Learn: Uniform surcharge earth thrust
A uniform surface surcharge adds horizontal pressure to a retaining wall in addition to the soil’s own weight. Under the stated active-pressure model, that added pressure is constant with depth.
What the formula is saying
Convert the vertical surcharge q to horizontal pressure Ka q. Integrating a constant pressure over wall height H gives a rectangular diagram area, so there is no one-half factor.
Read the symbols in plain language
- Ka
- Active coefficient
Active coefficient. The active coefficient scales the supplied vertical uniform surcharge pressure.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- q
- Uniform surcharge
Uniform surcharge. The active coefficient scales the supplied vertical uniform surcharge pressure.
kPaOne kilopascal equals one kN/m² and 1000 Pa.
- H
- Retained height
Retained height. Constant pressure multiplied by wall height gives thrust per metre of wall.
mMetres measure length; 1 m = 1000 mm.
- Pq
- Result to find
Uniform surcharge earth thrust. Constant pressure multiplied by wall height gives thrust per metre of wall.
kN/m
Sort out the units first
q is kPa, H is m and Ka is dimensionless. The thrust is kN/m of wall. q here means surcharge pressure, not flow rate or bearing resistance.
Assumptions before calculating
The surcharge is uniform and sufficiently extensive for the stated constant horizontal-pressure idealization. The active state and coefficient are appropriate to the backfill and wall movement.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find Pq and explain the result in the stated output unit.
- Ka · Active coefficient
- 0.333
- q · Uniform surcharge
- 10 kPa
- H · Retained height
- 5 m
Convert surcharge to horizontal pressure
The active coefficient scales the supplied vertical uniform surcharge pressure.
(0.333) × (10) = 3.33 kPaIntegrate the rectangular pressure diagram
Constant pressure multiplied by wall height gives thrust per metre of wall.
(3.33) × (5) = 16.65 kN/m
Does this worked answer make sense?
The resultant of the uniform added pressure acts at H/2 above the base. Doubling H doubles surcharge thrust, unlike the H² dependence of triangular self-weight thrust.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- Ka · Active coefficient
- 0.3
- q · Uniform surcharge
- 15 kPa
- H · Retained height
- 4 m
Convert surcharge to horizontal pressure
The active coefficient scales the supplied vertical uniform surcharge pressure.
(0.3) × (15) = 4.5 kPaIntegrate the rectangular pressure diagram
Constant pressure multiplied by wall height gives thrust per metre of wall.
(4.5) × (4) = 18 kN/m
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- Ka · Active coefficient
- 0.4
- q · Uniform surcharge
- 12 kPa
- H · Retained height
- 5 m
Find: Learn: Uniform surcharge earth thrust
A hint, not the answer
Convert the vertical surcharge q to horizontal pressure Ka q. Integrating a constant pressure over wall height H gives a rectangular diagram area, so there is no one-half factor.
q is kPa, H is m and Ka is dimensionless. The thrust is kN/m of wall. q here means surcharge pressure, not flow rate or bearing resistance.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Convert surcharge to horizontal pressure
The active coefficient scales the supplied vertical uniform surcharge pressure.
(0.4) × (12) = 4.8 kPaIntegrate the rectangular pressure diagram
Constant pressure multiplied by wall height gives thrust per metre of wall.
(4.8) × (5) = 24 kN/m
Avoid the common trap
Do not use the triangular self-weight factor 1/2 for this rectangular component. Do not add a surface line load in kN/m directly as a pressure in kPa.
When this method applies — and when it does not
Finite strip, line or point loads can produce a different distribution. This adds only the surcharge component; soil self-weight, water and other actions must be evaluated separately.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
One idea understood. Keep going.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Uniform surcharge earth thrust. Read the relevant soil phase, seepage, earth-pressure, settlement or foundation topic. Effective stress, drainage and idealized geometry determine whether the relationship applies.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.