Pre-failure Deformability of Geomaterials. Hsin-yu Shan Dept. of Civil Engineering National Chiao Tung University

Transcription

1 Pre-failure Deformability of Geomaterials Hsin-yu Shan Dept. of Civil Engineering National Chiao Tung University

2 Strain Levels Strain at failure Sand Clay Rock Distribution of strain of soil in the field when a structure/soil fails

3 Strain Distribution in the Field Shallow foundation Deep foundation Retaining structure Slope

4 Strain under Working Load Less than 1% Axial strain under footing % Shear strain along pile Less than 0.1% near the top of the pile

5 Variation of Deformation Parameters Small strain modulus? Equivalent Elastic Parameters E i = Initial tangent modulus (initial linear section) E f = Secant modulus (0 to strain at failure) E 50 = Modulus from (0 to 50% strength)

6 Variation of undrained Young s modulus E u with mean normal effective stress derived from various sites on London Clay (St. John, 1975)

7 Stress-Strain Relationship Under small strain Soil behaves like elastic material Linear stress-strain relationship Under large strain Nonlinear stress-strain relationship Transition from elastic to plastic behavior

8 Unconcolidated undrained triaxial compression tests on London Clay using local strain transducers (Costa-Filho and Vaughan, 1980)

9 Obtaining Stress-Strain Relationship Laboratory tests Traditionally determine the deformation of the whole specimen Average strain In-situ tests Need to use model to back calculate

10 Source of Errors in Conventional Deformation Measurement Seating errors caused by gaps closing between: Ram or internal load cell and top platen Platens and porous stones (after Baldi et al. 1988)

11 Sources of errors in external axial deformation measurements (Baldi et al., 1988)

12 Alignment errors resulting from equipment and specimen nonconformity, specially: Nonverticality and eccentricity of loading ram Nonhorizontality of platen surface Tilt of specimen

13 Bedding errors caused by surface irregularities and poor fit at the interface between the specimen and porous stone

14 Compliance errors which may occur because: The tie bars extend and cause relative displacement of the top of the cell with respect to the piston The internal load cell deflects The lubricant is compressed in systems using lubricated ends The porous paper is compressed

15 Strain Distribution How does the failure plane/zone in a specimen develop? Different stages of loading Axial strain? Shear Strain?

16

17 Improvement over Traditional Techniques Higher resolution More relevant to shear zone Reduction of boundary effects E.g. friction, inclination, off-center loading

18 Internal strain measuring systems Whole body (imaging) Local (electrical) X-ray Video tracking Contacting Noncontacting Proximity transducer (A, R) Cylindrical capacitance device (R) LVDT (A, R) Flexible strip radial strain caliper (R) Inclinometer gage (A) Hall effect gage (A, R) Local deformation transducer (A) Electrolevel Pendulum gage A: axial R: radial

19 Small Strain Measurement Instrument External proximeter External LVDT Internal proximeter Local LVDT Local LVDT Radial proximeter

20 Stress-strain response during consolidation

21 Stress-strain response during shearing

22 Requirements of Small Strain Measurement Strains must be measured to an accuracy of at least 10-3 % Measuring systems must be able to accommodate coupled axial and radial deformation without loss of accuracy Instrumentation must not interfere with the soil behavior

23 Axial strain measurement must ideally be made locally, over the central one third of the specimens so that end-restraint stress paths Instruments must be capable of operating under different stress path Instruments must be submersible and capable of operating under typical range of triaxial cell pressures Instruments must be capable of operating on triaxial specimens of any dimension typically used throughout the world

24 Instrument Location Resolution (µm) Accuracy (µm) Range (mm) Submersible LVDTs Internal central portion of specimen Noncontacting proximity transducer Internal between top cap and base pedestal Noncontacting proximity transducer External Inductive displacement transducer External measured differential movements between piston and top cap

25 Circular split-spring collar LVDT mounting mechanism for axial deformation measurement (Brown and Snaith, 1974)

26 Fixed LVDT support system (Costa-Filho, 1985)

27 Operating principle of inclinometer level (electrolevel) (Jardine et al., 1984)

28 Pendulum inclinometer (Ackerly et al., 1987)

29 Hall effect gage for axial strain measurement (Clayton and Khatrush, 1986)

30 Hall effect gage for radial strain measurement (Clayton et al, 1989)

31 Local deformation transducer (Tastuoka, 1988)

32 Radial deformation monitoring using proximity transducers mounted in cell wall (Cole, 1978)

33 Arrangement of proximity transducers for deformation measurement (Hird and Yung, 1989)

34 Lateral Deformation and Poisson s Ratio Do we need to know the Poisson s ratio? How to obtain Poisson s ratio? How to measure lateral deformation? Circumference displacement - extensometer Calculate from volume change

35 V V

36 Modulus Determined from Geophysical Tests Relationship between wave velocity and elastic modulus Level of strain induced by seismic waves Relevance of the obtained elastic modulus and shear modulus

37 What will happen when approaching failure? Degree of stress concentration decreases Expansion of highly-stressed zone Expansion of plastic zone From local to overall specimen Overall strain increases at a higher rate than local strain? Overall deformation is the sum of local deformation Overall strain is the average of local strains

38 What about shear stress? Do we need to know the stress distribution? Are we not using the average stress and the local strain to make the stress-strain curve? What is the effect of stress concentration?

39 Importance of Small Strain Parameters Deformation in the field When? Where? How much? Did we take it into account? Level of accuracy? Numerical simulation?

40 How Do We Make Use of the Parameters? Conventional analysis Numerical simulation