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RESEARCH ON MECHANICAL PROPERTIES OF QUATERNARY SEDIMENTS DISTRIBUTED IN HANOI AREA UNDER DYNAMIC LOADS

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Objectives Determining the soil dynamical properties, including strength and deformation of typical soils in the research area, as well as their variations, in order to serve the resear

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MINISTRY OF EDUCATION AND TRAINING

UNIVERSITY OF MINING AND GEOLOGY

NGUYEN VAN PHONG

RESEARCH ON MECHANICAL PROPERTIES OF QUATERNARY

SEDIMENTS DISTRIBUTED IN HANOI AREA

UNDER DYNAMIC LOADS

Specialty: Geological Technology

Code: 62.52.05.01

SUMMARY OF DOCTORAL THESIS IN GEOLOGY

HANOI - 2016

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The research has been accomplished at:

Engineering Geology Department, Faculty of Geosciences and

Geoengineering, Hanoi University of Mining and Geology

Supervisors:

Assoc Prof Dr Le Trong Thang

Hanoi University of Mining and Geology

Reviewer 1: Dr Nguyen Viet Tinh

Hanoi University of Mining and Geology Reviewer 2: Assoc Prof Dr Doan The Tuong

Vietnam Institute for Building Science and Technology

Reviewer 3: Assoc Prof Dr Do Minh Duc

University of Sciences, Vietnam National University

This thesis is going to be defended at the committee of doctorate thesis examiners of Hanoi University of Mining and Geology, Duc Thang ward, Bac Tu Liem district, Hanoi, Vietnam on 08:30 date … month… year 2016

This thesis can be found at National Library, Ha Noi or Library of Hanoi University of Mining and Geology

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INTRODUCTION

1 The urgency of the subject

Dynamic loads are temporary and generated by two sources: natural sources (earthquakes, collapsed caves, slides, .) and artificial sources (machines, hammers, transportation, .) The research on soil mechanical properties under dynamic load (referred to as "dynamic properties") is very important in the design foundation

Hanoi is the Capital of Vietnam with a population of greater focus, along with strong growth in economy, the construction activities are developing and giving rise various types of dynamic loads In addition, Hanoi is located in the 7-8 earthquake zone, some places are 9 As a greater construction, the impact of earthquakes and other seismic are also increasing Other hand, the loads (static and dynamic) decrease with the depth Whereas, the upper ground layers in Hanoi area are mainly sediments of the Holocene, Pleistocene of Hai Hung, Thai Binh and Vinh Phuc formations, these soils are quite sensitive to the effects of dynamic loads However, the information about the dynamical properties of these soils are not sufficient for the research, planning, designing and constructing of building foundation Therefore, “research on mechanical properties of quaternary sediments distributing in the Hanoi area under dynamic

loads” is urgent and topical

2 Objectives

Determining the soil dynamical properties, including strength and deformation of typical soils in the research area, as well as their variations, in order to serve the research, planning, designing and constructing of building foundation purposes under dynamic loads

3 Object and scope

The objects of the study are the dynamical properties of (cohesive and granular) soils belong to Hai Hung, Thai Binh and Vinh Phuc formations Scope areas of the study are the regions of urban districts and Thanh Tri district

of Hanoi City

4 Contents

- An overview of soil dynamics;

- Research on the theoretical basis of soil dynamical properties;

- Engineering geological characteristics of Quaternary sediments in Hanoi area and the methods to study dynamical properties of the soil;

- Experimental study of dynamical properties of Quaternary sediments in Hanoi area

5 The approach and methodology

+ The approach:

- Systematic approach: The problems are detected from the practice; research in an integrated way to find out the theoretical models and methods;

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identifying suitable ones; studied by experiment, synthesis and analysis of results to solve the problems

- Inherited approach of knowledge and experiences selectively in the dynamics studies

- Combining theory and experiment

+ Methodology:

- Synthetic and codified methods of documents on: soil dynamics studies

in and outside the country in order to detect the studied problems; geological and engineering geological studies in the area to clarify the objects and scope of the study

- Theoretical methods: to find the rules and the factors affecting the dynamic properties;

- Geological methods: study of geological characteristics in the area;

- Experimental methods: performing experiments to determine the physical and mechanical characteristics of the soil;

- Mathematical - informatical methods: data processing

6 Scientific and practical significances

Contributions to the science: the research results contribute to clarifying the dynamical properties of the sedimentary formations in the area and the behavior rules of them under the impact of the dynamic force, to serve the planning and construction design; contribute to improving and systematizing the theoretical basis of dynamic properties; providing additional information necessary for following dynamical studies

Contributions to practices and research: the research results are as a basis

to build the processes, to select input parameters for dynamic triaxial testing; the research results are also as the basis data for solving the ground model with dynamic loads; supplying information for forecasting the risk of the ground under the effect of the earthquake and studying the effects of seismic activities

on the geological environment and buildings

7 The scientific arguments

- Argument 1: the process of cyclic deformation of the soils was divided into four stages Each stage is characterized by a type of stress - strain loop and dynamical properties which depend on soil type, characteristics of the loads and stress conditions In particular, the linear limit of the deformation equivalents to the limit of volumetric strain

- Argument 2: the cohesive soils in the research area are collapsed in the form of plastic slip Whereas, the saturated sands of the Vinh Phuc and Thai Bình formations can be liquefied or not depend on the correlation between particle size, density and the parameters of the dynamic forces The boundaries

of cyclic resistance ratio (or liquefaction) of them are described by the expression based on Geniev theory with empirical coefficients of each soil

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8 Innovative aspects

- The thesis has identified the cyclic deformation characteristics of the research soils based on direct experiments by cyclic triaxial test, and dynamic deformation has been divided into four phases based on evaluation methods of stress - strain graphs and loops; clarifying the difference between static and cyclic deformation

- By the experimental data, the thesis has built up the expression that describing the variation of cyclic deformation of the soils in the research area The thesis also points out the similarities between the limit of linear deformation with the volumetric strain limit that is useful for further studies

- The cyclic strength of cohesive soils and the liquefaction of fine sand in the research area are determined directly by cyclic triaxial test The concept of liquefaction is clarified on the basis of quantifying specific criteria, thereby the liquefaction possibility of fine sands is evaluated depending on the density

- Using Geniev theoretical basis, the thesis has built up the expression combining theory and experiment to describe the rule of cyclic strength, and the experimental coefficients were determined for each soil type Thus, the rule of cyclic strength of each soils is described in a simple and clear way by mathematical expressions, that help the application of research results are more favorable

- The thesis has predicted quantitatively the possibility of instability of soils under earthquake effects in the most adverse conditions based on reliable experimental coefficients of each soil

07 chaired by Assoc Prof Dr Le Trong Thang, the candidate PhD is participation The thesis is also the result of "Project of capacity strengthening

of the Geotechnical Laboratory."

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Chapter 1 OVERVIEW OF SOIL DYNAMICS STUDIES

1.1 The concept and contents of soil dynamics studies

Soil dynamics is a part of Soil Mechanics, studies the behavior of soil under the effect of dynamic loads Its contents can be divided into 3 groups: 1) Research on the effect of dynamic loads to changing the physical properties of the soil; 2) Research on soil strength and deformation under the effect of dynamic loads; 3) The research on models of the soil behavior with dynamic loads

1.2 Overview of the research status in the world

The research on the change of soil properties under the effect of dynamic loads: the variation of soil cohesion force, friction angle (Porovski, 1934); void

ratio and permeability coefficient changing (Barkan, 1962); the variability of microstructure, thixotropy phenomenon (Sukina, 1985) and undrained strength characteristics under dynamic loads (Cadagrander, Seed, Onxon, )

The research on the sand liquefaction: determining the relationship

between the deviation of cyclic stress caused liquefaction with the duration of action (Seed and Lee, 1965); studying the variation of sand liquefaction and factors affecting by experiment (Seed and Idriss, 1971; Noorany and Uzdavines, 1989; Shamsher Prakash and Vijay K.puri, 2003; Sitharam, Ravishankar, Jayan Vinod, 2008); research on liquefaction of sand in different density and provided models of dynamic loads to determine the point of liquefaction (Ishihara, 1985); using the method of controlled deformation to study liquefaction (Sitharam, Ravishankar, Jayan Vinod, 2008); building the relationship between the ability of sand liquefaction with field test results (Seed and Alba, 1986; Ronald and Kenneth, 1999; Idriss and Bowlanger, 2004)

The research on cyclic strength of cohensive soil: determining the

collapsed point at the level of strain equal static collapse (Kokusho et al, 1971); research on cyclic strength of cohesive soil at the level of stress deviation close

to damaging static stress (Ishihara, Nagao, and Mano, 1983; Ishihara and Kasuda, 1984); studying the variability of cyclic strength by Kenvin - Voit adjustment model (Geniev, 1997)

The research on cyclic deformation of the soil: the theoretical basis based

on Kelvin - Voit model (Barkan; Arnold Verruijt; Kenji Ishihara; Shamsher Prakash, ); studying the soil cyclic deformation in the elastic phase (Hardin, Richart, 1963; Stokoe, 1978; Grant and Brown, 1981; Hardin and Black, 1968; ), and in the linear and nonlinear phase (Ishihara, 1984; Vučetić, 1994; ); the variation of cyclic strain characteristics (Ishihara, 1984; Vučetić, 1994; Bratosin, 2002, ); the factors affecting the cyclic strain characteristics (Alarcon, Guzman (1989); Darendeli, 2001; ); the influence of the sample (Kumar and Clayton, 2007); the experimental relationships to determine Gmaxaccording to the results of SPT, CPTU (Seed, Lee, Imai, )

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The research on models of the soil behavior with dynamic loads: study

modeling and parameter matrix (Miura, Masuda -1995; -1996 Naggar and Novak; ); modeling solution methods for ground – foundation system based on assumptions elastic deformation, equivalent linear deformation (Tamori, Kitagawa - 2001) and nonlinear deformation (Kusakabe, Yasuda -1994; Miura, Masuda – 1995)

1.3 Overview of the research status in Vietnam

Studies in Vietnam also includes three groups: 1) Research on the effect

of dynamic loads to changing the physical properties of the soil (Nguyen Huy Phuong and Tran Thuong Binh - 2006); 2) Evaluation of sand liquefaction of Thai Binh formation based on the results of SPT (Pham Van Ty et al - 1990); The study on the issue of dynamic consolidation, dynamic strength, sand liquefaction and evaluation of the sensitivity of the soil under the effect of the earthquake in Hanoi (Nguyen Huy Phuong et al - 2011); 3) The research on models of the soil behavior with dynamic loads: seismic zoning studies in Hanoi by Institute of Geophysics (1990); modeling studies the ground – pile system to calculate the transmission of seismic waves when driving pile (Pham Huy Tu - 2003); modeling the ground – pile under horizontal dynamic load (Ngo Quoc Trinh - 2014)

1.4 Comments and Recommendations

1.4.1 Commenting on the research results in the World

The study results showed that the influence of the dynamic load to the variation of soil properties The study of sand liquefaction showed: the liquefaction occurs in saturated sandy soil; the rule of liquefaction is represented by the boundary of liquefaction resistance ratio There are two methods commonly used to study the cyclic strength of cohesive soils: surveying the relations of stress and strain at the strain threshold close to static collapse, and using dynamic loading in the stress deviation close to collapsed static stress; the variation of soil dynamic strength can be expressed in terms of Geniev theory The cyclic strain characteristics vary with the soil deformation and can be determined by many different experimental methods The studies of soil behavior model under dynamic loads are used to study transmission stress

in the ground and the behavior of the ground - foundation system under dynamic loads

1.4.1 Commenting on the research results in Vietnam

1) Achieved results: These studies have adequately addressed the deserve

attention issues in soil dynamics

2) Some restrictions: the theoretical basis of soil dynamics has not been

systematized adequately; the dynamical characteristics of the soil have not been determined directly; The factor affecting the dynamic properties of the soil has not been studied; The study of soil behavior model has not used directly

dynamical characteristics of the soil;

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3) The issues should be studied in Vietnam: the theoretical basis of soil

dynamical properties should be systematized sufficiently; the characteristics of soil dynamical deformation and strength (or liquefaction) should be experimented directly; and simultaneous identification of the rules of their variation (build up the boundary of dynamical resistance ratio), in service for the evaluation of work stability under dynamic loads and earthquake; build up behavior models of ground - foundation system under dynamic loads for each type of background structure (in an area), which uses the dynamic characteristic

of the soil Based on the research objectives and domestic equipment conditions, this thesis focused on the first three issues based mainly on the results of cyclic triaxial test

Chapter 2 THE THEORETICAL BASIS OF SOIL DYNAMICAL

PROPERTIES 2.1 Concepts, classification and calculation of dynamic loads

The load that its eigenvalues change over time F = F (t) is known as dynamic load This load is temporary and is divided into types: circulatory, non-circulatory, harmonic, harmonic damping Harmonic load is described by a sinusoidal, while the circulatory load is described by a chain of harmonic oscillator

Dynamic loads (or stresses) are calculated based on ground earthquake acceleration or other seismic forces For machine foundation, the load is determined by the eccentricity and the angular frequency of the machine

2.2 Soil dynamical properties and research models

Soil dynamical properties are the ability of the soil to behave mechanically under the effect of dynamic load, including: cyclic deformation is the ability to change the shape and volume of the soil; cyclic strength is the ability of the soil bearing maximum stress in a certain period without being collapsed

Cyclic deformation is studies based on Kelvin - Voigt model, along with oscillation theory of a degree of freedom system Cyclic strength can be studies based on Kelvin - Voigt adjustment models (elastic element is replaced with plastic elements) and Geniev theory

2.3 Theoretical basis of soil cyclic deformation

Cyclic deformation theory based on the analysis of a degree of freedom system under harmonic oscillator force Accordingly, cyclic deformation of the soil is completely determined if known the dynamical characteristics, that are dynamic module (Gd) and damping ratio (D)

The phases of cyclic deformation

Based on the relationship between stress - strain, N M Ghexevanov divided soil deformation into three phases [9]: compaction phase; plastic deformation phase; sliding deformation phase In the cyclic deformation

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research, soil strain is divided into 3 phase based on the degree of strain [75]: very small strain, the strain ( is smaller than the threshold of elastic strain (tl); small strain, when  is larger than tl and smaller than the threshold of volumetric strain (tv); medium to large strain: the strain  is larger than 10-2

%

to a few percent

Based on the characteristics of each phase and mechanical models can be used, the thesis divided the soil deformation into four phases: elastic, assuming elastic (linear), elastic - plastic (non-linear) and slide (summarized in table 2.2)

Table 2.2 The phrases of soil cyclic deformation

The model of

the phases

Deformation phrases

The degree of strain

Volume change

Deformation characteristics Change

elastic

tl ≤  ≤ tv

linear (compaction)

small Yes Yes Transportation,

machine foundations, weak earthquakes Elastic - plastic

tv<  < 0,5÷2%

non-linear medium Yes Yes Strong earthquake

(Gmin, Dmax)

Strong earthquake

Factors affecting the cyclic deformation

Hardlin and Drnevich [35] has divided the influencing factors into 3 groups: very important factors: effective stress, void ratio, the degree of deformation and saturation; less important factors: overconsolidation ratio; and relatively unimportant: soil structure, frequency,

2.4 The theoretical basis of soil cyclic strength

2.4.1 The research methodology of soil cyclic strength

The research methodology of cyclic strength by experiment: according to

this method, the cyclic strength variation is expressed by a curve of the relationship between the cyclic resistance ratio with the time loading to reach a state of collapse (td), known as a boundary of the cyclic resistance ratio This boundary is determined by experiment

The research methodology of cyclic strength by Geniev theory: Geniev

using Kelvin - Voigt adjustment model (when the stress exceeds the elastic threshold, the soil deformation transferred to plastic deformation) to simulate the soil behavior under the effect of dynamic loads in short time From which, the expression describing the variation of cyclic strength was built:

otd 

1

1 cot

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Where, o is the coefficient depends on the soil;  is the coefficient depends on stress conditions; d is the ratio of cyclic strength with permanent strength

The expression (2:39) is the theoretical basis for the study of soil dynamic strength and help for the interpretation and orientation of empirical research However, the application of this theory in practice is still limited due to its complexity

Research methodology combining theory and experiment: to take

advantage of the strengths and overcome the limitations of the two methods above, the thesis proposed a method based on Geniev theory combined with empirical research: the expression (2.39) is transformed in the direction of simplification and used popular concepts by inserting the coefficients a and b,

then the expression (2.39) becomes:

td = b

1

1 cot

a CSR a

CSR arc

2 (s), known as a coefficient of cyclic collapse time Equation (2:43) describes the boundary of dynamic resistance ratio of the soil This equation is completely determined if known the coefficients a and b These coefficients are determined by experiment

2.4.2 Characteristics of cyclic collapsed point

Cyclic collapsed point is a point on the boundary of cyclic resistance ratio, where there is the value of maximum stress (d) and the time duration of this stress (td) in certain stress conditions of applications In the cyclic strength testing, this point is determined based on the analysis of variation of pore pressure ratio (Ru) for saturated sandy soils and the relationship of stress - strain over time (load cycles) for clayed soils

2.4.3 Factors affecting cyclic strength

There are many factors affect the cyclic strength such as: effective compressive stress; structure strength; drainage conditions; characteristics of grain; mineral composition; stress conditions; methodology of shearing; shear stress amplitude; frequency and duration of time action

2.5 The method of determining the dynamical properties of the soil

The laboratory tests include cyclic simple shear tests, cyclic triaxial tests; cyclic torsional shear tests, resonant column tests The field tests include seismic refraction test, seismic cross-hole test, spectral analysis of surface waves, seismic cone penetration test In addition, there are also indirect methodologies based on empirical relationships

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Chapter 3 CHARACTERISTICS OF ENGINEERING GEOLOGY OF QUATERNARY SEDIMENTS IN HANOI AREA AND RESEARCH METHODOLOGY OF THEIR DYNAMICAL PROPERTIES

3.1 Characteristics of stratigraphy and groundwater in Hanoi area

3.1.1 Summary of Quaternary sediments in research area

The structure of Quaternary sediments in this area are present of formations in order from the bottom up is Le Chi, Hanoi, Vinh Phuc, Hai Hung and Thai Binh:

- Le Chi formation includes alluvial deposits, that not exposed on the surface but appear only at a depth of 45 - 69,5m Its components consists of gravel, moving to the top of sand, silt and clay;

- Hanoi formation has distributed from 35,5m to 69,5m with components mostly pebbles, gravel, grit, sand and silt;

- Vinh Phuc formation reveal a small area in Co Nhue, Xuan Dinh, is composed of gravel, sand below moving to the is silt, clay The thickness varied sharply

- Hai Hung formation includes lake - swampy deposits (lbQ 21-2hh 1) Its components is silty clay, containing organic matter; marine deposits (mQ21-2

hh 2) is composed of clay, silty clay with blue grey, blue in colour

- Thai Binh formation has formations inside (Q23tb 1) and outside (Q23tb 2) the dike The lower extra-formation consists of: sand, clayer silt with grey-brown, yellow-grey in colour, few places is mixed with grey clay The upper extra-formation consists of: sand, clay and clayer silt with yellowish grey in colour

3.1.2 Engineering Geological characteristics of Quaternary sediments in the study area

Based on the analysis of documents on Quaternary geology and engineering geology, sedimentary components of Hanoi and Le Chi formation are mostly gravel and its distribution is in great depth, so studying their dynamic properties is less meaningful Meanwhile, sediments formations of Vinh Phuc, Hai Hung and Thai Binh distributed at a depth close to the surface and have sensitive component with the effect of dynamic loads So that, the soil

of this sediments is the object of study and divided in detail to 7 types of soil:

1 Alluvial deposits (aQ23tb1): stiff to very stiff clay - sandy clay with greyish brown to yellowish brown in colour (layer 1) The average depth of the top layer is around 3.0 m;

2 Alluvial - lake - bog deposits (albQ23tb1): soft clay - sandy clay with greyish brown, darkish grey in colour, mixed organic matters (layer 2) The depth distribution of the top layer is about 15m, the deepest is 28m

3 Alluvial deposits (aQ23tb1): medium dense, fine sand with blackish grey – brownish grey in colour (layer 3) The depth distribution of the top layer is about 10-20m, the deepest is 34m

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4 Marine deposits (mQ21-2hh2): firm to stiff, bluish grey clay (layer 4) The thickness of the layer is small and scattered

5 Lake - swampy deposits (lbQ21-2hh1): very soft to soft clay – sandy clay with blackish grey in colour, mixed organic matter (layer 5) Depth distribution

is from a few meters to over 20m

6 Alluvial deposits (aQ13vp2): stiff to very stiff clay - sandy clay with spotted yellowish brown – redish brown in colour (layer 6) The depth and thickness of the layer varies sharply from a few meters to tens of meters

7 Alluvial deposits (aQ13vp1): medium dense to dense, fine - medium sand with yellowish grey (layer 7)

3.1.3 Groundwater characteristics: The study area has three aquifers: qh, qp 2

and qp 1 In which, the water level of qh in the areas where not affected by

mining is usually a few meters below the ground

3.2 Methodology, contents, quantity of the research and experimental procedures

3.2.1 The basis of the research methodology selection

Table 3.4 The dynamic deformation phases, computational models and

appropriate methods

parameters

Assumptions and computational models

Appropriate methods

Elastic Gmax

(D =0)

Elastic deformation ground

The methods of wave propagation test in the field, cyclic torsional shear tests Assuming

elastic (linear) Gd, D

Linear deformation ground Cyclic simple shear tests,

cyclic triaxial tests; cyclic torsional shear tests, resonant column tests

Elastic - plastic

(non-linear) Gd, D

Non -linear deformation

ground Plastics

- At elastic phase, elastic modulus Gmax is determined based on the SPT results and the void ratio by the empirical formula (Section 2.5.3);

- The typical parameters for phases of assuming elastic and elastic - plastic were determined by cyclic triaxial test;

- At plastic phase (sliding), the soil is considered to have collapsed and should identify the parameters of cyclic strength These parameters are defined

by cyclic triaxial test

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3.2.2 The content and quantity of research

To ensure objective research, sampling locations were determined in accordance with common distribution area of study subjects The quantity and contents of specific research are summarized in Table 3.5 and 3.6

Table 3.5 Summary of the content and quantity study of soil deformation by

cyclic triaxial test

1 Determining the dynamic

deformation properties in

different phase for each soil

Each soil was tested in the same frequency and pressure chamber under the different amplitude of cyclic stress

66 samples in all types of specific soil

2 To study the effect of the

pressure chamber

The frequency and amplitude of the load is held constant, changing only the pressure chamber (3 = 0;

25; 50; 75; kPa)

Tested 4 samples Svpand 6 samples

1; 2; 3; 5; Hz)

Tested 7 samples S hhand 5 samples

Ytb

Table 3.6 Summary of the quantity study of cyclic strength

by cyclic triaxial test

Stiff, yellowish grey sandy Clay

(Layer 1-Stb2)

Determining cyclic collapsed point and the boundaries of cyclic resistance ratio for cohesive soils

7

Soft, blackish grey sandy Clay

(Layer 2-Ytb)

4

Soft, blackish grey sandy Clay

Bluish grey fine Sand (Layer 3-Ctb)

Determining liquefied point and the boundaries of liquefied resistance

ratio for sands

9 Yellowish grey fine Sand

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3.2.3 The experimental procedure for determination of the dynamical properties of soils using the Cyclic Triaxial Apparatus

Testing equipment is Tritech 100 made by Controls - Group (Italy) The experimental procedure for determination of the dynamical properties is done in accordance with ASTM - D3999 and ASTM - D5311

Stress conditions and loading parameters are determined accordance with the actual conditions of the ground and the local conditions Accordingly, loading frequency was selected in the range of f = 0.5 ÷ 10 Hz and focusing on the range 1 ÷ 5Hz; cyclic stress ratio CSR = 0.06 ÷ 0.40

3.3 The results of soil dynamical properties determination by empirical formulas

Summary of calculated results is represented in Table 3:14

Table 3.14 The results determining the elastic modulus G max for each soil

Chapter 4 RESEARCH ON CYCLIC DEFORMATION OF SOILS BY

CYCLIC TRIAXIAL TEST 4.1 Characteristics of cyclic deformation in different phases and specific graphs

The soil deformation characteristic is reflected by strain graphs, stress - strain loops, correlated curves of stress – strain and the increase of pore pressure Therefore, it is necessary to analyze these graphs to study dynamic deformation at different phases

- According to the test results, there are three types of strain graphs, depending on the experimental conditions: Type 1, strain amplitude and maximum strain values are stable; Type 2, constant strain amplitude but maximum strain values increase by cycles and exceed 0.5%; Type 3, the strain amplitude and strain values increase over time in excess of 0.5% to a few percent

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Hình 5.29. Biến đổi các hệ số a, b theo D r - RESEARCH ON MECHANICAL PROPERTIES OF QUATERNARY SEDIMENTS DISTRIBUTED IN HANOI AREA UNDER DYNAMIC LOADS
Hình 5.29. Biến đổi các hệ số a, b theo D r (Trang 22)

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