

-   Das, B. M., & Sivakugan, N. (2017). *Principles of Foundation Engineering*, SI edition, 9th ed. Cengage Learning. It gives each method on these pages with its original source.

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Source: https://rischio.io/docs/retaining-wall/theory/