selected aspects of designing deep excavations - zsoil · aspects of designing deep excavations s....

Selected aspects of designing deep excavations

using ZSoil.PC

Sébastien HARTMANN & Rafał OBRZUD

Aspects of designing deep excavations

S. Hartmann, R. Obrzud, GeoMod SA

28.08.2015, Lausanne, Switzerland

Selected aspects of designing deep excavations

Goal

recall for less experienced modelers

exchange users’ experience

Compare different approaches to serviceability state analysis

simplified (wall rigidity arbitrarily reduced to account for cracking in

concrete)

“true” serviceability control

Effect of analysis type in quasi-impermeable soils

steady-state (dissipated excess of pore water pressure)

consolidation (real time)

Content




Compare different approaches to serviceability state control

Berlin Sand benchmark ..\ZSoil v2013\Full\HS Model\HS-std-Exc-Berlin-Sand-2phase.inp

Sand I

= 35°

Eur = 180 MPa

Eur /E50 = 4

Sand II

= 38°

Eur = 300 MPa

Eur /E50 = 4

Wall

h = 0.8 m

Impermeable barrier

- 3.0 m




Simplified serviceability control

Assumptions:

• short term (creep neglected)

• reduced wall stiffness to account for concrete cracking

Results:

• intuitively a good approximation

of wall deflection and settlements

behind the wall

• pitfall:

results of internal forces

(Mk-Nk-Vk) may be carelessly

used to design concrete structures

Compare different approaches to serviceability control

Retaining wall:

Elastic-beam E = 20 GPa

(EC2 values 34 GPa)





Simplified approach

Single FE run Wall model: elastic E=20 GPa Results: 1. Wall deflection & soil deformations 2. Mk = Mk (E=20 GPa)

Design of concrete structure Md = 1.35 · Mk (E=20 GPa) Reinforcement: Ad = Ad(Md)

“True” control approach

1st First FE run Wall model: elastic E=34 GPa Results: Mk = Mk (E=34 GPa)

Design of concrete structure Md = 1.35 · Mk (E=34 GPa) Reinforcement: Ad = Ad(Md)

2nd FE run TRUE CONTROL Wall model: layered beam, elasto-plastic Einit=34 GPa 1. « True » wall deflection & soil deformations





Layered beam model used in

2nd FE run

s-e relationship according

to EC2 for C30

Einit = 34 GPa

fcm = 38 MPa

fctk = 0.1 MPa (neglected)

Es = 210 Gpa

fsd = 500 MPa

fsk = 435 MPa





Hypothesis Simplified model

h d z

xpl

e

As

Ac

─ Contribution of the compressed rebar

is not considered

─ Tension in concrete is neglected

Initial choice : 𝜙 = 30 mm

ℎ = 0.8 m

𝑏 = 1.0 m

𝑒 = 55 mm

Given :

𝒇𝒄𝒅

𝒇𝒔𝒅

𝑨𝒔 = 𝒃 ⋅ 𝒙𝒑𝒍 ⋅ 𝒇𝒄𝒅

𝒇𝒔𝒅

𝑵𝑪 = 𝑨𝒄 ⋅ 𝒇𝒄𝒅 𝑵𝑻 = 𝑨𝒔 ⋅ 𝒇𝒔𝒅 𝑵𝑻 = −𝑵𝑪 = 𝑴𝒅

𝒛





Start

Iterate

𝐴𝑠𝑑 =𝑀𝑑

𝑧 ⋅ 𝑓𝑠𝑑

𝑑 = ℎ − 𝑒 −𝜙

2 𝑧0 = 0.9 ⋅ 𝑑

𝑥𝑝𝑙 =𝑀𝑑

𝑏 ⋅ 𝑧 ⋅ 𝑓𝑐𝑑

𝑧 = 𝑑 −𝑥𝑝𝑙

2

Computation of Ad

Results E20 E34 RE

Asd+ [mm2] 3339 4016 –17%

Asd- [mm2] 1690 1792 –5.7%





Simplified approach

Beam elastic E=20GPa

1st run of “true” control


Mmax = 757 kNm Mmax = 901 kNm

Mmin =393 kNm Mmin = 416 kNm

Mmax RE = – 16%

Mmin RE = – 5.5%





Simplified approach


2nd run of “true” control

Beam elasto-plastic Einit=34GPa

uy = 1.89 cm

ux =3.88 cm

ux RE = – 5 %

uy RE = – 5.5 %

ux =4.09 cm

uy = 1.95 cm

1st run for elastic beam E=34 GPa

ux = 3.52 cm ARE = 14 %

uy = 1.75 cm ARE = 10%





Discrepancies might increase with increasing amplitude of

deformations …

Is the careless use of internal efforts for wall designing based on the simplified approach consistent with design codes?




Effective stress in ZSoil

12

Fluid is considered as a mixture of air and water (single-phase model of fluid)

p – pore water pressure

S = S(p) – degree of saturation depending on pore water pressure

suction stress if p > 0 (above GWT)




Deformation + flow analysis (soil water retention curve)

Effect of an apparent cohesion can be easily reproduced by coupling:

o constitutive model described by effective parameters

o Darcy’s flow in consolidation analysis

o Soil water retention curve model (van Genuchten’s model)

13

+

-

p

p>0

p<0





Berlin Sand benchmark reused

Sand replaced with impervious clay

Clay I

= 30°

Eur = 90 MPa

Eur /E50 = 4

k = 10-9 m/s

a = 0.1

Clay II

= 32°

Eur = 150 MPa

Eur /E50 = 4

k = 10-9 m/s

a = 0.1

Wall

h = 0.8 m

Impermeable barrier REMOVED





ANALYSIS TYPE

Steady – state

excess of excess pore water pressure is

dissipated at each state (full drainage)

Consolidation

real time analysis

development of partially saturated zones due to

undrained and partially-drained conditions

Positive pore pressures

No suction effect

False GWT lowering when in equilibrium in the case of homogenous hydraulic conductivity

Null pore pressure line





Construction stages

4 excavation steps, each includes:

I. Excavation N – N+20days(unloading over 5 days);

accounting for 3D effect

II. Realisation of prestressed anchors N+20 – N+30





0tot

ijs

kPappSij 20)(' s

Analysis type: Consolidation

Maps: S*p

4 m Thickness of

unsaturated zone





Steady - state


Consolidation


Assumed horizontal GWT (auxiliary superficial permeable layer)

Comparison in terms of J2 Strain





Steady - state


Consolidation


uy– = 7.8 cm

uy– = 4.6 cm

uy– = 5.1 cm

Instantaneous

After 25 days

uy+

=9.6 cm

uy+

=4.8 cm

uy+

=4.3 cm

Result RE

uy+

+ 100 %

uy– + 70 %

ux + 66 %

ux =11.0 cm ux =6.6 cm

ux =7.2 cm





Steady - state


Consolidation


Mmax = 1403 kNm Mmax = 919 kNm

Mmax RE = + 52 %





Steady - state + simplified approach


Consolidation + “true“ control

Beam elasto-plastic E=34 GPa

Ad=Ad(Mmax)

SERVICABILITY CONTROL

uy– = 8.2 cm

uy+

=10. cm

ux =11.8 cm uy

– = 5.3 cm

uy+

=4.9 cm

ux =7.6 cm

Result RE

uy+

+ 104 %

uy– + 55 %

ux + 55 %





Discrepancies are difficult to foresee due to a highly nonlinear

nature of the problem

In this example, the steady-state approach gives a superior

confidence limit for internal efforts with respect to consolidation

analysis

Is the “steady-state shortcut” profitable in the light of an optimal design?




Thank you for your attention

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