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Skattning av en akvifers hydrauliska egenskaper med stokastisk FEM. Med exempel från Malmöområdet

Wall, Henrik and Andersson, Jonas (1999) VSM820 19991
Structural Mechanics
Engineering Geology
Civil Engineering (M.Sc.Eng.)
Abstract
The purpose of this Master’s thesis has been to establish a method with which the stochastic field for the hydraulic conductivity within an aquifer can be determined. The stochastic field is characterised by the mean value and the standard deviation of the hydraulic conductivity together with a selected statistical distribution and the correlation between different points within the aquifer. The aquifer that has been studied is the upper parts of the limestone aquifer in and around the city of Malmö. Input data to the analysis have been values on the potentiometric levels (given in meters above sea level) in 82 points within the aquifer area. The input data have been provided by Techn. Lic. Åsa Håkansson at the Department of Engineering... (More)
The purpose of this Master’s thesis has been to establish a method with which the stochastic field for the hydraulic conductivity within an aquifer can be determined. The stochastic field is characterised by the mean value and the standard deviation of the hydraulic conductivity together with a selected statistical distribution and the correlation between different points within the aquifer. The aquifer that has been studied is the upper parts of the limestone aquifer in and around the city of Malmö. Input data to the analysis have been values on the potentiometric levels (given in meters above sea level) in 82 points within the aquifer area. The input data have been provided by Techn. Lic. Åsa Håkansson at the Department of Engineering Geology, Lund Institute of Technology and were recorded in May 1998. The variation of the groundwater recharge to the limestone aquifer used in this report has been estimated by Håkansson.

The numeric methods that have been used in this thesis are the Finite Element Method(FEM) and a Stochastic Finite Element Method (SFEM).
The two methods work in the same manner, except that in the SFEM the stochastic field is used for generating values on the hydraulic conductivity per element, with the aid of the Monte Carlo sampling method. Since the values of the hydraulic conductivity are random samples, results from two different calculations are not identical. This is not the case when a problem is solved deterministically with the "ordinary" FEM. When the problem is solved with the SFEM, the result, the drawdown of the groundwater surface when pumping within the aquifer for example, can be presented with a mean value and a standard deviation, if the number of calculations is large enough. The computer program MATLAB has been used for all calculations, together with the CALFEM toolbox.

Two models have been studied. In the first model the groundwater recharge to the limestone aquifer was assumed to be constant over the whole area. In the second model, the aquifer was divided into five smaller areas with different values on the infiltration down to the aquifer. The division of the aquifer is based on geological interpretations and previous analyses within the Malmö area. When comparing the models, it appears that the second model is preferable as the sum of the squared residuals has a 75% lower value than in the first model.

The mean value and the standard deviation for the hydraulic conductivity have been estimated with a least square method. However, it has not been possible to establish the correlation between the finite elements in the numeric models. The reason seems to be too large elements in the original model. This means that it was not possible to characterise the stochastic field unambiguously. To be able to continue the modelling, calculations were made for more than one value of the correlation between the elements.

When the stochastic field that describes the hydraulic conductivity within the aquifer had been determined, the planned City tunnel was introduced into the model. The assumed leakage into the tunnel was set to 0.1 l/s·km and the drawdown of the groundwater surface was calculated. The drawdown in a section in the middle of the tunnel and perpendicular to the tunnel was studied. The simulations indicate that the effects on the groundwater level caused by the planned City tunnel should be small. The calculated mean value of the drawdown in the centre of the tunnel varies between 0.2 metres and 0.3 metres depending on which one of the two recharge models is being used. The recharge model with five recharge areas yields the smaller value.

The problem in estimating the stochastic field for the hydraulic conductivity has been in describing the correlation between different points in the aquifer area. The size of the finite elements appears to have a great influence on how well the correlation can be modelled. Since the deviation of the result depends on both the deviation in input data
(standard deviation for the hydraulic conductivity) and the correlation between different points in the area, it is of great importance to find out how the correlation could be modelled.

Finally, the advantages of characterising the hydraulic properties of an aquifer with a stochastic field should be pointed out. As the field is characterised, it describes the hydraulic conductivity statistically as a function of the co-ordinates within the aquifer area irrespective of the location of the observation wells used when determining the field. The stochastic field can then be used for simulating the influence on the
groundwater level when, for example, pumping in the aquifer irrespective of the location of the extraction. Only one way to determine the stochastic field for the hydraulic conductivity has been presented here. Greater research efforts are needed in this area. Alternative ways to describe the field should be investigated, particularly in finding a method for modelling the correlation between different points within the
aquifer area.

It should be emphasised that the simulation of the drawdown caused by the planned City tunnel, should not be seen as a prediction of the influence of the tunnel on the groundwater level, only as a practical application of the method that has been developed in this thesis. (Less)
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author
Wall, Henrik and Andersson, Jonas
supervisor
organization
course
VSM820 19991
year
type
H3 - Professional qualifications (4 Years - )
subject
report number
TVSM-5097
ISSN
0281-6679
language
Swedish
id
3566588
date added to LUP
2013-06-03 12:57:12
date last changed
2014-09-04 08:30:25
@misc{3566588,
  abstract     = {The purpose of this Master’s thesis has been to establish a method with which the stochastic field for the hydraulic conductivity within an aquifer can be determined. The stochastic field is characterised by the mean value and the standard deviation of the hydraulic conductivity together with a selected statistical distribution and the correlation between different points within the aquifer. The aquifer that has been studied is the upper parts of the limestone aquifer in and around the city of Malmö. Input data to the analysis have been values on the potentiometric levels (given in meters above sea level) in 82 points within the aquifer area. The input data have been provided by Techn. Lic. Åsa Håkansson at the Department of Engineering Geology, Lund Institute of Technology and were recorded in May 1998. The variation of the groundwater recharge to the limestone aquifer used in this report has been estimated by Håkansson.

The numeric methods that have been used in this thesis are the Finite Element Method(FEM) and a Stochastic Finite Element Method (SFEM).
The two methods work in the same manner, except that in the SFEM the stochastic field is used for generating values on the hydraulic conductivity per element, with the aid of the Monte Carlo sampling method. Since the values of the hydraulic conductivity are random samples, results from two different calculations are not identical. This is not the case when a problem is solved deterministically with the "ordinary" FEM. When the problem is solved with the SFEM, the result, the drawdown of the groundwater surface when pumping within the aquifer for example, can be presented with a mean value and a standard deviation, if the number of calculations is large enough. The computer program MATLAB has been used for all calculations, together with the CALFEM toolbox.

Two models have been studied. In the first model the groundwater recharge to the limestone aquifer was assumed to be constant over the whole area. In the second model, the aquifer was divided into five smaller areas with different values on the infiltration down to the aquifer. The division of the aquifer is based on geological interpretations and previous analyses within the Malmö area. When comparing the models, it appears that the second model is preferable as the sum of the squared residuals has a 75% lower value than in the first model.

The mean value and the standard deviation for the hydraulic conductivity have been estimated with a least square method. However, it has not been possible to establish the correlation between the finite elements in the numeric models. The reason seems to be too large elements in the original model. This means that it was not possible to characterise the stochastic field unambiguously. To be able to continue the modelling, calculations were made for more than one value of the correlation between the elements.

When the stochastic field that describes the hydraulic conductivity within the aquifer had been determined, the planned City tunnel was introduced into the model. The assumed leakage into the tunnel was set to 0.1 l/s·km and the drawdown of the groundwater surface was calculated. The drawdown in a section in the middle of the tunnel and perpendicular to the tunnel was studied. The simulations indicate that the effects on the groundwater level caused by the planned City tunnel should be small. The calculated mean value of the drawdown in the centre of the tunnel varies between 0.2 metres and 0.3 metres depending on which one of the two recharge models is being used. The recharge model with five recharge areas yields the smaller value.

The problem in estimating the stochastic field for the hydraulic conductivity has been in describing the correlation between different points in the aquifer area. The size of the finite elements appears to have a great influence on how well the correlation can be modelled. Since the deviation of the result depends on both the deviation in input data
(standard deviation for the hydraulic conductivity) and the correlation between different points in the area, it is of great importance to find out how the correlation could be modelled.

Finally, the advantages of characterising the hydraulic properties of an aquifer with a stochastic field should be pointed out. As the field is characterised, it describes the hydraulic conductivity statistically as a function of the co-ordinates within the aquifer area irrespective of the location of the observation wells used when determining the field. The stochastic field can then be used for simulating the influence on the
groundwater level when, for example, pumping in the aquifer irrespective of the location of the extraction. Only one way to determine the stochastic field for the hydraulic conductivity has been presented here. Greater research efforts are needed in this area. Alternative ways to describe the field should be investigated, particularly in finding a method for modelling the correlation between different points within the
aquifer area.

It should be emphasised that the simulation of the drawdown caused by the planned City tunnel, should not be seen as a prediction of the influence of the tunnel on the groundwater level, only as a practical application of the method that has been developed in this thesis.},
  author       = {Wall, Henrik and Andersson, Jonas},
  issn         = {0281-6679},
  language     = {swe},
  note         = {Student Paper},
  title        = {Skattning av en akvifers hydrauliska egenskaper med stokastisk FEM. Med exempel från Malmöområdet},
  year         = {1999},
}