ANALYSIS OF THE LIGHT WEIGHT DEFLECTOMETER

IN-SITU STRESS AND STRAIN

Patrick K. Miller

BSCE Tufts UniversityMS Colorado School of Mines

Project Engineer – Olson Engineering

LWD Background

Prima 100 Zorn ZFG 2000

Purpose

To measure in-situ elastic modulus of soils

QC/QA device

Operation

1 person to operate

1-3 minutes per test

Weighs approximately 20 kg

Common Devices

Prima 100

Zorn ZFG 2000

Current Analysis TechniqueBased upon Boussinesq’s theoretical solution to a static load applied through a rigid circular plate on an elastic half-space.

( )0

1rGA

Fw ν−=

( )0

212rA

kE s ν−=

peak

peaks w

Fk =

Previous In-situ Stress and Strain Research

Fleming (2000)Used in-situ stress sensors to measure stress induced by the LWDDid not explore drop height, plate diameter and soil type effectsDid not measure in-situ strain

Several Researchers have used stress sensors to measure in-situ stress levels from various loading conditions and devices.

Few Researchers have used potentiometers, LVDT’s, or accelerometers to measure in-situ displacement and/or strain produced by various devices.

Main Research Objectives

Employ In-situ Sensors to Measure LWD Induced Stress and Strain Levels

Characterize stress and strain state under LWD loadingDetermine how stress and strain vary with loading plate diameterand drop height (applied force)

Compare Secant Modulus from in-situ stress and strain data to modulus value given by the current analysis method

Characterize “Influence Depth” of the LWD

In-situ Stress and Strain Sensors

Earth Pressure Cell(EPC)

Linear-Variable-Differential-Transformer (LVDT)

Displacement Transducer

Sensor Calibration

EPC CalibrationEPC’s calibrated in a laboratory calibration device at UMN.Potential Issues include: stress concentrations, shadowing effects, variable temperature effects, etc.

LVDT CalibrationFactory calibrationNo known calibration issues

Sensor Placement Procedure

EPC PlacementPlaced by hand in lightly compacted new liftEncased in a pocket of the calibration sand

LVDT PlacementPlaced by hand in lightly compacted new lift

Soil Profiles Tested

FF

Buried EPCs

FF

Test 1 Test 2

4 Locations tested for each profile(2 EPC, 2 LVDT)

In-situ Stress Results

Key Points

Magnitude and duration of the stress pulse is greater in the sand than in the clay

At the deepest layer, the homogeneous profile has a greater magnitude and duration than the layered profile

Contact Stress Distribution

( )0

212rA

kE s ν−=

Terzaghi (1943) theorized that arigid circular plate produces a:

Inverse Parabolic Distributionon cohesive soils

Parabolic Distributionon non-cohesive soils

Uniform Distributionon soils having mixed characteristics

4=A

π=A

4/3π=A

Therefore: Uniform and Parabolic loadings produce E’s of 127 and 170 % of the Inverse Parabolic loading

In-situ Stress Results

Employing Static Theory of Elasticity

The increase in stress at depth z due to a surface loading is given by:

Experimental data verifies Terzaghi’s theory of soil dependent contact stressSuggests that the LWD analysis should reflect the soil type tested

∫ ∫π α

+π=σ 2

0r0 2/522

3

)peak(z0 drd

)zr(rz

2)r(q3

In-situ Stress Results

Terzaghi also theorized that the contact stress between a rigid plate and soil is dependent upon the level of loading

A cohesive material exhibits an inverse parabolic distribution at low levels of loading and trends toward a uniform distribution at loads producing failure

The experimental data also appears to confirm this theory

Therefore understanding the level of loading due to the LWD may also be important in the data analysis

Plate Diameter and Drop Height Effects

Key Points

Stress magnitude of 200 mm load plate is greater near the surface but not at depth

The stress magnitude at each layer is proportional to the applied force (drop height)

Employing Static Theory of ElasticityThe increase in strain at depth z is given by:

Where:

In-situ Strain Results

)]([1θσσνσε +−= rzz E

( ) ( )∫ ∫π

θ α⎥⎥⎦

⎤

⎢⎢⎣

⎡

+

ν−−

+π=σ=σ 2

00r

0 2/3222/522

2

r drdzr

)21(z

zr

zr34

)r(rq

Using a constant modulus the in-situ strain data was fit

The strain decreased much more rapidly with depth than the stress

Note that only the 200 mm plate and largest drop height produced measurable strain at the second layer of sensors

In-situ Strain Results

An elastic modulus which increased with depth was utilized to fit the strain data

It is well know that E increases with a decrease in deviator stress and an increase in confining stress, both cases exist here

The exponentially increasing E provided the best fit

The deviator and confining stress dependent E equation provided a much better fit than the constant E

More data is needed to validate these findings

Stress/Strain Results

Fpeak (kN) 4.1 6.5 8.8

C/C/C 200 mm

Er (MPa) 3051.9 262.8 128.5 ELWD (MPa) 34.8 34.3 31.7 S/C 300 mm

Er (MPa) NA 117.1 104.9 ELWD (MPa) NA 60.3 63.7

Er vs. ELWD Values

The secant modulus of the vertical in-situ stress and strain data was calculated and deemed Er

Er and ELWD values were significantly different, and displayed different trends

ConclusionsContact stress between the soil and LWD is dependent on the soiltype and level of loading

Cohesive soil ~ inverse parabolic distributionNon-cohesive soil ~ parabolic distribution Mixed characteristic soil ~ uniform distribution

Strain decreased much more rapidly than stress with depthA modulus profile which increased with depth more closely matched the experimental strain data.

The secant modulus values calculated from the in-situ stress and strain data did not compare well with values obtained from the LWD

Continuing ResearchMore data needed from all soil types, focusing near the surfaceTactile sensors – to measure pressure distributionRefinement/Laboratory calibration of strain sensors

LWD Prototype

Key ComponentsPiezoelectric Force Transducer

Measures Applied Force

Urethane DamperEffects Impulse Duration and Magnitude

GeophoneMeasures Response of Loading Plate (velocity)