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Helwan UniversityFaculty of Engineering - MattariaCivil Engineering Department

NUMERICAL ANALYSIS FOR UNSYMMETRICAL SIDE SUPPORTING SYSTEMS

By

Mahmoud Mohamed El-Sayed Hamed B.Sc. Civil Engineering – Faculty of Engineering at Mattaria

Helwan University, 2007

A THESISSUBMITTED FOR THE PARTIAL FULFILMENT OF THE

REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE

INCIVIL ENGINEERING

SUPERVISORS

PROF. DR. FATMA BALIGHPROFESSOR OF SOIL MECHANICSAND FOUNDATION ENGINEERING.

FACULTY OF ENGINEERING AT MATTARIAHELWAN UNIVERSITY

DR. HUSSEIN MAHMOUD HUSSEINASSISTANT PROFESSOR OF SOIL MECHANICS

AND FOUNDATION ENGINEERINGFACULTY OF ENGINEERING, AT MATARIA,

HELWAN UNIVERSITY

THESIS OUTLINE

Chapter (1): Introduction Chapter (2): Literature Review Chapter (3): Geotechnical parameters for studied soil Chapter (4): Setup of numerical model Chapter (5): Result of analysis Chapter (6): Case study Chapter (7): Summary and Conclusions

The thesis is studying behaviour of unsymmetrical side supporting systems (strutted systems)

So why unsymmetrical side supporting systems (strutted systems) ?!Strutted side support system is one of the most common types of side support systems in Egypt and world.

It was observed that most of the designers are considering design models is in fully symmetry condition, which clearly appears by modelling one half of the system under study and assuming that the other half is typical to the studied one.

So the aim of the research is to study the effect of the asymmetry conditions surrounding to strutted side support systems on the systems behaviour.

Methods of unsymmetrical side support systems modelling:

Example for unsymmetrical side support system

Strut Q = Surcharge load from Building

Wall-1Wall-2 Building Foundation

1-Empirical method 2-Winkler method


Strut

Q = Surcharge load from Building

Wall-1

Act

ive

E.P

Pas

sive

E.P

Strut

Q = Surcharge load from Building

Wall-1

Act

ive

E.P


3-Finite element method (half model) 4-Finite element method (full model)

Rankine’s Theory (1857)

)2/45(tansin1sin1 2

Ka

)2/45(tansin1sin1 2

Kp

Coulomb’s theory (1773)

2

2

2

)cos()cos()}'sin()'sin(1)cos(cos

)'(cos

Ka

2

2

2

)cos()cos()}'sin()'sin(1)cos(cos

)'(cos

Kp

Active earth pressure

Passive earth pressure

2.1 Developing Earth Pressure

2.2 Empirical Design Methods

Cantilever Wall Stability Propped Wall Stability

Linear Elastic Model(Spring Model)

Elastic-Perfect Plastic Model(Mohr-Coulomb Model)

Elasto-Plastic Hardening Model(Hardening Soil Model)

2.3 Numerical approaches for soil modelling

The main goal of this chapter is to define types, formations and values of main geotechnical parameters for the studied soils in the analysis models.

3.1 Introduction

3.2 Selection of Soil types for study

The selected soils for study are the normally consolidated clay (soft clay) and the dense sand.

3.3 Basic assumptions

The studied Soil formation for both sand and clay is a homogenous layer extends from ground top level to 25.0 m depth.

The ground water level in clay condition is 2.0m depth from ground top level, while in sand condition water level is far away from ground top level (more than 50.0m depth).

The soft clay is normally consolidated Clay (OCR = 1). The maximum undrained cohesion for soft clay is 25 kPa The normally consolidated Clay plasticity index is 60%. The drained cohesion for the soft clay is 0.0 kPa. For the sand layer the range of SPT N value form ground

top level to depth 25.0m is ranging between 15 to 50 blows.

According to the BS 8004: 1986

3.4 Shear Strength Parameters3.4.1 Shear Strength Parameters for soft Clay

Undrained Cohesion (Cu) is taken equals 25 kPa

Undrained Cohesion (Cu):

Drained Cohesion (C`) : Zero for NCC Drained friction angle (`)

For PI=60% `=25o

1-Mitchell (1976):

sincv ≈ 0.8-0.094 ln PI

1-According to Peck (1974) :

3.4.2 Shear Strength Parameters for Sand Drained friction angle (`)

2-According to Schmertmann (1975):

' = tan-1 [N / (12.25 + 20.3 'vo)] 0.34

3-According to Giuliani and Nicoll (1982) :

Rd = N0.5 / (4.188 + 0.639 'vo0.606 )

tan '= 0.575 + 0.361 Rd0.866

The following chart is summarizing the result of applying the above mentioned relations:

Form this chart `=35o

3.5 Stiffness Parameters

Undrained stiffness (Eu):

For PI=60% Eu/Cu = 150

3.5.1 Stiffness Parameters for soft Clay

According to Duncan and Buchignani (1976), the undrained stiffness (Eu) is function of the Cu, OCR and PI

Undrained stiffness (Eu):

Drained stiffness (Ed):

By calculating (Cu) according to Skempton (1957). And by using Eu/Cu = 150, (Eu) can be determined with depth as shown in the following chart:

From the elastic theory for materials, (David Muir Wood- Soil behaviour and critical state soil mechanics)

(Ed)= 2Eu(1+ ')/3

Elastic modulus (E):3.5.2 Stiffness Parameters for Sand

1-According to Webb (1971):

E = a N +b , Where a, b = 478, 7170 kPa

2-According to AASHTO (1996):

3-According to Janbu (1963):

E = F ('ho /100)0.5

The following chart is summarizing the results of applying the above mentioned relations for the elastic modulus (E) :

3.6 Advanced stiffness Parameters

m

refref

pccEE

sincos.sin`cos. 3

5050

m

refrefoedoed pc

cEE

sincos.sin`cos. 1

The modelling of soil behaviour using HSM model requires a special set of stiffness parameters to encounter many of soil facets

(m) Stress dependent stiffness according to a power law.

(Eref50 ) Plastic straining due to primary deviatoric loading.

(Erefoed) Plastic straining due to primary compression.

• (Erefur/ur) Elastic unloading / reloading.

m

refrefurur pc

cEE

sincos.sin`cos. 1

3.7 Summary of Used Soil Parameters

Basic data for model Setup

Group (A)Data Related to

Geometry

Group (B)Data Related to

Meshing

Group (C)Data Related to Soil Modeling

Group (D)Data Related to

Structure Modeling

A-12D/3D Analysis

A-2Extended Geometry (model boundaries)

A-3Soil Stratigraphy

B-1Coarseness of the mesh

B-2Element Shape

B-3Element Order

B-4Interface Element

C-1Type of soil model

C-2Drained VS undrained Analysis

D-1Retaining Structure

D-2Propping System

Group (E)Data Related to Type of loading

E-2Dynamic Loading

E-1Static Loading

Finite Element software Plaxis 8.6 used for analyzing MCM and HSM models

4.1 Geometry

2D/3D Analysis 2D analysis used

Extended Geometry

Soil Stratigraphy as per (Item 3)

Recommended By K.J.Bakker

4.2 Meshing Mesh Coarseness Fine

Element Shape Triangular.

Element Order 15 node

4.3 Soil Modeling

Soil models Mohr-Coulomb and Hardening soil model

Drained versus undrained Drained is critical.

Finite Element software Plaxis 8.6 used for analyzing MCM and HSM models

4.4 Structure Modeling

Retaining structure Beam element with Flexural and normal stiffness

Propping system Node to node anchor with Normal stiffness (EA).

4.5 Type of loading

Static load case

Studied Models

Single strutted (M1) & (M2)

Multi strutted (M3) & (M4)

Sand (M1) Clay (M2) Sand (M3) Clay (M4)

(M1-a)(M1-b)(M1-c)(M1-d)

(M2-a)(M2-b)(M2-c)

(M3-a)(M3-b)(M3-c)

(M4-a)(M4-b)(M4-c)

Where, a=Different surcharge load, b=Slope of excavation level, c=Slope of ground surface and d=Nearby existing underground structure

5.1 Asymmetric conditions

Q (kN/m²)

Wall-1

D

S

Existing Structure

Wall-1 Wall-2

Excavation level slope

Ex.L Slope

Wall-1 Wall-2

Ground level slope

Ground Slope

D

Wall-1 Wall-2

Unsymmetrical Surcharge Loading Case

Wall-2

Q (kN/m²)

Nearby underground structure

5.2 Model M1 Configuration

1500010000 10000

2000

5000

4000

1400

0

15000 10000

Q(20 kN/m2) Q(20 kN/m2)

G.L=(0.00)

St.L=(-2.00)

Exc. L=(-7.00)

(-11.00)

SandSand

-All dimensions are in mm.

G.L=(0.00)

5.1.1 Model M1-a

Q (kN/m²)

Symmetric Wall

Q (kN/m²)

Wall-1 Wall-2

Q (kN/m²)

Unsymmetrical Surcharge Loading Case

Symmetric Wall

Symmetrical Surcharge Loading Case

5.1.1.1 Model M1-a Horizontal Displacement

Using MC Using HSM

Using MC Using HSM

5.1.1.2 Model M1-a Bending Moment

5.1.1.3 Model M1-a Force in strut

5.1.1 Model M1-d

Symmetric Wall

Symmetrical Case

Wall-1

D

S

Existing Structure

Q (20 kN/m²)

Q (20 kN/m²) Q (20 kN/m²)

Symmetric Wall

Q (20 kN/m²)

Wall-2

Unsymmetrical Case

5.1.1.1 Model M1-d Horizontal Displacement

Using MC Using HSM

Max Horizontal Displacement ratio for model M1-d

Using MC Using HSM

5.1.1.2 Model M1-d Bending Moment

Max Bending Moment ratio for model M1-d

5.1.1.3 Model M1-d Force in strut

2900010000 10000

3000

3000

1000

022

000

29000 10000

Q(20 kN/m2) Q(20 kN/m2)

G.L=(0.00)

Strut (1) El.=(-3.00)

Exc. El.=(-12.00)

Wall tip El.(-22.00)

-All dimensions are in mm.

G.L=(0.00)

3000

3000

Strut (2) El.=(-6.00)

Strut (3) El.=(-9.00)

Soft ClaySoft Clay

5.2 Model M4 Configuration

Symmetric Wall

Wall-1 Wall-2

Unsymmetrical Case

Symmetric Wall

Symmetrical Case

Ex.L Slope

DD

5.2.1 Model M4-b

Using MC Using HSM

5.2.1.1 Model M4-b Horizontal Displacement

Max Horizontal Displacement ratio for model M4-b

Using MC Using HSM

5.2.1.2 Model M4-b Bending Moment

Max. Bending Moment ratio for model M4-b

5.2.1.3 Model M4-b Force in struts Force in strut no.1

Force in strut no.2

Force in strut no.3

For case of unsymmetrical surcharge loading

5.3 Summary of analysis results

Soil model

Model Name

% of change in max. Hz. Displacement % of change in max. B.M % of change in

Strut force

(unsym. - sym.) / (unsym) (Munsym - Msym) / (Munsym) (Funsym -Fsym.) /

Wall-1 Wall-2 Wall-1 Wall-2 (Fsym.)

Max. Min. Max. Min. Max. Min. Max. Min. Max. Min.

MCM1-a 56 13 -18 -42 -9 -14 -8 -14 -13 -21M2-a 126 25 -22 -60 -2 -4 15 3 -3 -4

HSMM1-a 67 25 -45 -91 -5 -9 -16 -24 -5 -10

M2-a 36 9 -19 -49 0 -2 -12 -14 -2 -5

MCM3-a 31 6 -7 -22 -2 -13 5 -15 -4 -23

M4-a 217 9 -8 -38 26 -7 23 -6 9 -31

HSMM3-a 170 27 -37 -88 3 -21 4 -16 -2 -9M4-a 11 4 -6 -25 2 -3 -1 -17 36 -12

For case of excavation level slope

Soil model

Model Name


Strut force




MCM1-b -8 -16 -3 -9 -11 -38 -3 -12 -5 -14

M2-b -11 -23 -2 -6 -14 -30 -10 -27 -3 -13

HSMM1-b -27 -69 24 4 -13 -43 -7 -21 -5 -15

M2-b -19 -47 -10 -23 -15 -39 -12 -33 -8 -22

MCM3-b 6 -16 -8 -20 -2 -57 12 -39 2 -17

M4-b -6 -15 -5 -9 -13 -43 -10 -51 107 -28

HSMM3-b -24 -61 22 -7 -7 -72 4 -44 2 -19

M4-b -8 -25 -8 -22 -11 -37 -10 -43 59 -25

For case of ground level slope

Soil model

Model Name


Strut force




MCM1-c 29 -1 110 10 38 7 -3 -12 16 0M2-c -28 -38 394 60 91 12 34 3 65 12

HSMM1-c -43 -66 372 51 36 5 -5 -12 29 3M2-c -34 -82 298 41 60 4 13 0 24 3

MCM3-c 32 9 215 2 37 -22 98 -18 43 -40M4-c -14 -16 356 59 54 -5 92 -7 67 -62

HSMM3-c -38 -68 714 109 2 -16 42 -2 39 -2M4-c -20 -60 283 23 31 -2 51 5 21 -42

For case of nearby underground structures

Soil model

Model Name


Strut force




MC M1-d -9 -16 13 6 -6 -29 3 -6 7 -4

HSM M1-d -6 -67 28 -3 -4 -35 0 -5 1 -4

This chapter present a Case study for Behaviour of strutted d-walls under asymmetric lateral loading along the Chao Phraya River formation, (Bangkok)

This case study is for Thamasart University Project.

The case study had previously been reported by Thasnanipan and Teparaksa et al. (1999)

General layout for area under study

6.1 Introduction

6.2 Subsoil conditions

Summary of subsoil properties

Basement section and soil profile

6.3 Description of side support system under study and instrumentation

Description of side support system under study :

0.8 m thick.D-WallRiver

River wall

Strut (1) at level (-2.00),(WF400x400)

Strut (2)at level (-7.00), 2x(WF350x350)

0.8 m thick.D-Wall

(-28.00) (-28.00)

(0.00) (0.00)GWT (-1.00)(-3.00)

(-12.00)(-9.70)

(-12.70)(-14.00)

(-25.00)

(-35.00)

(-41.00)

(-60.00)

Soft Clay

Med. Clay

Stiff Clay

Stiff Clay

Very Dense Sand

Very Dense Sand

50.0m 55.0m8.0m3.0m24.0m20.0m

Layout of temporary bracing and instrumentation :

6.4 Excavation work sequence

The excavation work sequence on site passes through the following steps respectively:

1. Construction of 0.8m thick. D-walls

2. Excavation to level (-2.50), at day 67

3. Install first strut at level (-2.00), at day 100

4. Excavation to level (-7.50) , at day 133

5. Install second strut at level (-7.00), at day 150

6. Excavation to final level (-9.70), at day 155

6.5 Instrumentation results

6.6 Finite element analysis6.6.1 General From back analysis study for the same soil formation by

Teparaksa W. and N. Thasnanipan & Pornpot Tanseng et al. (1999), the soil stiffness parameters was given in terms of Eu/Cu = 500 and 2000 for soft Bangkok clay and stiff clay, respectively.

6.6.2 Soil properties for constitutive soil models (MC and HSM)

Parameters Soft clay Med. clay Stiff clay Dense sandLayer top level 0.0 -12.7 -14.0 -35.0 -25.0 -42.0Layer thick. (m) 12.7 1.3 11.0 7.0 10.0 18.0

Soil model HSM MC HSM MC HSM MC HSM MCsat/sub (kN/m3) 18 18 19 19 20 20 20 20Ko 0.593 0.593 0.546 0.546 0.455 0.455 0.357 0.357` 24 24 27 27 33 33 40 40C` (kN /m2) 0.0 0.0 1.0 1.0 1.0 1.0 0.0 0.0Rinter 65% 65% 65% 65% 65% 65% 70% 70%

E` (kN /m2) - 15000 - 30500 - 74000 - 75000

Eincrement (kN /m2/m) - - - - - 40190 - 10000

- 0.35 - 0.35 - 0.30 - 0.3

E50ref (kN /m2) 35960 - 47220 - 356200 - 123800 -

Eoedref (kN /m2) 34050 - 41680 - 227100 - 99970 -

Eurref (kN /m2) 179800 - 236100 - 1781000 - 371300 -

ur 0.2 - 0.2 - 0.2 - 0.2 -m 1.0 - 1.0 - 1.0 - 0.5 -

6.6.3 Model geometry

Soft Clay

Strut (1) EL.(-2.00)

Med. Clay

Stiff Clay

Stiff Clay

EL.(-28.0)Very Dense Sand

Very Dense Sand

EL.(0.00)

EL.(-12.70)

EL.(-25.00)

EL.(-35.00)

EL.(-41.00)

EL.(-60.00)

Strut (2) EL.(-7.00)

0.8m Thick. D-wall

EL.(-9.70)

0.8 m thick.D-WallRiver

River wall

Strut (1) at level (-2.00),(WF400x400)

Strut (2)at level (-7.00), 2x(WF350x350)

0.8 m thick.D-Wall

(-28.00) (-28.00)

(0.00) (0.00)GWT (-1.00)(-3.00)

(-12.00)(-9.70)

(-12.70)(-14.00)

(-25.00)

(-35.00)

(-41.00)

(-60.00)

Soft Clay

Med. Clay

Stiff Clay

Stiff Clay

Very Dense Sand

Very Dense Sand

50.0m 55.0m8.0m3.0m24.0m20.0m

River wall

6.7 Result of analysis6.7.1 Horizontal displacement

Day 67 Day 133 Day 155

6.7.2 Strut force

Measured Force in struts Vs. Predicted Forces from Plaxis at day 133


6.8 Comparative study between symmetric and unsymmetrical FEM’s

6.8.1 Model Geometry

Soft Clay

Strut (1) EL.(-2.00)

Med. Clay

Stiff Clay

Stiff Clay

EL.(-28.0)Very Dense Sand

Very Dense Sand

EL.(0.00)

EL.(-12.70)

EL.(-25.00)

EL.(-35.00)

EL.(-41.00)

EL.(-60.00)

Strut (2) EL.(-7.00)

0.8m Thick. D-wall

Model geometry for sym. model

EL.(-9.70)

6.8.2 Results of comparative study analysis6.8.2.1 Horizontal displacement

Day 67 Day 133 Day 155

6.8.2.2 Strut force



7.1 General conclusions 1. For symmetric loading case, the two walls move towards the

excavation side. In contrary for unsymmetrical loading case, the wall adjacent to high loaded side moves towards excavation while the upper quarter of the other wall was found to move toward soil side.

2. The unsymmetrical condition due to (unsymmetrical surcharge loading and excavation level slope) causes decrease in most of straining action values, and vice versa for unsymmetrical condition due to (ground level slope).

3. The maximum bending moments obtained from HSM is higher than that obtained from MC for both symmetric and asymmetric cases, and vice versa for maximum Hz. Displacement values.

7.2 For case of unsymmetrical surcharge loadingThe increase of unsymmetrical loading (within studied range) causes :

1.Increase in the maximum deflection of wall-1 (nearby loaded side) reaches 170% of symmetric wall maximum deflection, while the decrease of maximum deflection for wall-2 had reaches -91% of symmetric wall maximum deflection.

2.Change in values of maximum B.M for both wall-2 and wall-1 ranges between (26% and -24%) of the symmetric wall maximum B.M.

3.Change in values of strut force ranges between (26% and -24%) of strut force of symmetric case.

7.3 For case of excavation level slopeThe increase of excavation level slope (within studied range) causes :

1.Decrease in both wall -1 and wall-2 maximum deflection by values reaches -69% of symmetric wall maximum deflection.

2.Decrease in the value of maximum B.M for both wall-1 and wall-2 by values reaches -72% of symmetric wall maximum B.M.


7.4 For case of ground level slopeThe increase of ground level slope (within studied range) causes:

1.Increase in the maximum deflection of wall-2 (nearby higher ground level) reaches 714% of symmetric wall maximum deflection, and decrease of maximum deflection for wall-1 had reaches -68% of symmetric wall maximum deflection.

2.Change in values of maximum B.M for both wall-2 and wall-1 ranges between (98% and -22%) of the symmetric wall maximum B.M.


7.5 For case of nearby underground structuresThe decrease in S/D ratio causes:

1.Decrease in the maximum deflection of wall-1 (nearby underground structure) reaches -67% of symmetric wall maximum deflection, and increase of maximum deflection for wall-2 reaches 28% of symmetric wall maximum deflection.

2.Decrease in value of maximum B.M for wall-1 by values reaches -35% of symmetric wall maximum B.M, and negligible change in value of maximum B.M for wall-2 (less than 6%).

3.Negligible Change in values of strut force.

7.6 General conclusions for case study1. The unbalanced loading condition resulting from the

existence of river slope in one side of the excavation caused different horizontal displacement values for both walls.

2. Horizontal displacement values for the wall nearby the existing river slope is less than that for the other side wall.

3. The Horizontal displacement values obtained from the analysis using the asymmetric model for both walls is clearly closer to the field measured data than that obtained from the analysis using symmetric model.

4. The strut forces values obtained from the analysis using the asymmetric model is clearly closer to the field measured data than that obtained from the analysis using symmetric model.

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