Analysis of liquefaction potential and slope stability of red river dike

34 Figure 4.3 Relationship between Excess Pore Water Pressure Ratio and Number of Loading Cycles .... 37 Figure 4.9 Relationship between Excess Pore Water Pressure Ratio and Number of Lo

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REASSUARANCES

Name: TRAN ANH DUY

Major: Sustainable Hydraulic Structure

Student number: 148ULG015

I hereby declare that this is my own research which was scientifically instructed by Assoc.Prof Nguyen Hong Nam The research content and results in this master thesis are honest and unpublished in any previous form or not overlapped with any dissertation The input data in the tables supporting for analysis, comments and assessment are collected by the author from other sources which was clearly specified in the References

Besides, my thesis also use some comments and data of other authors, agencies and organizations with clear citations and source notes

If there is any fraudulent in the content of my thesis I would like to take full responsibility as prescribed

Signature

Tran Anh Duy

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ACKNOWLEDGEMENT

I would like to express my deep gratitude to my supervisor Associate Professor Nguyen Hong Nam at Thuy Loi University for his full support, expert guidance, understanding and encouragement throughout my study and research Without his incredible patience and timely wisdom and counsel, my thesis work would have been a frustrating and overwhelming pursuit

Additionally, I express my appreciation to my co-supervisor Professor COLLIN Frédéric

at University of Liege for his valuable comments about this thesis Thank also goes to Dr Pham Quang Tu at Thuy Loi University who teach and support me in Module Foundation

of Hydraulic Structures and guide me to choose my thesis in this field

Also, my deep gratitude is to Department of Academic Affairs of Thuy Loi University and University of Liege for giving me the golden chance to apply the Msc Program in major of Sustainable Hydraulic Structure

Finally, I would like to thank the Ministry of Science and Technology of Vietnam for providing the financial support for the experimental work within the framework of the state-funded research project No KC08.23/11-15

November, 2016 Tran Anh Duy

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TABLE OF CONTENTS

CHAPTER 1: INTRODUCTION 1

1.1 The theoretical basis of liquefaction 1

1.1.1 Earthquake definition 1

1.1.2 Liquefaction phenomenon 1

1.1.3 Liquefaction of river dikes 3

1.2 The situation of earthquake problem and dike system in Vietnam 6

1.3 Past studies related to the problem and area 8

1.4 Research objectives 10

1.5 Research methodology 10

1.6 Organization of thesis 11

CHAPTER 2: LIQUEFACTION ANALYSIS AND SLOPE STABILITY THEORETICAL BASIS 12

2.1 Overview of analysis methods 12

2.2 Experimental method 13

2.3 Modeling the problem of Red river dike – modeling method 15

2.3.1 Overview of modeling method 15

2.3.2 Modeling the problem 17

2.3.3 Output of modeling 21

CHAPTER 3: TEST MATERIAL, APPARATUS, PROCEDURE AND OUTPUT PARAMETERS 23

3.1 Test material 23

3.2 Dynamic triaxial apparatus 23

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3.3 Test procedure 24

3.3.1 Sample preparation 25

3.3.2 Water supply and Pressure supply 26

3.3.3 Carbon dioxide (CO 2 ) pervasion 27

3.3.4 De-air water supply 27

3.3.5 Saturation checking 28

3.3.6 Consolidation 28

3.3.7 Cyclic undrained loading 29

3.4 Output parameters 29

CHAPTER 4: TEST RESULTS AND DISCUSSION 32

4.1 Experimental results 32

4.2 Discussion 45

CHAPTER 5: LIQUEFACTION MODELING OF RED RIVER DIKE AND SLOPE STABILITY ANALYSIS 46

5.1 General overview of study area 46

5.1.1 Project location 46

5.1.2 Geological characteristics (TLU, 2015) 49

5.1.3 Hydrology 52

5.1.4 Peak ground acceleration 53

5.2 Modeling liquefaction and slope stability results 57

5.2.1 Liquefaction zone 57

5.2.2 Parameter studies 62

5.2.3 Slope stability 65

5.2.4 Displacement 70

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CHAPTER 6: CONCLUSIONS AND RECOMMENDATION 76

6.1 Achieved results 76

6.1.1 Experimental results 76

6.1.2 Modeling results 76

6.2 Existing problem 77

6.3 Recommendation 77

REFERENCES 78

ANNOTATION 81

APPENDIX A 82

APPENDIX B 85

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LIST OF FIGURES

Figure 1.1 Earthquake simple visualization (University of California, San Diego, 2013) 1

Figure 1.2 The mechanism of liquefaction (Bhandari, 2015) 2

Figure 1.3 Schematic illustration of mechanism of liquefaction inside a levee (Maugeri, 2014) 4

Figure 1.4 Tokachi earthquake, 2003 (Ehime University, 2015) 4

Figure 1.5 Tohoku earthquake, 2011 (Japan) (Ehime University, 2015) 5

Figure 1.6 Map of fault system of South East Sea area (Cao Dinh Trieu, 2005) 6

Figure 2.1 Factor of safety versus time during the earthquake 16

Figure 2.2 Modeling of problem for section K73+750 17

Figure 2.3 Diagram of model parameters for each soil layer 18

Figure 2.4 Diagram of modeling initial stress problem 19

Figure 2.5 Diagram of modeling dynamic problem 19

Figure 2.6 Diagram of modeling dike slope stability subjected to earthquake loading 20

Figure 2.7 Number of slipping surfaces 20

Figure 2.8 Cyclic stress path from B to the collapse surface (QUAKE/W manual, 2010) 21 Figure 3.1 Sand material dumped at the Hanoi harbor 23

Figure 3.2 Cyclic Triaxial Apparatus DTC – 367D, SEIKEN Japan 24

Figure 3.3 Sand specimen preparation 25

Figure 3.4 Water supply and Pressure supply for specimen inside the triaxial cell 26

Figure 3.5 The system of CO2 gas tank and controller 27

Figure 3.6 Stresses on the specimen 30

Figure 4.1 Soil particle distribution curve of a typical sample from a sieve analysis 33

Figure 4.2 Relationship between Cyclic Stress Ratio and Number of Loading Cycles 34

Figure 4.3 Relationship between Excess Pore Water Pressure Ratio and Number of Loading Cycles 34

Figure 4.4 Relationship between Axial Strain and Number of Loading Cycles 35 Figure 4.5 Relationship between Deviatoric Stress and Mean Effective Principal Stress 35

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Figure 4.6 Relationship between Deviatoric Stress and Axial Strain 36

Figure 4.7 Relationship between Excess Pore Water Pressure Ratio and Axial Strain 36

Figure 4.10 Relationship between Axial Strain and Number of Loading Cycles 38

Figure 4.11 Relationship between Deviatoric Stress and Mean Effective Principal Stress 38

Figure 4.16 Relationship between Axial Strain and Number of Loading Cycles 41

Figure 4.17 Relationship between Deviatoric Stress and Mean Effective Principal Stress 41

Figure 4.20 Schematic Definition of the Number of Cycles Nc for the Specified DA value 44

Figure 4.21 Liquefaction curve of soil samples from Hanoi harbor area 45

Figure 5.1 Location of the research Red River Dike, Km73+500 – Km74+100 46

Figure 5.2 General Plan of Red river dike and location of cross-section and boring holes (TLU, 2015) 47

Figure 5.3 Section 1-1, Km73+750 (TLU, 2015) 48

Figure 5.6 Acceleration time histories (ATH) with return period of T475 years 55

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Figure 5.7 Acceleration time histories with return period of T475 years for initial 10

second 55

Figure 5.8 Acceleration time histories with return period of T2475 years 56

Figure 5.9 Acceleration time histories with return period of T2475 years for initial 10 second 56

Figure 5.10 Liquefaction zone, T = 475 years, acceleration record: 475r1a 57

Figure 5.13 Liquefaction zone, T = 475 years, acceleration record: 475s1a 58

Figure 5.22 Liquefaction zone, T = 475 years, acceleration record: 475s3a, WL: +10.5 63

Figure 5.23 Liquefaction zone, T = 2475 years, acceleration record: 475s3a, WL: +13.4 63 Figure 5.24 Liquefaction zone, T = 2475 years, acceleration record: 2475s3a, WL: +10.5 63

Figure 5.25 Liquefaction zone, T = 2475 years, acceleration record: 2475s3a, WL: +13.4 64

Figure 5.26 Slope stability, safety factor K = 2.846, acceleration record: 475r1a 65

Figure 5.29 Slope stability, safety factor K = 2.737, acceleration record: 475s1a 66

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Figure 5.38 Total displacement (m), acceleration record: 475r1a 70

Figure 5.41 Total displacement (m), acceleration record: 475s1a 71

APPENDIX FIGURES Figure A.1 Initial horizontal effective stress (kPa), acceleration record: 475s3a 82

Figure A.2 Initial vertical effective stress (kPa), acceleration record: 475s3a 82

Figure A.3 Dynamic horizontal effective stress (kPa), acceleration record: 475s3a 82

Figure A.4 Dynamic vertical effective stress (kPa), acceleration record: 475s3a 83

Figure A.5 Liquefaction zone, acceleration record: 475s3a 83

Figure A.6 Horizontal displacement (m), acceleration record: 475s3a 83

Figure A.7 Vertical displacement (m), acceleration record: 475s3a 83

Figure A.8 Total displacement (m), acceleration record: 475s3a 84

Figure A.9 Slope stability, safety factor K = 2.882, acceleration record: 475s3a 84

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Figure B.1 Initial horizontal effective stress (kPa), acceleration record: 2475s3a 85

Figure B.2 Initial vertical effective stress (kPa), acceleration record: 2475s3a 85

Figure B.3 Dynamic horizontal effective stress (kPa), acceleration record: 2475s3a 85

Figure B.4 Dynamic vertical effective stress (kPa), acceleration record: 2475s3a 86

Figure B.5 Liquefaction zone, acceleration record: 2475s3a 86

Figure B.6 Horizontal displacement (m), acceleration record: 2475s3a 86

Figure B.7 Vertical displacement (m), acceleration record: 2475s3a 86

Figure B.8 Total displacement (m), acceleration record: 2475s3a 87

Figure B.9 Slope stability, safety factor K = 2.474, acceleration record: 2475s3a 87

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LIST OF TABLES

Table 3.1 Saturation degree calculation 28

Table 3.2 Necessary diagrams for the analysis of triaxial test 31

Table 4.1 Soil particle distribution table from sieve analysis (ASTM D422-63) 32

Table 4.2 Input data from 4 samples of the harbor soil 33

Table 4.3 Analysis data from 4 samples of the harbour soil 43

Table 5.1 Soil properties of each layers 52

Table 5.2 Peak Ground Acceleration (PGA) value of the return period of 475 years at the boring holes 54

Table 5.3 Peak Ground Acceleration (PGA) value of the return period of 2475 years at the boring holes 54

Table 5.4 Liquefaction calculation results of Red river dike, section K73+750 61

Table 5.5 The water level corresponding to the warning level at Hanoi river dike 62

Table 5.6 Liquefaction potential results corresponding to different water levels at Hanoi river dike 64

Table 5.7 Slope stability results of Red river dike, section K73+750 69

Table 5.8 Displacement results of Red river dike, section K73+750 74

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Figure 1.1 Earthquake simple visualization (University of California, San Diego, 2013)

1.1.2 Liquefaction phenomenon

Due to the earthquake loading, the pore water pressure increases significantly which leads to the volume decrease of soil particle Therefore, load bearing

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capacity and shear resistance of soil are decreased, called as soil liquefaction Liquefaction is considered as the transition of state that the soil changes from discrete state to liquid state It can be represented that the shear stress of saturated discrete soil decrease to equalize with the shear stress subjected to dynamic loading, which makes the soil transfer to liquid state

In normal state, each soil particle interacts with the other surrounding particles, and the interaction force is formed by the loading on the ground and self-weights of the above particle layers Additionally, this force makes the particles interact with each other at a position without movement, and it also creates the load bearing capacity

of soil In terms of saturated soil, the interaction force acts on the particles and pore

water as seen in Figure 1.2a

Figure 1.2 The mechanism of liquefaction (Bhandari, 2015)

Note: - The blue column in the right side represents for pore water pressure

- The length of the arrow represents for the magnitude of interaction forces between particles

At the initial time, the interaction of particles and pore water pressure is relatively

low as seen in Figure 1.2b When earthquake happens, it causes strong stress in

short period The seismic waves transmit through the saturated soil layers, which changes the position of particles and distribute them to the new order The discrete particles have the trend to move closer and make the soil denser At that time, these

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particles take the place and push water away in the pore, which makes the pore water pressure increase Therefore, water tends to dissipate around where the water pressure is less than

The saturated soil does not have enough time to drain out the water, so the pore water pressure increase and the friction connection of those particles is weakened

(Figure 1.2c) When the pore water pressure increases to the certain value, the

connection of particles will be lost and the soil is in the liquid state, called as soil liquefaction (Bhandari, 2015)

Therefore, the soil liquefaction phenomenon happens, which may cause the deformation and destruction of the structure Evaluation of soil liquefaction potential subjected to earthquake loading is an important aspect of geotechnical engineering practice

1.1.3 Liquefaction of river dikes

It is obviously that the seismic motion of earthquake might cause damages to many structures These structures include river dikes or levees which display in cracks, settlement or sand boils caused by liquefaction The in situ tests about earthquake

on embankments resting on loose saturated sand show that the major cause of dike settlement is the lateral deformation of liquefied soil beneath dike away from the embankment centerline (Ehime University, 2015) The mechanism of liquefaction

of river dike soil (Figure 1.3) can be summarized as follows:

− Construction of levee with highly compressive and less permeable soils causes consolidation and settlement on foundation ground

− Rain and underground water infiltrated through the dike will be accumulated in the bowl and formed as the saturated zone

− During the strong earthquake, the sandy soils in saturated zone might be liquefied which causes the significant deformation to the levee

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Figure 1.3 Schematic illustration of mechanism of liquefaction inside a levee

(Maugeri, 2014)

When the liquefaction phenomenon exits in the foundation, the foundation has no load bearing capacity, which leads to the settlement, horizontal displacement and cracks on the river dike Additionally, in terms of high ground water level, the liquefaction happens in dike body leading to the loss of connection capability and initial shape of construction Hence, it causes the deformation and destruction of construction

Some historical figures (Figure 1.4 and 1.5) represent the dike destruction due to the liquefaction as follow:

− Tokachi river dike in Japan was damaged with significant cracks and sand boils;

Figure 1.4 Tokachi earthquake, 2003 (Ehime University, 2015)

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− The liquefied levee slope slide down and spread laterally with convex toes

Figure 1.5 Tohoku earthquake, 2011 (Japan) (Ehime University, 2015)

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1.2 The situation of earthquake problem and dike system in Vietnam

In recent years, the frequency of earthquake in Vietnam is relatively high, especially

in 2010 with the biggest earthquake reached 5.0 Richter Some regions are noticed in the fault line with 6.0 – 7.0 Richter earthquake potential such as Red – Chay River following the Figure 1.6 In the past, Vietnam has recorded two big earthquakes: Dien Bien earthquake (1935) with 6.75 Richter at Ma river fault line and Tuan Giao earthquake (1983) with 6.8 Richter at Son La fault line When earthquake happens, soil is easily liquefied in the presence of water such as along rivers, lakes, bays, Therefore, hydraulic structures like embankment, dike are most commonly affected and damaged when soil liquefaction happens

Figure 1.6 Map of fault system of South East Sea area (Cao Dinh Trieu, 2005)

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The stability studies of in-situ material dikes or embankments filled have been implemented in hydraulic construction for 50 years However, the stability studies of earth works due to earthquake effects are very limited, mainly for concrete dam

Dike is the structure against river flood or seawater The total length of dike in Vietnam is more than 13,200km, including 10,600km of river dikes, 2,600km of sea dikes and 2,500km of special dikes for flood control It is necessary to regularly repair and upgrade these special dikes, especially in the condition of climate change and sea level rise in the future Currently, Vietnam dike system has been designed against storm grade 9 with the maximum tide of 5% Many dikes have been constructed on the thick sand layer which is easily liquefied if the strong earthquake happens Additionally, there are some dikes on the soft soil foundation leading to potential instability due to the poor filling soil quality by using handcrafted filling method (Nam 1997 & 1998) The government has recently approved two big projects: sea dike improvement project, from Quang Ninh to Quang Nam provinces and from Quang Ngai to Kien Giang provinces and river dike improvement project at 19 provinces having the decentralized dikes, with total funds above 50 thousand billion dong, lasted until 2020

Note that Vietnam construction law has few rules and standards for taking account of soil liquefaction in hydraulic construction design such as TCXDVN 285-2002, 14TCN 157-2005 However, the stability evaluation method was mainly based on the pseudo-static method with earthquake acceleration coefficient corresponding to the construction grade Recently, designing construction under earthquake loading was mentioned in TCXDVN 375-2006, which was compiled based on EUROCODE 8 Nevertheless, the limitations of TCXDVN 375-2006 do not consist of seismic recordings, peak ground acceleration with the earthquake return period of more than

475 years in comparison with EUROCODE 8

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The reasons of the selection of Red river dike at Hanoi as a case study in this thesis are based on the following basis:

− Hanoi dike system has the special mission in protecting Hanoi – the center of economic, culture, politics of Vietnam with the population of 6.45 million people (Census Steering Committee on Population and Housing, 2010);

− Hanoi was in the zone of fault line Red river – Chay river; some historical strong earthquakes happened with grade 7, grade 8 in 1277, 1278, 1285 (earthquake magnitude scale MSK-64);

− The soil stratigraphy of dike foundation consist the thick sand layer which is easily liquefied when strong earthquake happens;

− Some water supply projects will be constructed

1.3 Past studies related to the problem and area

In order to have a general view of the problem and study area, so we should refer to some researches related to the study area, application in the world

Nam (2015) studied and modeled the liquefaction potential and stability of an actual river dike at Hanoi under the different earthquake scenarios according to Finite Element method, using Quake/W software The analysis results showed that with the thick sand layer, the right bank of Red river dike has the liquefaction potential of soil soil inside dike with the earthquake return period of 475 years and 2475 years, which endangers the dike and the constructions on it

Nam (2012) analyzed the cause of slope failure of the right bank of Red river, corresponding to K29+850 – K30+050 Red river dike at Son Tay The analysis results showed that the main causes of the failure of the right bank of Red river was the placement of heavy sand pile and the soft soil 2a in the foundation through critical cross section 2-2’ The liquefaction phenomenon was not considered because of no earthquake

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Duong (2012) studied the liquefaction mechanism of in-situ material dam Nam Khau

Hu, Dien Bien province The analysis results showed that the in-situ material dam was totally complied with dam quality, eliminated the seepage flow drawbacks and the liquefaction risk if earthquake happens

Tam- et al (2011) analyzed the liquefaction potential of Red river dike Km29+900 to Km30+050 in Son Tay district The analysis results showed that the level of earthquake was corresponding to the scope of liquefaction area The result with employing the linear equivalent model was smaller than that with the linear elastic model

Binh and Phuong (2008) studied experimentally the change of Pore Water Pressure for sedimentary clays Holocen at Red River Delta subjected to dynamic loading cycles However, the experimental results were still limited, and the accuracy of results, the experimental condition and the apparatus need to be clarified

Youd- et al (2001) summarized the method of evaluation of liquefaction resistance of soil known as simplified procedure The CPT and SPT provide detailed soil stratigraphy and robust filed-data based liquefaction resistance curve Procedures for evaluation of liquefaction resistance beneath sloping ground or embankments have not been developed (slope greater than 6%)

Nghia (2003) study and determine the coefficients of soil dynamic to apply for computing the works under dynamic loading Stress waves were loading transmission including compress wave (P-wave) and shear wave (S-wave) The liquefaction was due to expansion causing shear deformation The shear resistance module D was calculated approximately through Vane Shear Test

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1.4 Research objectives

The main objective of this research can be represented as follows:

− Determining the liquefaction risk due to strong earthquake

− Evaluating the liquefaction potential of Red river dike foundation for different calculation scenarios

− Slope Stability assessment of Red river dike caused by earthquake

− Recommendation for the improvement of the safety of Red river dike when strong earthquake happens

1.5 Research methodology

The research can be implemented by two methods: experimental method and numerical modeling method based on Finite Element Method (FEM) The following approach will be implemented in the research:

− Collecting the necessary data from all related sources including:

• Basic data of topography, hydrology, water level

• Soil properties of each layer for all boring holes

• Historical records of earthquake and acceleration time history in the study area

− Clarify the formation mechanism of liquefaction

− Experimental studies using dynamic triaxial apparatus on Red river sand samples

− Modeling of liquefaction and slope stability based on Finite Element Method, calibrating and validating using measured data

− Assess and determine the safety of Red river dike based on the measured and simulated results

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1.6 Organization of thesis

The thesis is organized and presented mainly in 5 Chapters and 2 Appendices:

Chapter 1: Introduction

Chapter 2: Liquefaction analysis and Slope stability theoretical basis

Chapter 3: Test material, apparatus, procedure and output parameters

Chapter 4: Test results and discussion

Chapter 5: Liquefaction modeling of Red river dike and Slope stability analysis

Chapter 6: Conclusion and Recommendation

Appendix A: Liquefaction results corresponding to 475-year earthquake return

period

Appendix B: Liquefaction results corresponding to 2475-year earthquake return

period

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CHAPTER 2: LIQUEFACTION ANALYSIS AND SLOPE STABILITY

THEORETICAL BASIS

2.1 Overview of analysis methods

In terms of soil liquefaction analysis and assessment, there are many methods to implement in the past studies in all over the world such as simplified procedure, experimental method, numerical modeling method and physical modeling method

Over the past 45 years, a methodology termed the ‘‘simplified procedure’’ (Seed and Idriss, 1971) has evolved as a standard of practice for evaluating the liquefaction resistance of soils The simplified procedure was developed from empirical evaluations of field observations and field and laboratory test data Two variables are required for evaluation of liquefaction resistance of soils: the seismic demand on a soil layer, expressed in terms of CSR, and the capacity of the soil to resist liquefaction, expressed in terms of CRR The equation 2-1 for factor of safety (FS) against liquefaction is written in terms of CRR and CSR as follows:

Where: - CSR = cyclic stress ratio generated by the earthquake shaking;

by the earthquake

• g = acceleration of gravity

• σvoand σ’vo are total and effective vertical overburden stresses

• r d = stress reduction coefficient

experimental test data (cyclic triaxial test, simple shear test or hollow cylinder torsional shear test)

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This research will be implemented by combining the experimental method and the numerical modeling method

To begin with, the experimental method uses the laboratory experimental apparatus to study the liquefaction parameters (as described in section 2.2), mechanism and soil behavior due to cyclic loading Firstly, the liquefaction parameters need to be clarified

to have the general view about the parameters obtained from the test After that, the Cyclic Undrained Triaxial Test will be implemented with the sand samples by using Cyclic Triaxial apparatus Following the test procedure, the output data of triaxial test can be determined and analyzed to get the relationship between liquefaction parameters corresponding to the representative diagrams

Additionally, these above output data of experiment and the representative diagrams will be applied as the input data in modeling problem based on the numerical modeling method First of all, the model will be set up following Finite Element method with the specified boundary conditions and the necessary input parameters Hence, the model results can be analyzed more clearly with the accurate figures and summarized in the tables

2.2 Experimental method

Liquefaction parameters

 Cyclic Stress Ratio, CSR

The relationship between density, cyclic stress amplitude and number of cycles

to liquefaction failure can be expressed graphically by laboratory cyclic strength curves Cyclic strength values are normalized by the initial effective overburden pressure to produce a cyclic stress ratio (CSR) For the cyclic tri-

axial test, the CSR is defined as the ratio of the maximum cyclic shear stress to the initial effective confining pressure (2-1)

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𝑪𝑺𝑹 = 𝝈𝒅

𝟐𝝈𝟑𝒄′

 Excess Pore Water Pressure

To quantify pore pressure build-up during a tri-axial test, the excess pore water pressure ratio Ru is often used This can be defined as the ratio of excess pore pressure change during loading to the effective stress applied at the beginning

of loading (2-2)

𝑹𝒖 = ∆𝒖 𝝈 � 𝟑𝒄′ (2-3)

= 1 the pore pressure is equal to the confining pressure and the effective stress has reduced to zero

 Axial Strain

The number of cycles can be obtained based on the specified value of the double amplitude of axial strain, DA (%), which is calculated by the formula (2-3):

𝜺𝒂 = 𝒔 𝑯 � 𝟎 (2-4)

The DA value becomes 1%, 2% and 5% to evaluate the single amplitude of cyclic deviator stress, σd, and the corresponding cyclic stress ratio

 Deviatoric Stress versus Mean Effective Principal Stress, q ~ p’

During cyclic triaxial testing, it is impractical to use Mohr’s circle in σ-τ diagram when analyzing soil behavior because of the different circles changing both in size and position Therefore, in order to picture stress condition, the deviatoric stress, q is represented as a function of mean effective stress, p’

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2.3 Modeling the problem of Red river dike – modeling method

2.3.1 Overview of modeling method

In order to understand clearly about the liquefaction potential and slope stability of case study, the numerical modeling using the Finite Element Method (FEM) should

be applied by one of the most common geotechnical software – module QUAKE/W in GeoStudio 2007 –developed by GEO-Slope International Ltd, Canada This software supports for analyzing the response and behavior of earth structures subjected to earthquake shaking including:

• The movement, internal forces during the shaking

• The generation of excess pore water pressure

• The potential reduction of the soil shear strength

• The effect on stability

The Finite Element Stress-based method is applied to evaluate the stability variation due to ground shaking during an earthquake (SLOPE/W manual, 2008) The stresses can come from a QUAKE/W dynamic finite element analysis the same as they can from a static stress analysis The stresses computed during a dynamic earthquake analysis can be saved at regular intervals during the shaking

The Finite element stress can be imported into a conventional limit equilibrium analysis The stresses σx, σy, and τxy are known within each element, and the normal and mobilized shear stresses can be computed at the base mid-point of each slice Therefore, the forces can be integrated over the length of the slip surface to determine a stability factor as formula 2.5

𝑭𝑺 = ∑ 𝑺𝒓

∑ 𝑺𝒎 (2-5)

- Sm is the total mobilized shear along the entire length of the slip surface

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A factor of safety then can be computed for each moment in that that the stresses are available, and in the end a plot of factor of safety versus time graph can be created, as shown in Figure 2.1 This type of plot can be created for each and every trial slip surface

Figure 2.1 Factor of safety versus time during the earthquake

The Finite element based approach overcomes any of the limitations inherit in a limit equilibrium analysis, and it has many advantages as follow:

− There is no need to make assumptions about interslice forces

− The stability factor is deterministic once the stresses have been computed, and consequently, there are no iterative convergence problems

− The issue of displacement compatibility is satisfied

− The computed ground stresses are much closer to reality

− Stress concentrations are indirectly considered in the stability analysis

− Soil-structure interaction effects are readily handled in the stability analysis

− Dynamic stresses arising from earthquake shaking can be directly considered in a stability analysis

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2.3.2 Modeling the problem

Based on the cross-sections following the topographical and geological investigation document of Red river dike Km73+500 to Km74+100, TLU (2015),

the section K73+750 is selected to model and analyze with maximum historical

flood level (+13.4) in 1971 at the river side and no water at the land side Figure

2.2 illustrates the mesh and boundaries of section K73+750 of Red river dike

Figure 2.2 Modeling of problem for section K73+750

After determining the geometry and mesh of problem, the soil behaviour model

need to be specified with linear elastic model for all layers According to the geological document, some required soil properties were determined, including:

• Unit weight, (γ)

• Poisson ‘s ratio, (ν)

• Damping ratio, (D)

Following the laboratory experiment results, the relationship diagrams will be used

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The soil behaivor model is presented in the Figure 2.3 with the specified value of

model parameters for each soil layer

Figure 2.3 Diagram of model parameters for each soil layer

The process of analyzing the liquefaction problem as below:

− Step 1:

Using module Quake/W to analyze the initial stress problem before earthquake happens Figure 2.4 presents the diagram of modeling initial stress problem

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Figure 2.4 Diagram of modeling initial stress problem

− Step 2:

Using module Quake/W to analyze the dynamic problem (Figure 2.5) The duration of earthquake in Red river dike happens in 10 seconds which is divided into 2000 time steps with 0.005 second for each step For every 10 steps, the program will save the results The earthquake analysis results will be used to analyze the slope stability based on FEM

Figure 2.5 Diagram of modeling dynamic problem

− Step 3:

From the earthquake analysis results of module Quake/W, we use the Finite Element Stress method by integrating these above results into module Slope/W to analyze the slope stability for the downstream slope seen in the Figure 2.6

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Figure 2.6 Diagram of modeling dike slope stability subjected to earthquake loading

The most critical slip surface is selected from the stability factor result with the different assumed slipping centers and slipping radius for the different time periods For each time period, the number of analysis slipping surface is 1331 slipping surfaces by selecting number of radius increments equal 10 The total number of slipping arc is 1331x2000/10=266200 potential sliding arcs

Figure 2.7 Number of slipping surfaces

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2.3.3 Output of modeling

2.3.3.1 Liquefaction zone

Loose sand fundamentally has a collapsible soil-grain structure, and when the grain-structure collapses the shear strenth under undrained conditions may diminish to what is known as the steady-state strength The soil liquefaction behavior can be described in the context of a q-p’ diagram (shear stress vesus mean principal stress) A collapse surface definition together with a specified steady-state strength can optionally be used in QUAKE/W to flag elements as

“liquefied” and assign these elements a steady-state strength in SLOPE/W stability analysis or a SIGMA/W stress re-distribution analysis The excess pore water pressure will continue to increase until the stress cyclic path reaches the collapse surface Then, the soil will liquefy and the strength falls along the collapse surface to the steady state point

Figure 2.8 Cyclic stress path from B to the collapse surface (QUAKE/W

manual, 2010)

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The deformed mesh presents a clear picture of displacements for a single time step

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CHAPTER 3: TEST MATERIAL, APPARATUS, PROCEDURE AND

OUTPUT PARAMETERS

By applying the modeling analytical method, the experiment results in the laboratory will play the vital role in not only the next step of analysis and modeling but also the general results of this research Therefore, we need to figure out the general characteristics of specimens, the experiment apparatus, the method and the output of triaxial test

by using thin-walled tube samplers after removing ground surface

Figure 3.1 Sand material dumped at the Hanoi harbor

3.2 Dynamic triaxial apparatus

The employed apparatus is Cyclic Triaxial Apparatus, the model DTC–367D manufactured by SEIKEN Company, Japan (Figure 3.2) This apparatus consists of a

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triaxial cell, cell pressure and back pressure control devices, a data acquisition and recording system for axial load, axial displacement, volume change, and pore water pressure of specimen The whole machine is connected to a laptop through data amplifiers and Sensor Interface including a sampling software in order to obtain the raw test data

Figure 3.2 Cyclic Triaxial Apparatus DTC – 367D, SEIKEN Japan

3.3 Test procedure

The method used for carrying out the test is followed the JGS standard: JGS

0541-2000 “Method for Cyclic Undrained Triaxial Test on Soils” Following is the description of test procedure employed in this study

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3.3.1 Sample preparation

The red river sand sample collected at the field was set in accordance with the JGS standard: JGS 0520-2000 “Preparation of Soil Specimens for Triaxial Test” as seen

in Figure 3.3

Figure 3.3 Sand specimen preparation

The cylindrical specimen was prepared with the initial dimension: diameter D=50mm, height H=100mm The specimen was formed by pluviating sand particles through air in which air-dried sand falls through a funnel with the desired calculated height of fall maintained constant by using the string liner to get the uniform relative density Dr based on the following formula (3-1):

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emax: Maximum void ratio

emin: Minimum void ratio

Note that: the initial void ratio e0 was determined based on density at site

3.3.2 Water supply and Pressure supply

After the specimen preparation, the de-aired water was supplied to the cylindrical tank by opening the valve Confining water Until water reached the target level in order to guarantee that the specimen is submerged, but it is not higher than the upper part of membrane attached to the top cap in case that water might go inside the specimen (Figure 3.4)

Then, we supplied the initial confining pressure of 30 kPa for this cylindrical tank

Figure 3.4 Water supply and Pressure supply for specimen inside the triaxial cell

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3.3.3 Carbon dioxide (CO 2 ) pervasion

pervaded into the specimen for 30 minutes with the recommended rate of 2-3

(44) being higher than air (~29), which leads to the air pump through the upper stone by CO2

Figure 3.5 The system of CO 2 gas tank and controller

3.3.4 De-air water supply

minutes until there is no more air bubbles coming out

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3.3.5 Saturation checking

We check the saturated condition of the specimen based on the B value which was measured by the ratio of the pore water pressure (PWP) and cell pressure (CP) by equation (3-2):

Where:

Δu: a change of Pore Water Pressure (PWP)

Δσ: a change of Cell Pressure (CP)

Firstly, we increased the back pressure to get 80kPa of CP and 50kPa of PWP Secondly, we locked the valve for undrained condition and increase the cell pressure to 150kPa, then we checked the measured value of PWP by the sampling software as shown in the Table 3.1 Then, we decreased the cell pressure back to 80kPa and released the valve The process was repeated with each increment of 50kPa until the accepted B value was greater than 95%

Table 3.1 Saturation degree calculation

3.3.6 Consolidation

We released the load cell to take isotropic consolidation for about 30 minutes, and then recorded the data from burette and measurement device

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3.3.7 Cyclic undrained loading

In the cyclic loading stage, the sinusoidal cyclic load with frequency of 0.1 Hz was applied under undrained condition The load amplitude values were varied for each specimen We recorded the data until the specimen was liquefied with certain number of loading cycles The condition for liquefaction is that the excess pore

5% (JGS 0541 – 2000)

When conducting the liquefaction test, the load frequency and magnitude were controlled by Pneumatic Servo Controller E0-260 From this machine, a signal voltage would be sent to the piston to apply the force in the load cell The Sensor Interface would receive the results and transfer it to the computer so that the measured data was recorded and controlled by the program DCS-10A Electronic Instrument

3.4 Output parameters

The output data obtained when performing the cyclic triaxial test include:

• Pore pressure: u (kPa) measured by sensor PGM-10KE

• External vertical displacement: LD (mm) measured by ODC-25

• Small displacement: SD (mm) measured by Model LP-200

• Elapsed time: t (s) measured by DCS-10A Electronic Instrument

• Volume change: ΔV (ml) measured by burette and OUTPUT (V)

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