Determination of the Diffusion Coefficient for Sands for the Prediction of Enhanced Scour on Beaches

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Determination of the Diffusion Coefficient for
Sands for the Prediction of Enhanced Scour on
Beaches due to Tsunamis

• Eric Heller
• University of Washington
• Department of Civil Engineering

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Introduction

• Tonkin-de Vries (2001) performed scale model
  scour tests in wave tank
• Traditional scour model uses only shear stress,
  scour not correctly predicted
• Account for effective stresses in new model,
  scour more accurately predicted
• Effective stresses controlled by rate of
  diffusion
• Conclusion diffusion coefficient has effect in
  scour

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Objectives

• Determine Cv (diffusion coefficient) in sands
• Develop procedure and apparatus for determination
  of Cv in sands
• Find factors that influence Cv in sands
• Validate values of Cv estimated by Tonkin-de
  Vries (2001)

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Literature Review

• Most research considers wave induced liquefaction
• Cv an input parameter in several models
  (Zen Yamazaki, 1990b Nago Maeno, 1986
  Madsen, 1978 Okusa, 1985)
• Cv determined by standard lab procedure
• standard method assumed to be oedometer test

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Field Conditions

• Pressure increases under wave peak
• Pressure decreases as wave passes
• Applied (wave) pressure decreases faster than
  pressure in pores can dissipate
• Pressure dissipation described by Cv

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Scour Enhancement Parameter

• Quantify effect of effective stresses in scour
• L Scour enhancement parameter
• r density of water
• rsat saturated density of soil
• DP Change in pore pressure
• DT time for DP to occur
• Cv diffusion coefficient

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Diffusion Coefficient

• Need to quantify Cv in sands for use in L
• Natural phenomenon, occurs in many situations
• Cv relates change in pressure over time with
  change in pressure over space
• P pressure
• t time
• z vertical distance

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Estimation of Cv

• Current laboratory methods estimate av
• related to Cv by
• k and e can be accurately estimated in sands

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Estimation of Cv

• Current lab methods designed for clays
• Oedometer
• Isometric consolidation
• Not suitable for sands
• May be adapted for use in sands

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Values of Cv

• Few studies for Cv of Sands, mainly used for
  clays
• SANDS (cm2 / s) CLAYS (cm2 / s )
• 12 ( Zen Yamazaki, 1990b) 0.000018
  (Mitchell, 1992)
• 80 (Tonkin Yeh 2002) 0.000115
  (Al-Dahir Tan, 1968)
• 800 (Tonkin Yeh 2002) 0.00044
  (Sridharan et al, 1995)
• 11520 (Zen Yamazaki, 1991) 0.505
  (Sridharan prakash, 2001)
• Analytical methods estimate modulus ? av k e
  ? Cv

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Finite Difference Estimation of Diffusion Equation
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Test Apparatus
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Test Apparatus

• Pressure Control
• Bottom Lower head pipe
• Top Upper head pipe orifice
• Pore Pressure Transducers
• Pore pressures measured temporally spatially
• Data Acquisition
• Labtech

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Transducer Probes
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• Photos by Eric Heller

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• Photo by Eric
  Heller
• Photo by Brian Bennetts

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Sample Preparation

• 4 methods considered
• Dry pluviation
• Wet pluviation
• Moist tamping
• Slurry method (Kuebris Vaid, 1988)
• Wet pluviation used
• Ensure saturation
• Model depositional environment

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Test Procedure

• Sediment sample
• Attach cap assembly and lower head pipe
• Equilibrate head pipes
• Open valve and record data
• Close valve when done

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Analysis Methods

• Data filtered
• Data analyzed
• Manual analysis
• Point estimate analysis
• Linear regression analysis
• Quadratic

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Raw Data
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Filtered Data w/ Time Window
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Manual analysis

• Mean value

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Point estimate analysis

• Initial, average, and final values

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Linear regression analysis

• Initial, mean, and final values

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Quadratic approximation analysis

• Initial, average, and final values

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Initial Cv vs. void ratio
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Mean Cv vs. void ratio
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Final Cv vs. void ratio
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Trends
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Results

• gt100 values estimated

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Comparison with other values
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Estimate Scour Depth

• Estimate DP DT
• Estimate critical gradient g
• Satisfy
• Calculate G
• Estimate z from plot
• Estimate ds,

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Estimate of Scour Depth

• Drawdown velocity vs. depth of scour. g0.5.
  Cv800cm2/s for Tonkin-de Vries, Cv 812cm2/s
  for Heller1, and Cv 447cm2/s for Heller2.

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Estimate Enhanced Scour

• Estimate L,

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Conclusions

• The design of the testing apparatus has performed
  adequately
• The test method seems to be suitable to determine
  the coefficient of diffusion, Cv
• An experimental estimate of the diffusion
  coefficient, Cv, of 812cm2/s for a particular
  sand was obtained
• The Cv for sand decreases with increasing void
  ratio
• The values of Cv determined in this study
  correlate well with values determined by
  Tonkin-de Vries (2001)
• Cv decreases as the head falls ending at a nearly
  constant value for all tests
• The values of Cv are within one order of
  magnitude of other published values

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Further Research

• Investigate and ensure that void ratio is
  constant throughout sample.
• The effect of the aspect ratio of the test cell
  must be investigated.
• The effect of other soil properties besides void
  ratio on Cv must be investigated
• The effect of different sizes of orifices should
  also be investigated
• It is recommended that field research also be
  done
• Use other methods to find Cv such as the modified
  permeability test proposed by Al-Dhahir Tan
  (1968)
• Other models that use Cv to predict liquefaction
  besides Tonkin-de Vries (2001) and Tonkin et al
  (2002) should be considered.

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• Questions