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**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

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**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

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**Current Analysis Technique**

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

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**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.

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**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

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**In-situ Stress and Strain Sensors**

Earth Pressure Cell (EPC) Linear-Variable-Differential-Transformer (LVDT) Displacement Transducer

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**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

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**Sensor Placement Procedure**

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

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**Soil Profiles Tested 4 Locations tested for each profile**

(2 EPC, 2 LVDT) 0.14 m 0.42 m 0.68 m Buried EPCs

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**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

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**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

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**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

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**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

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**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)

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**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

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**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

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**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

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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

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**LWD Prototype Key Components Piezoelectric Force Transducer**

Measures Applied Force Urethane Damper Effects Impulse Duration and Magnitude Geophone Measures Response of Loading Plate (velocity)

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