Calculate hydraulic gradient, critical gradient and a simple heave stability ratio, with clear limits for piping and internal erosion assessment.
Critical Hydraulic Gradient and Hydraulic Heave
Upward seepage reduces effective stress. When the hydraulic gradient approaches a critical value, soil particles can lose effective confinement and the ground may become unstable. This page presents a screening calculation for hydraulic heave and clearly separates it from a full piping or internal erosion assessment.
Note: This is draft calculation guidance and should be reviewed by a qualified geotechnical engineer. Excavation, cofferdam and dewatering design requires a site-specific seepage and stability assessment.
Inputs and units
| Symbol | Description | Typical unit |
|---|---|---|
| \(\Delta h\) | Hydraulic head difference | m |
| \(L\) | Seepage path length over which the head loss is assessed | m |
| \(i\) | Hydraulic gradient | dimensionless |
| \(G_s\) | Specific gravity of soil solids | dimensionless |
| \(e\) | Void ratio | dimensionless |
| \(\gamma'\) | Submerged unit weight of soil | kN/m³ |
| \(\gamma_w\) | Unit weight of water | kN/m³ |
| \(i_c\) | Critical hydraulic gradient | dimensionless |
| \(i_{exit}\) | Assessed exit gradient | dimensionless |
Hydraulic gradient
For a head loss \(\Delta h\) over a seepage length \(L\):
$$ i=\frac{\Delta h}{L} $$The relevant value for heave is commonly the upward gradient in the critical soil zone. A simple overall head difference divided by a convenient distance may not represent the local exit gradient.
Critical hydraulic gradient
For a saturated soil, the idealised critical gradient can be expressed as:
$$ i_c=\frac{\gamma'}{\gamma_w} $$Using phase relationships, this becomes:
$$ i_c=\frac{G_s-1}{1+e} $$This relationship represents the condition at which upward seepage force balances the submerged weight in the idealised soil mass. Soil fabric, stratification, anisotropy, defects and internal erosion susceptibility are not captured by the equation.
Simple heave stability ratio
A screening ratio may be calculated as:
$$ FS_{heave}=\frac{i_c}{i_{exit}} $$This ratio should be labelled as a hydraulic heave ratio or factor of safety, according to the project convention. The required value is not universal and must come from the applicable design basis, consequence assessment and engineering judgement.
Worked example
Assume:
- \(G_s=2.65\)
- \(e=0.65\)
- assessed upward exit gradient \(i_{exit}=0.40\)
The idealised critical gradient is:
$$ i_c=\frac{2.65-1}{1+0.65}=1.00 $$The simple heave stability ratio is:
$$ FS_{heave}=\frac{1.00}{0.40}=2.50 $$The numerical result is illustrative. It does not by itself demonstrate that an excavation or structure is safe.
Important limitations
- A hydraulic heave check is not a complete piping or internal erosion assessment.
- The exit gradient should come from an appropriate seepage model, flow net, instrumented field assessment or other defensible method.
- Concentrated leakage, joints, filters, drains, layered soils and three-dimensional flow can control behaviour.
- Verify the groundwater boundary conditions and whether soil properties represent the critical layer and design state.
- Dewatering-induced settlement, base uplift, hydraulic fracture and global stability may require separate checks.
- No default acceptable factor of safety is applied on this page.
Related calculations
- Darcy Flow and Hydraulic Gradient
- Effective Stress in Soil
- Soil Phase Relationships and Soil Properties