1

A Digital Model for 3D Characterization of Groundwater

Quality Parameters around a Landfill Site

Sameh S. Ahmed Hassan I. MohamedAssociate Prof. of Environmental Engineering Associate Prof. of Hydraulics & Water

Resources

Civil Engineering Department, Majmaah University , KSA

OutlinesOutlines

•Objectives

•Groundwater Quality Parameters

•Groundwater Sampling Techniques

•Problem and Suggested Solution

•Multiquadric Technique

•Development of the 3D Methodology

•Results and Interpretation

•Conclusions and Future Work

2

3

ObjectivesObjectives Develop a methodology that could cope with a

few numbers of water samples and used for monitoring the changes in the parameter (s) in fast, accurate and cost-effectiveness manner.

Provide a clear visualization of monitoring parameters using contour maps and three dimensional representation using the developed model and computer software.

Data Sources:

P Penetrometric data measured at known X, Y and Z coordinates near a landfill site, and for several groundwater quality parameters.

4

Groundwater Quality Groundwater Quality ParametersParameters

TemperatureWater levelpHDissolved OxygenConductivityChlorideNitrateAmmoniumTDS….

Field

Laboratory

Ca, Mg, K, Na, F, Cl, Br, NO2, S, HCO3, Li

Cu, Fe, Pb, Zn,..Others

Tip resistance Pore pressurePermeability

Geotechnical

5

Sources of Groundwater Sources of Groundwater ContaminationContamination

6

LandfillsLandfills

7

Landfills and Landfills and GroundwaterGroundwater

8

Groundwater Sampling Groundwater Sampling TechniquesTechniques

9

Problem and Suggested Problem and Suggested SolutionSolution

Sparsity of the data and limited

numberof penetration

points

Estimate the variable at non - sampled location

within the defined domain

in 3D

Problem

Target

10

Methods of Point EstimationMethods of Point Estimation

11

Multiquadric TechniqueMultiquadric Technique

Geometric interpolation of the multiquadric equation 1/2 2 2

1 YYXXC jj

n

jjZ

• The above equation represents a system of linear simultaneous equations. The solution of the system results in unique determination of the algebraic sign and magnitude of every coefficient Cj.

• A multiquadric solution will fit all the data points. • The derived equation treats the surface as natural.• The flatness or sharpness of the slope change in

the surface is totally depends on the flatness or sharpness of the cone at that particular point.

12

Development of the 3D Development of the 3D MethodologyMethodology

• Multiquadric function was selected as an interpolation function to develop the 3D model

• Groundwater samples of one variable gathered from limited penetration points at a test area were used to characterise the variable in 2D.

• The process is repeated at different depths and estimation of the variables at any XYZ point being available.

13

Computer ProgramComputer Program

• To apply the multiquadric technique for 3D estimation, one needs to interpolate the data in the XY plane at all given Z levels.

• Then, one moves to the perpendicular plane YZ and does the same procedure using all the X intervals and for all the original and estimated values.

• The final task is to enter the X, Y and Z co-ordinates for the variable to obtain its estimated value.

14

INPUT-1Original measured pH observations at one of the 37 penetration points.Other Variables:Cations: Ca and MgAnions: Br and HCO3

Others: Temp & conductivity

Program 1:Poly.m

MATLAB MACROTo fit the data within the depth using Polynomial

Function

Program 1:Poly.m

MATLAB MACROTo fit the data within the depth using Polynomial

Function

OUTPUT-1Cof.dat: the coefficients of the polynomial equations to fit the data at each penetration point.

Example of “Cof.dat” output

2.7068e-4 –0.0149 0.2899 -2.2988 12.8701

2.6589e-5 -1.9676e-3 .05145 –0.5595 8.695

-2.225e-6 2.118e-4 4.056e-3 –0.232 8.547

4.521e-4 -1.876e-2 0.252 -1.210 8.728

4.811e-5 -2.785e-3 5.668e-2 –0.488 8.207

-2.757e-5 1.328e-3 -1.356e-2 –0.113 7.835

-1.686e-4 7.655e-3 –0.112 0.584 6.702

15

INPUT-2Cof4.dat: output of program 1 Input6.dat: includes:• Number of significant points in each XY plane =37• Number of sections in XY plane = 4 • Best fitting using polynomial f• The selected depths, here, 5,10,15 & 20m

Input3.dat37 4 35.010.015.020.0

Program 2:Cof.f

Fortran program

Program 2:Cof.f

Fortran program

OUTPUT-2Phsl.datIncludes the significant points and used as input for the sections.f.Phslchk.datIncludes the significant values for the tested levels and used to check the output before using final program.

Phsl.dat6.9270606.9544507.5139616.9120776.8674237.0799127.664041

16

Modelling MethodologyModelling Methodology

• XYZ and V for one of the variables at 37 penetration points

• Fitting the best 2D function for each equal Z level

• Multiquadric digital model has been developed to estimate the values at equal intervals.

17

INPUT-3SXXYY.dat: X & Y coordinates of the significant points.Phsl.dat: output of program 2 which includes the significant points of all required levels.Inputt.dat: o Number of levelso XY grid and its offseto Depths of the levels oYZ grid and its offseto Number of required vertical planeso X coordinates for the sections

input.data660 60 20 20 800.0 200.05.10.15.20.60 25 20 1 200.0 0.03900.01300.01900.0

Program 3:Sections.f

Fortran program

Program 3:Sections.f

Fortran program

XXYY.DATA grid 20x20m generated inside the program for XY plane

Boundaries Test area Landfill site (if any)

YYZZ.DATA grid 20x1m generated inside the program for YZ plane

18

Results: Contour Maps and Results: Contour Maps and 3D Representation of pH3D Representation of pH

X-section and 3D representation of pH at Z = 10m.

19

Distribution of pH values along the XY plane at four depthsand one cross-section in YZ plane

20

No X(m)

Y(m)

pH1

pH2

pH3

pH4

pH2 (est.)

Diff

1 43.5 1102.0 6.8 7.2 7.0 7.1 7.1999 0.0001

2 175.6 1880.4 6.0 5.9 6.0 6.1 5.8998 0.0002

3 200.0 500.0 7.2 7.1 6.9 7.3 7.1000 0.0

4 245.2 1340.0 7.7 7.8 7.4 7.8 7.7999 0.0001

34 1256.0 1452.0 9.4 9.3 9.2 9.0 9.2999 0.0001

35 1266.5 625.7 9.0 8.8 8.7 9.2 8.8000 0.0

36 1400.0 1250.0 8.6 8.6 8.4 8.2 8.5999 0.0001

37 1571.8 2228.2 8.9 8.6 8.9 9.1 8.5998 0.0002

X,Y co-ordinates for 37 points and their pH values at 4 different levels

Ranges of tested water quality parameters

Min. Max. Mean Range

pH 5.9 10 8.262 4.1EC 175 275 220.824 100

DO 0.8 10.0 5.010 9.2

22

23

24

25

ConclusionsConclusions• A digital model based on the multiquadric

technique is introduced.

• The model provides a tool for 3D characterisation of groundwater parameters from a small number of penetration points that would help prepare a cost effective monitoring programme.

• The technique was first examined for 2D estimation and then modified to handle the data in 3D. In both cases, the output data were used to plot contour maps and represent the variable in 3D.

• An example, of creating a digital model for pH variable, is introduced. Several other groundwater parameters were also tested.

26

Possible Future WorkPossible Future Work

The 3D methodology could be modified using X, Y, Z, variable and time to conduct a digital model for supervising the change in the behaviour of groundwater parameters with time. In other wards, to carry out a 4D study.

Thanks for your Thanks for your attentionattention