Lecture #9

Deformation analysis Simplified methods

Stress & deformation analysis

Simplified (experimental) - Beam on elastic foundation - Finite element method

Surface settlement due to diaphragm

walls trench excavation

Deep excavation Theory and practice: after Clough and ORourke, 1990

Surface settlement due to diaphragm

walls trench excavation

Deep excavation Theory and practice: after Ou and Yang, 2000

Wall deformation effect of excavation width

Deep excavation Theory and practice

arching effect

Wall deformation effect of excavation width

Deep excavation Theory and practice: after Clough and ORourke, 1990

system stiffness of the retaining structure

maxim

um

defo

rmation

Factor of safety

aginst basal heave

Wall deformation effect of excavation depth

Deep excavation Theory and practice: after Ou et al., 1993

excavation depth

maxim

um

defo

rmation

Maximum deformation:

Wall deformation effect of embedment (penetration depth)

Deep excavation Theory and practice (based on FE studies)

Wall deformation effect of strut (anchor) stiffness

HIGH strut stiffness

LOW strut stiffness

Wall deformation effect of strut (anchor) spacing & strut (anchor) preload

The smaller the strut spacing the larger the strut stiffness

the smaller the deformation

The deformation also depends on unsupported length (in each step)

The smaller the unsupported length the larger the deformation

The preload pushes the wall against the soil it reduces

deformation

Surface settlement induced by excavation

Surface settlement induced by excavation

Influence zones*:

Granular soils: ~2He (excavation depth)

Stiff cohesive soils: ~3He

Soft cohesive soils: ~2He

*Limited settlements can be experienced even further

Location of maximum settlements:

Sprandel type: at the back of the wall

Concave type: at ~1/3 of the influence zone

Surface settlement induced by excavation >

> magnitude of maximum settlement

Surface settlement induced by excavation >

> movements during construction

Surface settlement induced by excavation >

> estimation of settlements (Peck, 1969)

Deep excavation Theory and practice: after Peck, 1969

I. sand and soft to stiff clay

II. very soft to soft clay (till limited depth, or high factor of

safety against basal heave)

III. very soft to soft clay (till large depth, or low factor of

safety against basal heave)

Surface settlement induced by excavation >

> estimation of settlements

Deep excavation Theory and practice: after Clough and ORourke, 1990

SAND stiff to very stiff CLAY

soft to medium soft CLAY

Surface settlement induced by excavation >

> base movements

Elastic deformation

due to unloading

Due to lateral movement

of the retaining wall

Due to plastic basal heave

(failure-like behaviour)

Surface settlement induced by excavation >

> 3D effect (diaphragm wall)

Surface settlement induced by excavation >

> Time-dependent behaviour

STRESS ANALYSIS

Apparent earth pressure (Peck, 1969)

SAND soft to medium soft CLAY

He/su > 4 stiff CLAY

He/su < 4

m: empirical factor m < 1.0 m=1.0

Assumed support method

It simplifies the soil structure interaction to a single assumed support Hand calculation becomes possible

Partial factors

DA-2 approach, GEO, STR limit states

Action A1

Permanent favourable gG 1.35

unfavourable 1.0

Variable favourable gQ 1.5

unfavourable 0.0

Resistance gR 1.4

Calculation Q: using gQ/ gG1.1 values G: using characteristic value

GEO limit state: resistance using gR gG1.9 values STR limit state: internal forces multiplied by gG

Q

Ld

dd

Hd

d

H

H

F

a p

O

Free earth support, no struts

Embedment (GEO)

Bending moments (STR)

Free earth support, with struts

(anchors)

Q

Ld

dd

Hd

H

H

a

p

A

dA

Bending moments

Embedded wall with struts (anchors)

Q

Ld

dd

Hd

d

H

H

F

a

p

O

A

dA

Blum method

Statically indeterminate

Defomation criteria:

Restraint (no rotation) at point O

No horizontal displacement at the strut

(anchor)

Serviceability limit state calculation with characteristic values

Required wall depths

Excavation

Free earth

support,

design values

Blum method,

characteristic

values

Blum method,

design values

SHALLOW STRUCTURE

Uplift (UPL)

Q

G

W

E0

F= E0tan F= E0tan

E0

F.S.= Fstab/Fmob

Increasing the factor of safety

Increasing the thickness

of the base slab

Increasing the width

of the slab

Anchoring

Design cases

Location Load Earth pressure Groundwater

Floor slab, middle vehicle load active minimum

Corners vehicle load at rest maximum

Side wall, middle - at rest maximum

Bending moments from vertical loads Bending moments from horizontal loads

Distribution of earth presure on

base slab

Ls: rigidity length

l: rigidity ratio

RIGID