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

## 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

*a*_{c},*a*_{cw},*a*_{h}Factors defined by Eq. (3)

*A*1,*B*1,*Ao**a*,*b*Parameters of Eq. (10)

*C*_{r},*α*_{r}Compression index under unloading, factor of Eq. (16)

*C*_{c},*C*_{c−i}Compression index under loading, Compression index under loading of layer

*i**c*_{v},*c*_{v−i}Coefficient of consolidation, coefficient of consolidation of layer

*i**c*_{o}Constant given by Eq. (17b)

*D*,*D*_{c−i},*D*_{c},*D*_{ca},*D*_{cb}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*D*_{cc−i},*D*_{cc}Drainage height of layer

*i*, the average drainage height*e*,*e*_{o},*e*_{o−i},*e*_{av},*e*_{L}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- err
_{n2},*n*2 Error in the prediction of

*n*2 data points, number of data points*f*Function

*h*_{w}, Δ*h*_{w−j−i}, Δ*h*_{w−i},*h*_{w−m},*dh*_{w}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 }*h*_{w−m}(*t*),*h*_{w−m}(*to*),*h*_{w−m}(*t*1),*h*_{w−m}(*t*2)Maximum change in the water table line depth at time

*t*,*to*,*t*1,*t*2*n*,*m*Total number of clay sub-layers and water level change times considered, respectively

*M*,*μ*Dimensionless parameters of Eq. (1c)

- PI, PI
_{i} Plasticity index, plasticity index of layer

*i**q*_{pred−i},*q*_{meas−i}Predicted and measured value of data point

*i**Q*In Eq. (5),

*C*_{ c },*c*_{ v },*e*_{ o },*γ*_{ t }*R*1,*R*2Two regions defined in Fig. 13a

*S*(*t*),*S*_{i}(*t*),*S*_{f},*S*_{i},*S*_{f(i−j)},*S*_{f}(*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*,*t*_{j}*T*,*T*_{i−j},*T*_{i},*T*_{av}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*t*_{1},*t*_{2},*t*_{o}Times of measurements 1 and 2 and time where measurements start

*th*_{w}Final time in case of linear variation of water table with time

*th*_{w2}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

*t*_{h−w−m}(*t*),*t*_{cr}(*t*),*t*_{cr}(*t*1),*t*_{cr}(*t*2)Time of application of the change in

*h*_{w−m}(*t*),*t*_{h−w−m}(*t*)/2,*t*_{ cr }at time*t*1 and at time*t*2*U*(*t*),*U*_{i−j}(*t*),*U*_{i}(*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**U*_{com},*t*_{com}(0.95),*S*_{f−com}Computed values of

*U*,*t*(0.95),*S*_{ f }- WL, WL
_{i} Liquid limit, liquid limit of layer

*i*- WTL
Water table line

*z*_{i},*z*_{av},*z*_{w−o}Clay sub-layer

*i*average depth, average depth of all the clay layers, water table initial depth- Δ
_{tο}*s*(*t*_{1}), Δ_{tο}*s*(*t*_{2}) Settlement change relative to settlement at time

*to*, at times*t*1 and*t*2- \(\sigma_{v}^{\prime } ,\sigma_{v - i}^{\prime } ,\sigma_{v - av}^{\prime } , \, \Delta \sigma^{\prime } v,\Delta \sigma_{v - i - j}^{\prime } ,\Delta \sigma_{v\left( a \right)}^{\prime } ,\Delta \sigma_{v(b)}^{\prime }\)
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 Δ*h*_{w−i−j}, additional vertical effective stress of regions (*a*) and (*b*) at parts*a*and*b*(defined in Sect. 2.2)*γ*_{t−ave−i},*γ*_{t−ave},*γ*_{w}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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