Retaining Walls
Earth pressure on cantilever and gravity walls, with overturning, sliding and bearing checks, also in earthquakes.
Computes the active earth pressure behind a cantilever or gravity wall by Rankine or Coulomb theory, adds the surcharge, the Mononobe–Okabe seismic increment and the inertia of the wall, and checks the wall against overturning, sliding, eccentricity and bearing pressure with the factors of safety used in design practice. The section is drawn to scale with the pressure diagrams, the forces and the contact pressure under the base, and every force and moment is listed.
Overview
Retaining walls hold back the ground at road cuts, basements, bridge abutments, river banks and terraces. Most failures come from underestimating the thrust: a sloping backfill, a road surcharge, blocked drainage or an earthquake. The tool shows how each of these changes the safety of the wall.
The geometry is the same for both wall types: a gravity wall is entered with a wide stem, a cantilever wall with a thin stem and a long heel that carries soil.
What you enter · What you get
What you enter
- Wall height, base width, toe, base thickness, stem widths and unit weight
- Backfill friction angle, unit weight, slope, surcharge and wall friction
- Foundation soil strength, embedment, allowable bearing pressure and seismic coefficient
What you get
- Factors of safety against overturning and sliding
- Eccentricity and maximum and minimum base pressure
- Scaled section with pressure diagrams and forces
- Table of forces and moments (CSV)
How it works in the field
Method and equations
Active earth pressure
Rankine for a sloping backfill on the vertical plane through the heel (soil above the heel moves with the wall), or Coulomb with wall friction δ on a vertical back. The surcharge adds a uniform pressure Ka·q.
Earthquake
Mononobe–Okabe coefficient KAE; the increment ½γH′²(KAE − Ka) acts at 0.6 H′ (Seed & Whitman 1970), and the wall inertia kh·W acts at the centroids of the stem and base.
Stability checks
Overturning about the toe (required 2.0, or 1.5 with earthquake); sliding with base friction tan(⅔φ′), adhesion ⅔c′ and optional Rankine passive resistance (required 1.5, or 1.1); resultant within the middle third (B/6, or B/4 with earthquake); trapezoidal or triangular base pressure against the allowable value.
Accuracy and error limits
- Classical earth pressure theories give the thrust within about ±10–15 % when the wall moves enough to mobilise active conditions; for a stiff wall that cannot move, the at-rest pressure is 40–60 % higher. Mononobe–Okabe is approximate and becomes unreliable for high kh or steep backfills.
- The largest uncertainties are the backfill friction angle (2° changes Ka by about 7 %), water pressure behind a badly drained wall (not modelled; it can double the thrust) and the base friction. The tool checks external stability only, not the reinforcement or global slope stability.
- To reduce the error: test the backfill material that will actually be placed, specify a drainage layer with weep holes, count passive resistance only where the front soil cannot be removed, and check global stability of walls on slopes with the Slope Stability tool.
Who uses it
Standards and references
- Rankine, W.J.M. (1857). On the stability of loose earth. Philosophical Transactions of the Royal Society of London, 147, 9–27.
- Coulomb, C.A. (1776). Essai sur une application des règles de maximis et minimis à quelques problèmes de statique relatifs à l’architecture. Mémoires de l’Académie Royale des Sciences, 7, 343–382.
- Okabe, S. (1926). General theory of earth pressure. Journal of the Japan Society of Civil Engineers, 12; Mononobe, N. & Matsuo, H. (1929). On the determination of earth pressure during earthquakes. World Engineering Congress, Tokyo.
- Seed, H.B. & Whitman, R.V. (1970). Design of earth retaining structures for dynamic loads. ASCE Specialty Conference on Lateral Stresses in the Ground and Design of Earth-Retaining Structures, 103–147.
- Das, B.M. & Sivakugan, N. (2019). Principles of Foundation Engineering, 9th ed. Cengage.
At a glance
- Category
- Engineering & geotechnics
- Runs on
- Phone, tablet and desktop browser
- Export
- Wall section as PNG, JPG and PDF; forces and moments as CSV; full PDF report
- Access
- Free
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