Formula used
Active earth coefficient (Rankine): Ka = tan²(45° − φ/2). The soil pressure resultant is Pa = ½·Ka·γ·H², acting at H/3.
Surcharge pressure: Pq = Ka·q·H, acting at H/2.
Hydrostatic pressure: Pw = ½·γw·h², acting at h/3. Land-side water is driving; sea-side water is resisting.
Uplift under base (trapezoid): U = ½·γw·B·(hheel + htoe)·Cu. Net vertical is V = W + Vq − U, where W = γc·A.
Sliding check: FS = (μ·V + Pp + T) / Hd. Passive is optional: Pp = ½·Kp·γ·d²·Rp, with Kp = tan²(45° + φ/2).
Overturning and bearing: Moments are taken about the toe. Bearing uses eccentricity e = B/2 − x and qmax = (V/B)(1 + 6e/B), qmin = (V/B)(1 − 6e/B).
How to use this calculator
- Enter geometry, then choose wall area input or B × H.
- Provide soil unit weight and friction angle for Ka and Kp.
- Add surcharge and water levels for land and sea sides.
- Set uplift heads and coefficient to reflect drainage conditions.
- Optionally include toe passive resistance and anchorage force.
- Press Calculate, then review safety factors and pressures.
- Export CSV or PDF to store the current run.
Stability checks supported
The calculator evaluates sliding, overturning, and bearing pressure for a gravity quay wall per meter run. Horizontal driving force combines Rankine active soil pressure, surcharge pressure, and land-side hydrostatic pressure, minus sea-side hydrostatic pressure. Sliding resistance includes base friction, optional passive resistance at the toe, and optional tie-back force, enabling rapid comparisons between unanchored and anchored conditions.
Input data and practical ranges
Backfill unit weight typically ranges from 16–20 kN/m³, while friction angle often falls between 28–38 degrees for granular materials. Surcharge values can represent container stacking, vehicle loads, or storage zones, commonly 5–50 kPa depending on operations. Water levels should reflect design tide, storm surge, and drainage behind the wall. Base friction coefficients between 0.4–0.7 are common, but should match interface conditions and construction details.
How to read safety factors
Sliding factor of safety compares resisting horizontal capacity to the net driving force. Overturning factor of safety compares stabilizing moments about the toe to overturning moments from lateral loads. Bearing checks compute average contact pressure and adjust it using eccentricity to estimate qmax and qmin. If qmin becomes negative, part of the base is in tension and a wider base, reduced loads, or a revised wall section is usually required.
Water, uplift, and drainage sensitivity
Water has two competing effects: hydrostatic pressure can add or reduce driving demand depending on the level difference, while uplift reduces effective vertical load and therefore sliding resistance and bearing capacity. The uplift coefficient and heel/toe heads allow you to model improved drainage (lower uplift) versus blocked drains (higher uplift). Small changes in assumed uplift can shift qmax and sliding FS noticeably, so confirm drainage, filters, and weep paths early.
Documentation and engineering review
Use the export options to keep a calculation trail for design reviews. Record the governing case, input assumptions, and the resulting safety factors and bearing pressures. For concept design, run multiple scenarios: maximum surcharge, highest retained water, lowest friction, and reduced passive mobilization. For detailed design, verify earth pressure models, staged construction, seismic methods, and geotechnical bearing parameters with project-specific standards.
FAQs
Which wall types does this tool fit best?
It is most suitable for gravity-type quay walls where stability is governed by weight, base friction, and lateral pressures. It can also screen anchored gravity walls by including a tie-back force.
What does Ka represent in the results?
Ka is the Rankine active earth pressure coefficient computed from the friction angle. It scales both the triangular soil pressure from unit weight and the rectangular surcharge component.
Why can qmin become negative?
Negative qmin indicates the resultant shifts toward the toe enough to create uplift (tension) at the heel. This suggests potential rocking, loss of contact, or cracking unless the section is revised.
How should I choose the uplift coefficient?
Use lower values when drainage and pressure relief are reliable, and higher values when drains may clog or water can be trapped. Confirm with site drainage details and groundwater observations.
Does the seismic option replace a detailed method?
No. The seismic option applies a simple multiplier to driving actions for screening only. Final design should use a recognized seismic earth-pressure approach and project code requirements.
What should I export for a design submittal?
Export the governing scenario and include geometry, soil parameters, water levels, uplift assumptions, surcharge, and anchors. Attach the CSV for traceability and the PDF for quick review.
Example data table
| Case | H (m) | B (m) | φ (deg) | q (kPa) | Hw (m) | Hwt (m) | μ | T (kN/m) | FS slide | FS overturn | qmax (kPa) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Typical | 10 | 6 | 30 | 15 | 6 | 6 | 0.55 | 0 | ≈ 1.7 | ≈ 2.2 | ≈ 160 |
| High surcharge | 10 | 6 | 30 | 40 | 6 | 6 | 0.55 | 0 | ≈ 1.1 | ≈ 1.5 | ≈ 210 |
| Anchored | 10 | 6 | 30 | 40 | 6 | 6 | 0.55 | 200 | ≈ 2.0 | ≈ 2.8 | ≈ 150 |
Notes and limitations
- This is a screening-level tool for gravity-type quay walls.
- It uses Rankine pressures and simplified water and uplift assumptions.
- Seismic adjustment is a simple multiplier, not Mononobe–Okabe.
- For final design, perform detailed geotechnical and structural checks.