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
Purpose LWD Background 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
Current Analysis Technique Based upon Boussinesq s theoretical solution to a static load applied through a rigid circular plate on an elastic half-space. w = ( 1 ν ) F AGr 0 k = s F w peak peak 2 ( 1 ) 2ks ν E = Ar 0
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.
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
In-situ Stress and Strain Sensors Earth Pressure Cell (EPC) Linear-Variable-Differential- Transformer (LVDT) Displacement Transducer
Sensor Calibration EPC 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
Sensor Placement Procedure EPC Placement Placed by hand in lightly compacted new lift Encased in a pocket of the calibration sand LVDT Placement Placed by hand in lightly compacted new lift
Soil Profiles Tested Test 1 Test 2 4 Locations tested for each profile (2 EPC, 2 LVDT) F F Buried EPCs
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 Terzaghi (1943) theorized that a rigid circular plate produces a: Inverse Parabolic Distribution on cohesive soils 2 ( 1 ) 2ks ν E = Ar A = 4 0 Parabolic Distribution on non-cohesive soils A = 3π / 4 Uniform Distribution on soils having mixed characteristics A = π Therefore: Uniform and Parabolic loadings produce E s of 127 and 170 % of the Inverse Parabolic loading
Employing Static Theory of Elasticity In-situ Stress Results The increase in stress at depth z due to a surface loading is given by: σ z(peak) = 2π 0 3 r 0 2 0 3q(r) z r drdα 2π 2 2 5 / (r + z ) Experimental data verifies Terzaghi s theory of soil dependent contact stress Suggests that the LWD analysis should reflect the soil type tested
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 Elasticity The increase in strain at depth z is given by: Where: σ r In-situ Strain Results = σ θ = 2π 0 rq(r) 4π Using a constant modulus the insitu strain data was fit 2 r0 3zr z(1 2ν) 0 3/ 2 2 2 5/ 2 2 2 ( r + z ) ( r + z ) 1 ε z = [ σ z ν ( σ r + E drdα σ θ )] 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 The secant modulus of the vertical in-situ stress and strain data was calculated and deemed E r E r and E LWD values were significantly different, and displayed different trends E r vs. E LWD Values F peak (kn) 4.1 6.5 8.8 C/C/C 200 mm E r (MPa) 3051.9 262.8 128.5 E LWD (MPa) 34.8 34.3 31.7 S/C 300 mm E r (MPa) NA 117.1 104.9 E LWD (MPa) NA 60.3 63.7
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
LWD Prototype Key Components Piezoelectric Force Transducer Measures Applied Force Urethane Damper Effects Impulse Duration and Magnitude Geophone Measures Response of Loading Plate (velocity)