Analysis tools for ground-related structures and improvement.
Retaining wall
Foundation
Tunnels
Ground improvement
Slope stability
Gravity Wall Stability
Method: Coulomb earth pressure; EN 1997-1 DA1 (or factors of safety) for sliding, overturning about the toe and bearing (Annex D) with eccentricity.
Geometry
Rubble base
Water, loads and concrete
Soil layers characteristic values · bulk γ (γ − 10 used below water)
| Layer | Level (m) | γ kN/m³ | c′ kPa | φ′ deg | cu kPa |
|---|---|---|---|---|---|
| 1 Backfill | – | ||||
| 2 Embedment ds | – | ||||
| 3 Beside slab dc | – | ||||
| 4 Foundation | – |
Interface friction and passive
δ = ratio × φ′d (wall back, wall front, base). fp = fraction of passive relied on; Δa = unplanned lowering of front ground (EC7 9.3.2.2).
| Combination | γQ | γG,sup | γG,inf | γR,c′ | γR,φ′ | γR,cu |
|---|---|---|---|---|---|---|
| EC7-DA1C1 | ||||||
| EC7-DA1C2 |
Both combinations are calculated. γR,c′, γR,φ′, γR,cu divide c′, tan φ′, cu; γR,v = γR,h = 1.0.
Required factors of safety (editable). All loads and soil parameters un-factored.
Consolidation Settlement
Method: One-dimensional consolidation (Cc, Cr, OCR) solved by finite differences in time; radial drainage to PVDs by Hansbo (1981) with smear and well resistance.
Loads
Timing and live load
Levels in m (e.g. mCD / mRL). The fill is placed to FL0 at t = 0. Its effective weight is γ1·(part above WL) + (γsat − γw)·(part below WL), recalculated as it settles: fill that sinks below WL loses (γ1 − γ'1)·Δδ. At tr the fill is cut down so that its top is at DPL when the live load starts; the cut thickness is found by iteration (it allows for the settlement or rebound between tr and tLL).
Soil parameters layers from the top down · z = depth below the top of the profile
New fill: a layer placed on the existing ground (e.g. soft clay fill); it consolidates too and its weight loads the existing soil. Fill layers must be at the top. Pc(z) = Pc + ΔPc/Δz·(z − z0) below z0; where Pc is below the in-situ stress the soil is taken as normally consolidated. ρ = bulk (saturated) density; the page checks it against (Gs + e0)/(1 + e0).
Settlement at time t
Drainage
Hansbo (1981): de = 1.128 S (square) or 1.05 S (triangular), dw = (a + b)/2, μ = ln(n/s) + (kh/ks)·ln(s) − 0.75 (well resistance not included). Radial drainage acts above the PVD toe, vertical drainage everywhere.
Smear defaults – Singapore marine clay: s = ds/dw = 4 and kh/ks = 2, from the back-analysis of the Changi East reclamation pilot tests (design range s = 4–5, kh/ks = 2–3; PVD 100 × 3–4 mm at 1.5 m square). The same work gives ch = 2–4 m²/yr (upper marine clay) and 3–6 m²/yr (lower marine clay) in the normally consolidated range. Use these smear values with ch from laboratory or CPTU tests (undisturbed soil). If ch is back-calculated from field settlement (e.g. Asaoka, about 1 m²/yr at Changi), smear is already included in it: set s = 1 and kh/ks = 1 to avoid counting it twice.
Ref.: Chu, J., Bo, M.W. & Arulrajah, A. (2009). Soil improvement works for an offshore land reclamation. Proc. ICE – Geotechnical Engineering 162(GE1), 21–32. See also Chu, Bo & Choa (2004), Geotextiles and Geomembranes 22, 101–117; Bo et al. (2002), ASCE JGGE 128(9).
Inputs changed – press Calculate at time t to update all results.
Stone Column – Settlement Improvement
Method: Priebe (1995): basic improvement factor n0, column compressibility, depth factor fd and compatibility limits, sublayers of 0.5 m; bulging by Hughes & Withers (1974); consolidation by Hansbo with Han & Ye (2001).
Stone columns
Load and ground water
Soil layers from the top of the soil down · Ds = constrained (oedometer) modulus = 1/mv · cu = 0 for granular soil
Priebe (1995): the columns improve the soil down to their toe; below the toe the soil is unimproved and carries the full pressure p (wide load, no spreading). Settlement without columns s0 = p·h/Ds for each sublayer of up to 0.5 m. γ′ = effective unit weight below the water table (normally γ − 10).
Column capacity (bulging)
Rate of consolidation
Shallow Footing – Bearing Capacity
Method: Bearing capacity factors with shape, depth and inclination factors (EN 1997-1 Annex D, Vesić, Hansen, Meyerhof or Terzaghi, after Bowles); effective width B′ = B − 2e; EC7 DA1 or factor of safety.
Geometry
Loads per footing
| Loads at column top | Fv kN | Fh kN | M kNm |
|---|---|---|---|
| Permanent (G) | |||
| Variable (Q) |
Fh and M act in the B direction at the top of the column (h above ground); positive as drawn.
Soil layers characteristic values
| Layer | Condition | γ kN/m³ | c′ kPa | φ′ deg | cu kPa |
|---|---|---|---|---|---|
| 1 Foundation soil | |||||
| 2 Hardcore / gravel | Drained | – |
Bulk unit weights; γ − 10 is used below the water table. Layer 1 also fills above the footing.
Calculation method
| Combination | γQ | γG,sup | γG,inf | γR,c′ | γR,φ′ | γR,cu |
|---|---|---|---|---|---|---|
| EC7-DA1C1 | ||||||
| EC7-DA1C2 |
Both combinations are calculated. Bearing: permanent loads × γG,sup, variable × γQ. Sliding: vertical permanent × γG,inf, vertical variable ignored, horizontal × γG,sup / γQ.
Required factors of safety (editable). All loads and soil parameters un-factored.
Pile Foundation – Axial Capacity
Method: SPT-N correlations or α / β and Nc / Nq; EN 1997-1 DA1 with model factor; drag load from negative skin friction; Converse–Labarre group efficiency; settlement by Vesić (1977).
Pile and ground
Soil layers characteristic values · max. 10 · bulk γ (γ − 10 below GWL) · clay cu = 5N unless edited
Pile group check
. Minimum spacing: Qs,k > 75 % Qt → s ≥ 3D; 50–75 % → s ≥ 2.5D; < 50 % → s ≥ 2D. If not met, the group efficiency Eg (Converse–Labarre) is applied to the compression resistance.
Calculation method
| Pile in compression | Rc,d = min{Qs,k/γs + Qb,k/γb ; (Qs,k + Qb,k)/γt} / γMF,comp | ||
|---|---|---|---|
| Pile in tension | Rt,d = (Qs,k/γs,t) / γMF,tens | ||
| Pile in compression | Qa = min{(Qs,k + Qb,k)/FS ; Qs,k/FSs + Qb,k/FSb} | ||
| Pile in tension | Qa,t = Qs,k/FSt | ||
| Where, | Qs,k = Σ fs,k·As = Σ fs,k·πD·Δz ; Qb,k = fb,k·Ab = fb,k·πD²/4 | ||
| Shaft friction – sand | fs,k = | Ks·N = N (kPa)K·σ′v·tanδ, K = (1 − sinφ′), δ = ·φ′ | ≤ kPa |
| Base resistance – sand | fb,k = | Kb·N = N (kPa)c′Nc + σ′vNq, Nq = eπ tanφ′tan²(45° + φ′/2) | ≤ kPa |
| Shaft friction – clay | fs,k = | Ks·N = N (kPa)α·cu, α = | ≤ kPa |
| Base resistance – clay | fb,k = | Kb·N = N (kPa)·cu (Nc) | ≤ kPa |
Design load per pile · kN · tension as a positive value
| Load case | At cut-off level | γG | Wk | ηPdd,k | Total design force | ||
|---|---|---|---|---|---|---|---|
| Compr. | Tension | Fc | Ft | ||||
| DA1C1 | |||||||
| DA1C2 | |||||||
| Working load | 1.00 | ||||||
Partial factors for resistance
| Set | γb | γs | γt | γs,t |
|---|---|---|---|---|
| R1 DA1C1 | ||||
| R4 DA1C2 | ||||
| Model factor | γMF,comp | γMF,tens |
Factors of safety
Settlement under working load Vesić (1977) · admin only until verified
Embedded Retaining Wall
Method: Cantilever: fixed earth support (simplified Blum, design embedment 1.2·d0). Single prop: free earth support about the prop, with construction stages. Earth pressure EN 1997-1 Annex C, as the ERSS toe-stability check.
Levels and loads levels in m · retained side on the right
Supports struts, props or anchors · 1 to 6 levels · top down
Soil layers characteristic values · max. 10 · from GL down · bulk γ (γ − 10 below GWL)
Drained layers use c′ and φ′ with pore water pressure; undrained layers use cu with total stress (short term). Earth pressure coefficients from EN 1997-1 Annex C, as in the ERSS toe-stability check.
Wall friction, water and embedment
TL (optional) is checked against the required toe level. Leave it blank to only calculate the required embedment.
| Combination | γG | γQ | γφ′ | γc′ | γcu |
|---|---|---|---|---|---|
| EC7-DA1-C1 | |||||
| EC7-DA1-C2 |
Both combinations are calculated. γG multiplies the retained-side earth and water pressure (and the excavation-side water if “both sides” is chosen); γQ the surcharge part; passive earth pressure is unfactored (favourable). γφ′ divides tan φ′, γc′ and γcu divide c′ and cu.
Passive earth pressure divided by Fp; active and water pressures unfactored.
ERSS Stability toe stability · base heave · hydraulic heave (piping) · uplift
Method: Toe stability: moments about the lowest strut with EN 1997-1 Annex C coefficients. Base heave: Terzaghi with an embedded toe. Hydraulic heave and uplift: EN 1997-1 HYD and UPL on a Terzaghi prism. DCM and bored piles optional.
Excavation levels in m · retained side on the right
Soil layers characteristic values · max. 10 · from GL down · bulk γ
The same layers are used on both sides of the wall; below FEL the excavation side starts at zero vertical stress (plus any water standing above FEL).
| Toe stability and base heave | γG | γQ | γφ′ | γc′ | γcu |
|---|---|---|---|---|---|
| EC7-DA1-C1 | |||||
| EC7-DA1-C2 |
Toe stability: γG and γQ on the overturning moment (retained-side earth and water pressure below the lowest support), the resisting moment unfactored; required ODF ≥ 1.0. Base heave: γG on the net column weight, γQ on q; ODF = R/F ≥ 1.0. Piping and uplift use their own UPL / HYD factors below.
Toe stability rotation about the lowest support · EN 1997-1 Annex C coefficients
Base heave Terzaghi, embedded toe
Hydraulic heave / piping Terzaghi prism d × d/2 · linear head loss
Uplift of the excavation base EN 1997-1 2.4.7.4 (UPL)
Soil Nail Wall BS 8006-2 / EN 1997-1 or FHWA GEC 7 · Bishop circles with nails
Method: Bishop's simplified method on circular slip surfaces with nail forces T = min(tension, pull-out behind, facing + pull-out in front). BS 8006-2 with EN 1997-1 DA1-C2 partial factors, or FHWA GEC 7 (FHWA-NHI-14-007) allowable stress design.
Geometry toe of the face at level 0
Soil layers characteristic · from the crest down · qs = ultimate bond stress grout–soil
Nails
EC7: soil strength to DA1-C2 (M2), nail resistances divided by γt and γpo; ODF ≥ 1.0 required. Check the factors against the National Annex and BS 8006-2 for your project.
Reinforced Soil Wall geosynthetic · BS 8006-1:2010+A1:2016 · tie-back wedge
Method: BS 8006-1:2010+A1:2016 tie-back wedge method; sliding, bearing and eccentricity; rupture and pull-out of each layer with combinations A, B and C.
Geometry and loads
Soils characteristic · dry (no water in the wall)
| γkN/m³ | φ′° | c′kPa | cukPa | |
|---|---|---|---|---|
| Reinforced fill | 0 | – | ||
| Retained fill | 0 | – | ||
| Foundation |
Geosynthetic
Partial factors BS 8006-1 defaults – check against the standard and the project
| Combination | ffsfill weight | ffearth pressure | fddead surcharge | fqtraffic | fmstan φ′ | fmsc′ | fmscu |
|---|
Beam on Elastic Foundation
Method: Euler–Bernoulli beam elements with a consistent Winkler foundation stiffness k = ks·B; optional tensionless foundation solved iteratively.
Beam
Foundation
Loads downward positive · moments clockwise positive · x and a from the left end · max. 10
Bearing capacity check
| Partial factors | γGpermanent | γQvariable | γφ′tan φ′ | γc′ | γcu | γR,vbearing |
|---|---|---|---|---|---|---|
| DA1-C1 A1+M1+R1 | ||||||
| DA1-C2 A2+M2+R1 |
EC7: every load is factored by γG or γQ (column “Action” in the load table; upward loads count as favourable) and the beam is re-analysed for each combination. The design contact pressure is checked against the design bearing resistance qRd = qult(φ′d, c′d, cu,d)/γR,v (EN 1997-1 Annex D): local – peak pressure pd,max on the strip B × L; overall – resultant Vd on the effective area B × L′ with L′ = L − 2e. With hardcore the load spreads at 1H:2V to the soil below (B + d2, L′ + d2) and the hardcore itself is checked too.
Factor of safety: characteristic loads and strengths, qa = qult/FS; local and overall checks as for EC7. Hardcore spread 1H:2V.
Boxed Tunnel – Cut and Cover Box
Method: Closed frame on the member centrelines on Winkler springs or a uniform base pressure; load cases with at-rest and active pressure; ULS and SLS.
Box section internal dimensions and thicknesses · per metre run
Ground and loads
Load factors ULS = γG·G + γQ·Q · SLS = G + Q
Bored Tunnel – Segmental Lining
Method: Bedded-beam (spring) model of the ring with compression-only radial springs (ITA / Duddeck); Muir Wood joint reduction.
Lining per metre of tunnel
Ground
Slope Stability – Bishop Simplified
Method: Bishop's simplified method on circular slip surfaces with an automatic grid search; drained or undrained layers; factor of safety or EN 1997-1 DA1-C2.
Ground surface points from left to right · x horizontal, z level (m) · max. 12
Soil layers characteristic values · max. 10 · from the highest ground point down · bulk γ
Water and surcharge
Search for the critical circle
Analyse a specified circle instead (optional)
Leave blank for the automatic search.
Over-design factor ODF = F with design strengths and loads; ODF ≥ 1.0 is required (γR,e = 1.0).
Sand Compaction Pile – Settlement and Strength
Method: Japanese design method (OCDI; Aboshi et al. 1979): stress concentration ratio, settlement reduction β = μc, Hansbo radial drainage, composite shear strength.
Sand compaction piles
Load and water
Soil layers from the top down · normally consolidated clay (Cc = 0 for sand / no settlement) · cu at the top of the layer + gradient k
Rate of consolidation
Deep Soil Mixing – Column Design
Method: Equal-strain stress sharing and composite modulus; column material strength from qu with a field/lab factor; geotechnical capacity after Broms (1999).
DSM columns
Load and water
Soil layers from the top down · Ds = constrained modulus (1/mv) · cu for the column capacity
Mined Tunnel – Convergence–Confinement
Method: Convergence–confinement method: Mohr–Coulomb ground reaction (Duncan Fama 1993), longitudinal profile (Vlachopoulos & Diederichs 2009), shotcrete and bolt support curves.
Tunnel and ground circular tunnel, hydrostatic in-situ stress p0 = γz
Support
Tools on this page
- Gravity retaining wall stability to EN 1997-1
- Sliding, overturning and bearing checks of a gravity wall, with or without a rubble base. Method: Coulomb earth pressure; EN 1997-1 DA1 (or factors of safety) for sliding, overturning about the toe and bearing (Annex D) with eccentricity.
- Shallow footing bearing capacity – EC7 Annex D, Vesić, Hansen, Meyerhof, Terzaghi
- Bearing resistance, sliding and eccentricity of pad and strip footings, drained or undrained. Method: Bearing capacity factors with shape, depth and inclination factors (EN 1997-1 Annex D, Vesić, Hansen, Meyerhof or Terzaghi, after Bowles); effective width B′ = B − 2e; EC7 DA1 or factor of safety.
- Pile axial capacity and settlement – single pile and pile group
- Shaft and base resistance in compression and tension, negative skin friction, group efficiency and settlement. Method: SPT-N correlations or α / β and Nc / Nq; EN 1997-1 DA1 with model factor; drag load from negative skin friction; Converse–Labarre group efficiency; settlement by Vesić (1977).
- Beam on elastic (Winkler) foundation
- Deflection, bending moment, shear and soil pressure of a beam or strip footing on a Winkler foundation. Method: Euler–Bernoulli beam elements with a consistent Winkler foundation stiffness k = ks·B; optional tensionless foundation solved iteratively.
- Embedded retaining wall – cantilever and propped walls
- Required embedment, bending moment, shear and strut forces of sheet pile, contiguous pile and diaphragm walls. Method: Cantilever: fixed earth support (simplified Blum, design embedment 1.2·d0). Single prop: free earth support about the prop, with construction stages. Earth pressure EN 1997-1 Annex C, as the ERSS toe-stability check.
- ERSS stability – toe stability, base heave, piping and uplift
- Stability checks of an excavation between embedded walls. Method: Toe stability: moments about the lowest strut with EN 1997-1 Annex C coefficients. Base heave: Terzaghi with an embedded toe. Hydraulic heave and uplift: EN 1997-1 HYD and UPL on a Terzaghi prism. DCM and bored piles optional.
- Soil nail wall – BS 8006-2 and FHWA GEC 7
- Global stability with nails, sliding and facing head load of a soil nail wall. Method: Bishop's simplified method on circular slip surfaces with nail forces T = min(tension, pull-out behind, facing + pull-out in front). BS 8006-2 with EN 1997-1 DA1-C2 partial factors, or FHWA GEC 7 (FHWA-NHI-14-007) allowable stress design.
- Reinforced soil wall – geosynthetic, BS 8006-1
- External and internal stability of a geosynthetic reinforced soil wall. Method: BS 8006-1:2010+A1:2016 tie-back wedge method; sliding, bearing and eccentricity; rupture and pull-out of each layer with combinations A, B and C.
- Consolidation settlement and PVD design
- Primary consolidation settlement against time of a layered profile, with prefabricated vertical drains and reclamation fill. Method: One-dimensional consolidation (Cc, Cr, OCR) solved by finite differences in time; radial drainage to PVDs by Hansbo (1981) with smear and well resistance.
- Stone columns – Priebe settlement improvement
- Settlement with and without stone columns on a triangular or rectangular grid, bulging capacity and consolidation time. Method: Priebe (1995): basic improvement factor n0, column compressibility, depth factor fd and compatibility limits, sublayers of 0.5 m; bulging by Hughes & Withers (1974); consolidation by Hansbo with Han & Ye (2001).
- Sand compaction pile – settlement and strength
- Settlement reduction, rate of consolidation and composite strength of SCP-improved clay. Method: Japanese design method (OCDI; Aboshi et al. 1979): stress concentration ratio, settlement reduction β = μc, Hansbo radial drainage, composite shear strength.
- Deep soil mixing columns
- Settlement, column stress and capacity of DSM columns. Method: Equal-strain stress sharing and composite modulus; column material strength from qu with a field/lab factor; geotechnical capacity after Broms (1999).
- Slope stability – Bishop simplified
- Critical circular slip surface and factor of safety of a layered slope. Method: Bishop's simplified method on circular slip surfaces with an automatic grid search; drained or undrained layers; factor of safety or EN 1997-1 DA1-C2.
- Cut-and-cover box tunnel
- Bending moments and forces in a single-cell box under earth and water pressure. Method: Closed frame on the member centrelines on Winkler springs or a uniform base pressure; load cases with at-rest and active pressure; ULS and SLS.
- Bored tunnel segmental lining
- Thrust and bending moment in a segmental tunnel lining. Method: Bedded-beam (spring) model of the ring with compression-only radial springs (ITA / Duddeck); Muir Wood joint reduction.
- Mined tunnel – convergence–confinement
- Ground reaction curve, support characteristic and equilibrium of a circular tunnel. Method: Convergence–confinement method: Mohr–Coulomb ground reaction (Duncan Fama 1993), longitudinal profile (Vlachopoulos & Diederichs 2009), shotcrete and bolt support curves.