A method predicting pumping-induced ground settlement using back-analysis and its application in the Karla region of Greece

  • Constantine Stamatopoulos
  • Petros Petridis
  • Issaak Parcharidis
  • Michael Foumelis
Original Paper

Abstract

In many arid planar regions of the world, ground subsidence induced by the lowering of the water table line due to pumping has recently caused damage to houses and other overlying structures. The depth of the water table lowering is usually tens of meters, the depth of the underlying soil layers may be hundreds of meters, and the region where the lowering is applied may extend tens of square kilometers. In this aspect, the problem under consideration differs drastically from other geotechnical engineering problems and the application of the physical models may have the serious deficiency that required geotechnical information may be incomplete and very costly to obtain: The change in water table variation and the depth of rock are usually known from results of pumping borings and geophysical investigations, but the location, width, compressibility and consolidation characteristics of the clay layers, are usually not known. New space technologies, such as the phase shifting interferometry radar method, provide cost-effective measurements of past displacement data. Based on past displacement measurements, an alternative approach is proposed to predict ground subsidence induced by the lowering of the water table. In particular, the work derives a simplified equation and corresponding methodology which predicts ground subsidence in terms of water table history, based primarily on data of past ground subsidence. This equation was derived and validated based on a state-of-the-art proposed model predicting one-dimensional ground subsidence induced by water level lowering in planar regions. Based on the derived simplified expression, a method predicting the risk at the built environment due to future ground subsidence induced by water level lowering was proposed and applied successfully in a well-documented case study of ground subsidence: the Niki village at Thessaly, Greece.

Keywords

Consolidation Ground subsidence Change in water table elevation Pumping Clays Differential interferometry radar Back-analysis Thessaly plain Karla region 

List of symbols

ac, acw, ah

Factors defined by Eq. (3)

A1, B1, Ao

Factors given by Eqs. (12), (28b)

a, b

Parameters of Eq. (10)

Cr, αr

Compression index under unloading, factor of Eq. (16)

Cc, Cci

Compression index under loading, Compression index under loading of layer i

cv, cvi

Coefficient of consolidation, coefficient of consolidation of layer i

co

Constant given by Eq. (17b)

D, Dci, Dc, Dca, Dcb

Depth of rock below the initial depth of the water table line, thickness of the clay layer i, total thickness of the clay layers, total thickness of the clay layers at parts a and b (defined in Sect. 2.2), respectively

Dcci, Dcc

Drainage height of layer i, the average drainage height

e, eo, eoi, eav, eL

Void ratio, initial value of void ratio, initial value of void ratio of layer i, average void ratio, the void ratio at the liquid limit

errn2, n2

Error in the prediction of n2 data points, number of data points

f

Function

hw, Δhwji, Δhwi, hwm, dhw

Water table depth, water level depth change at step j above layer i, total water level depth change at layer i, maximum change in the water table level depth, the peak-to-peak change in h w in the case of yearly cyclic variation of h w

hwm (t), hwm (to), hwm (t1), hwm (t2)

Maximum change in the water table line depth at time t, to, t1, t2

n, m

Total number of clay sub-layers and water level change times considered, respectively

M, μ

Dimensionless parameters of Eq. (1c)

PI, PIi

Plasticity index, plasticity index of layer i

qpred−i, qmeas−i

Predicted and measured value of data point i

Q

In Eq. (5), C c , c v , e o , γ t

R1, R2

Two regions defined in Fig. 13a

S (t), Si (t), Sf, Si, Sf(ij), Sf (t)

Settlement at time t, Settlement at time t for layer i, total (final) settlement, settlement of layer i, total settlement due to water table lowering j for layer i, total settlement due to current (at time t) water table change

t, tjT, Tij, Ti, Tav

Time, time of water fall j, dimensionless time, dimensionless time of layer i at water fall j, average dimensionless time of layer i, average value of dimensionless time

t1, t2, to

Times of measurements 1 and 2 and time where measurements start

thw

Final time in case of linear variation of water table with time

thw2

In the case where h w returns at its initial position the time that this occurs

t(0.95)

Time where 95% of the total settlement accumulates

thwm (t), tcr (t), tcr (t1), tcr (t2)

Time of application of the change in hwm (t), thwm (t)/2, t cr at time t1 and at time t2

U (t), Uij (t), Ui (t)

Degree of consolidation in terms of time, degree of consolidation for layer i at time of water change j, degree of consolidation for layer i

Ucom, tcom (0.95), Sf−com

Computed values of U, t (0.95), S f

WL, WLi

Liquid limit, liquid limit of layer i

WTL

Water table line

zi, zav, zwo

Clay sub-layer i average depth, average depth of all the clay layers, water table initial depth

Δtοs (t1), Δtοs (t2)

Settlement change relative to settlement at time to, at times t1 and t2

\(\sigma_{v}^{\prime } ,\sigma_{v - i}^{\prime } ,\sigma_{v - av}^{\prime } , \, \Delta \sigma^{\prime } v,\Delta \sigma_{v - i - j}^{\prime } ,\Delta \sigma_{v\left( a \right)}^{\prime } ,\Delta \sigma_{v(b)}^{\prime }\)

Effective initial vertical stress, effective initial vertical stress at layer i, average effective vertical stress, additional vertical effective stress, additional vertical effective stress of layer i due to Δhwij, additional vertical effective stress of regions (a) and (b) at parts a and b (defined in Sect. 2.2)

γt−ave−i, γtave, γw

Average total unit weight of the soil above the midpoint of layer i, average total unit weight of the soil, unit weight of water

Notes

Acknowledgements

The work was funded by the project “Novel methodologies for the assessment of risk of ground displacement” under ESPA 2007–2013 of Greece, under action: Bilateral S&T Cooperation between China and Greece (Grant No. 12CHN245). The scientists Miranda Dandoulaki, Eleni Stavroyanopoulou, Lydia Balla assisted in parts of this work.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Constantine Stamatopoulos
    • 1
  • Petros Petridis
    • 2
  • Issaak Parcharidis
    • 3
  • Michael Foumelis
    • 4
  1. 1.Stamatopoulos and Associates Co, Hellenic Open UniversityAthensGreece
  2. 2.Stamatopoulos and Associates CoAthensGreece
  3. 3.Department of GeographyHarokopio UniversityAthensGreece
  4. 4.Risk and Prevention Unit at the French Geological Survey (BRGM)OrléansFrance

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