Settlement of Shallow Footings

Excessof VerticalStress

Stress Increment under Footing Subsoil Settlement due to Stress Change

Settlement Consists of:

• Immediate settlement: si– No volume change of subsoil, displacements only

• Settlement caused by primary consolidation: sp– Dissipation of pore-water pressure connected with

water flow and significant volume change of the soil• Settlement by secondary consolidation: ss

– Volume change due to secondary compression and u=0 – long-term development

Immediate Settlement

si

uu

i IEBqs ⋅⋅=

01 µµ ⋅=uI

Square

Circular

Settlement by Primary Consolidation

• Based on:– Oedometer modulus and subsoil composed of

individual layers,– Calculation of Origin Stress and Stress

Increment,– Calculation of Settlement:

i

n

i ioed

zi hE

s ⋅= ∑=1 ,

σi

n

i ioed

iorizi hEm

s ⋅⋅−

= ∑=1 ,

,σσ

Settlement by Secondary Consolidation

Calculation of Settlement ss

Coefficient of Secondary Consolidation:

Sand approx.0,00003-0,00006

Loess soil approx. 0,0004

Clay approx. 0,001

12 loglog1

tthh

s −⋅

∆=α

( )12 loglog tths ss −⋅⋅= α

Boussinesq - Point load

Boussinesq - Point load

2cos

RAR

βσ ⋅=

V / H Stress

Stress increment calculation

Stress increment calculation

Stress IncrementLarge Embankment Construction Footing Depth

Stress IncrementRe-construction Dewatering

Stress: Origin / Increment due to Vds

Vertical Stress Distribution

Distribution of vertical stress increment bellow indicated points -section

Uniform loaded rectangular area –site plan

Contact Stress Distribution

k = E/Edef . (t/l)3 If k > 1.0 Stiff Footing

Stress Increment Calculationσol/f

Rectangular / Strip Footing

StressIncrementCalculation

Circular Footing

Footing Depth – Stress Correction

Rectangular Footing

Strip Footing

Rock Base - Stress Correction

Rock Base