Spatial Variability

8/15/2019 Spatial Variability

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Spatial variability


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Spatial variability

• Measured soil properties can exhibit considerablespatial variation even within relativelyhomogeneous deposits

• They exhibit similar values at neighbouringlocations than that at locations far away.

• The common use of mean and point variance of aset of measurements for design ignores this

aspect.• A unique character exhibited by soil and rock

• Characterized by autocorrelation distance, thedistance upto which the correlation of soil

properties deemed to be appropriate.


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Spatial variability

• Useful in random field modeling

• Useful in the evaluation of variance

reduction

• Enables to critically assess and compare

various site investigation and testing

programs, and also to evaluate their

effectiveness.


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Spatial variability

• For getting autocorrelation or scale of fluctuation

of a soil property, autocorrelation function is first

obtained for the data under consideration.

• Autocorrelation function is a plot of autocorrelationcoefficients at various lags.

• Autocorrelation coefficient at a lag, k, is the ratio

of autocovariance at that lag (ck

) and the variance

of the data (c0).


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Spatial variability

• Since we always play with limited dataset

in geotechnical engineering, the

correlation coefficients are obtained from

sample, represented as r k. Theautocorrelation function, thus obtained, is

called sample autocorrelation function.


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(Auto)correlation distance

• Autocorrelation function is used to estimate theautocorrelation distance.

• Mathematically, autocorrelation distance (or

correlation length) is defined as the area underthe autocorrelation function.

• The distance at which autocorrelation

coefficient corresponds to 1/e (i.e. 37%), is

termed as autocorrelation distance (DeGroot,1996).

• Scale of fluctuation is numerically related to

autocorrelation distance; and its value depends

on the shape of the autocorrelation function.


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Scale of fluctuation


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Scale of fluctuation

(Spry et al., 1988)


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Correlation distance

• Commonly used analytical models to fitsample autocorrelation functions:


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Observed scales of fluctuation

(Phoon et al., 1995)


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Spatial variability – Keswick Clay –

Adelaide University, Australia

Jaksa et al. (1999)


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How to estimate autocorrelation

distance?

where, theta is autocorrelation distance (or correlation

length) , and r(t) is the autocorrelation function.

If correlation distance is to be finite then r(t) must

decrease sufficiently quickly to zero as t increases.


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Vertical Spatial variability

(C8 profile) – Dasaka (2005)


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Vertical Scale of fluctuation



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Spatial variability analysis at a power

plant site in India (Dasaka, 2005)

Autocorrelation distance and scale of fluctuation of

vertical qc are 0.22 and 0.39 m, respectively.


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Variance reduction function

(Babu et al., 2006)


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Spatial variability – Keswick Clay –

Adelaide University, Australia

Jaksa et al. (1999)


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Vertical Scale of fluctuation



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Spatial variability analysis at a power

plant site in India (Dasaka, 2005)

Autocorrelation distance and scale of fluctuation of

vertical qc are 0.22 and 0.39 m, respectively.


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Variance reduction function

(Babu et al., 2006)


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Important topics

• 3. Reliability of shallow foundations

designed to Eurocode 7, Forrest et

al.Volume 4, Issue 4, 2010, Georisk

• 4. A probabilistic evaluation of the size

of earthquake induced slope failure for

an embankment, Hata et al. 2001, pages73-88


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Important topics

• 5. Load-displacement uncertainty of

vertically loaded shallow footings on

sands and effects on probabilistic

settlement estimation, Uzielli & Maynepages 50-69, 2011, Georisk


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Important topics

• 6. Probabilistic seismic hazard analysis

for rock sites in the cities of Abu Dhabi,

Dubai and Ra's Al Khaymah, United

Arab Emirates, Aldama-Bustos et al.pages 1-29, 2009, Georisk

• 7. Reliability analysis of strength of

cement treated soils, Sivakumar Babu etal. pages 157-162, 2010, Georisk


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Important topics

• 8. Slope reliability analysis accounting

for spatial variation, Low et al. pages

177-189. 2007, Georisk

• 9. Assessment of flood risks in Pearl

River Delta due to levee breaching,

Zhang, et al. pages 122-133, Georisk

• 10. Reliability analysis of soil nail wallsSivakumar Babu & Vikas, pages 44-54,

2009, Georisk


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Important topics

• 11. Probabilistic analysis of strip

footings resting on a spatially random

soil using subset simulation approach,

Ahmed & Soubra, pages 188-201, 2012,Georisk

• 12. Probability of scour depth

exceedance owing to hydrologicuncertainty, Briaud et al. pages 77-88,

2007, Georisk


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Important topics

• 13. Probabilistic analysis of a one-

dimensional soil consolidation

problem, Houmadi et al. pages 36-49,

2011, Georisk

• 14. MCS-based probabilistic design of

embedded sheet pile walls, Wang,

pages 151-162, 2013, Georisk


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Important topics

• 15. Probability distribution for

mobilised shear strengths of spatially

variable soils under uniform stress

states, Ching & Phoon, pages 209-224,2013

• 16. System reliability analysis of the

external stability of reinforced soilstructures, Zevgolis & Bourdeau

pages 148-156, 2010, Georisk


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Important topics

• 17. Risk Assessment in Geotechnical

Engineering: Stability Analysis of Highly

Variable Soils, Griffiths et al. Proceedings:

Geotechnical Engineering State of the Artand Practice, 2012, GSP-226, pp. 78-101

• 18. Whitman, R. (1984). ”Evaluating

Calculated Risk in GeotechnicalEngineering.” J. Geotech. Engrg., 110(2),

143 –188.


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Important topics

• 21. Impact of Routine Quality

Assurance on Reliability of Bored Piles,

Zhang et al. Geotech. Geoenviron. Eng.,

May 2006, Vol. 132, No. 5, pp. 622-630

• 22. Reliability-Based Design for Internal

Stability of Mechanically Stabilized

Earth Walls, Chalermyanont and Benson,Geotech. Geoenviron. Eng., 2004, Vol.

130, No. 2, pp. 163-173


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Important topics

• 23. Reliability Analysis and Updating of

Excavation-Induced Ground Settlement for

Building Serviceability Assessment, Hsiao et

al. , Geotech. Geoenviron. Eng., 2008, Vol. 134,No. 10, pp. 1448-1458

•

24. Reliability Assessment of Basal-Heave

Stability for Braced Excavations in Clay Gohet al. Geotech. Geoenviron. Eng., 2008, Vol.

134, No. 2, pp. 145-153
http://ascelibrary.org/doi/abs/10.1061/%28ASCE%291090-0241%282008%29134%3A2%28145%29

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Spatial Variability

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