1. ANALYSIS OF THE LIGHT WEIGHT DEFLECTOMETER IN-SITU STRESS AND STRAIN
Patrick K. Miller
BSCE Tufts University
MS Colorado School of Mines
Project Engineer – Olson Engineering

2. LWD Background 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
Prima 100 Zorn ZFG 2000

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

4. Previous In-situ Stress and Strain Research
Fleming (2000)
Used in-situ stress sensors to measure stress induced by the LWD
Did not explore drop height, plate diameter and soil type effects
Did 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.

5. Main Research Objectives
Employ In-situ Sensors to Measure LWD Induced Stress and Strain Levels
Characterize stress and strain state under LWD loading
Determine how stress and strain vary with loading plate diameter and 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

6. In-situ Stress and Strain Sensors
Earth Pressure Cell
(EPC)
Linear-Variable-Differential-Transformer (LVDT) Displacement Transducer

7. Sensor Calibration EPC Calibration LVDT Calibration
EPC’s calibrated in a laboratory calibration device at UMN.
Potential Issues include: stress concentrations, shadowing effects, variable temperature effects, etc.
LVDT Calibration
Factory calibration
No known calibration issues

8. Sensor Placement Procedure
EPC Placement
Placed by hand in lightly compacted new lift
Encased in a pocket of the calibration sand
LVDT Placement

9. Soil Profiles Tested 4 Locations tested for each profile
(2 EPC, 2 LVDT)
0.14 m
0.42 m
0.68 m
Buried EPCs

10. 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

11. Contact Stress Distribution
Terzaghi (1943) theorized that a
rigid circular plate produces a:
Inverse Parabolic Distribution
on cohesive soils
Parabolic Distribution
on non-cohesive soils
Uniform Distribution
on soils having mixed
characteristics
Therefore: Uniform and Parabolic loadings produce E’s of
127 and 170 % of the Inverse Parabolic loading

12. 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 stress
Suggests that the LWD analysis should reflect the soil type tested

13. 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

14. 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)

15. In-situ Strain Results
Employing Static Theory of Elasticity
The increase in strain at depth z is given by:
Where:
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

16. 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

17. Stress/Strain Results
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
Er vs. ELWD Values

18. Conclusions
Contact stress between the soil and LWD is dependent on the soil type and level of loading
Cohesive soil ~ inverse parabolic distribution
Non-cohesive soil ~ parabolic distribution
Mixed characteristic soil ~ uniform distribution
Strain decreased much more rapidly than stress with depth
A 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 Research
More data needed from all soil types, focusing near the surface
Tactile sensors – to measure pressure distribution
Refinement/Laboratory calibration of strain sensors

20. LWD Prototype Key Components Piezoelectric Force Transducer
Measures Applied Force
Urethane Damper
Effects Impulse Duration and Magnitude
Geophone
Measures Response of Loading Plate (velocity)