INTRODUCTION
Road accidents involving the release of toxic or hazardous materials (such as hydrocarbons and chlorinated solvents, which are non-aqueous phase liquids or NAPL) during their transportation may cause severe environmental problems. A particular attention is given to denser than water NAPLs (DNAPLs), which may reach deep into the aquifer and thus durably contaminate the groundwater. This study is concerned with the impact of a DNAPL spill on the water resource for a road project infringing a zone of drinking water catchments in the case of a road accident involving a DNAPL transporting vehicle. The zone of study spans over several kilometers, along which soil properties vary significantly.
Simulation metamodelling is based on the substitution of the simulation model by an approximation of the input–output relationship. Metamodelling, first proposed by Blanning, makes the computations much faster, allowing for more cases to be studied. Originally based on regression methods ,metamodels now use various approaches such as artificial neural networks (ANN) or kriging . ANN have the advantage over regression that the form of the model need not be predetermined. Moreover, ANN can theoretically approximate any function to any level of accuracy, which is very interesting when the governing physical mechanisms are highly non-linear like in pollution transfer in soils.
A database was built with four input parameters
· cover layer permeability and thickness,
· water table
· depth and
· soil–pollutant contact time
Two output parameters,
· depth of contaminated soil and
· infiltrated pollutant
Different artificial neural networks have been trained and tested on this database using the error backpropagation algorithm and cross-validation. Their performances have been analyzed and compared in statistical terms, and the optimum network has been used to predict the depth of contaminated soil in the practical case of an accidental DNAPL spill along the axis of a projected highway.
PROBLEM UNDER CONSIDERATION
1. Presentation of the road project
The highway project crosses a valley where important drinking water resources are located. Geological and hydrogeological surveys showed fractured carboniferous lime stones overlaid with 5–15 m of silts, silty sands and silty clays, with a water table lying at 5–25 m from the soil surface, inside the fractured limestone, Piezometers allowed the monitoring of water table variations with time over an almost 2 year period (September 2000 until April 2002).
Parameters for problem under consideration
Fig. shows the soil profile with projected cuts and fills. In cut zones the scouring of the protective silt cover layer may increase the aquifer vulnerability during the construction phase, but these zones will be protected after the highway construction (impervious road platform, runoff retention basins). In fill zones there is a risk for vehicles to fall down from the platform during accidents and potentially cause a pollution to the unprotected natural soil, eventually
threatening groundwater resources. Pollutant migration through silty cover soils should hence be thoroughly analysedin fill zones.
2. Numerical simulation
The reference two-layer soil used in simulations is typical of a geological profile met in the north of France (Fig),with a cover of silty soil of thickness Hc. Field and laboratory permeability tests were undertaken; the measured hydraulic conductivity K of the cover layer ranged between 8 × 10−10 and 5 × 10−7 m/s depending on clay content.
The water retention curves for silty cover soils were also measured from borehole samples using the pressure plate method. An approximately 40 m chalk layer constitutes the exploited aquifer. Hwdesignates the depth of the water table. The main parameters governing the pollutant transfer are summarised in Fig. Fluid and porous media properties, and parameters for the Van Genuchtensaturationpressure relationships are given.The domain is modelled as a one-dimensional system. Simulations were performed with a chlorinated organic solvent (trichloroethylene or TCE) as the pollutant. This chemical is a major environmental threat, due to its low viscosity and high relative density.
Simulations were carried out in two steps:
Ø the first one aims at reproducing the initial water saturation profile in the soil.
Ø the second one concerns the application of a constant head of pollutant at the soil surface during a given lapse of time.
For each simulation the pollutant saturation profile as well as the quantity of infiltrated pollutant were computed over time.
CONSTRUCTION OF THE ANN METAMODEL
1. Artificial Neural Networks (ANN)
The ANN is an artificial intelligence technique that mimics the human brain’s biological neural network in the problem solving processes. As humans solve a new problem based on the past experience, a neural network takes previously solved examples, looks for patterns in these examples, learns these patterns and develops the ability to correctly classify new patterns. In addition, the neural network has the ability to resemble human characteristics inproblem solving that is difficult to simulate using the logical, analytical techniques of expert system and standard software technologies.A neural network is defined as a system of simple processing elements called neurons, which are connected to a network by a set of weights The network is determined by the architecture of the network, the magnitude of the weights and the processing element’s mode of operation.
Themetamodel adopted is based upon the use of artificial neural networks (ANN). ANN operatelike a “black box” model, requiring no detailed information about the physical parameters of the system. Instead, they learn the relationship between the input and output parameters as a result of training with previously recorded data. ANN can handle large and complex systems with many interrelated parameters. In the water resources field, they have been used successfully to assess spatial distribution of soil permeability for landfill siting, or to predict catchments flow.
2. Selection of input parameters
Analyse the influence of the input parameters on the contamination of soil and groundwater for the reference two-layer unsaturated soil. Parameters were classified in three categories :
· physicochemical properties (soil permeability and retention properties, density, viscosity and surface tension of fluids)
· hydrogeological properties (silty soil thickness, water table depth) and
· parameters quantifying the circumstances of the accidental spill (soil–pollutant contact time, pollutant pressure head on the soil surface).
For the above selected parameters different values bracketing a chosen reference were used as input for the numerical model and their influence on the output (depth of contaminated soil and infiltrated pollutant quantity) was observed.
The parametric study showed that the permeability K of the cover soil has a major impact on the pollution: it controls both the depth and velocity of the pollutant transfer into the soil. The effect of field variability of geometric parameters such as thickness of silty layer Hc and water table level Hw is also very significant.
Obviously a thicker silty cover soil with low permeability as compared to that of the chalky aquifer forms a better protection against contamination. On the other hand a shallower groundwater level leads to a faster pollutant migration, because retention forces in the unsaturated zone are then weaker. Finally soil–pollutant contact time tchas been shown to be a key parameter in the estimation of pollution migration: the faster the pollutant is removed from the soil surface, the more superficial the pollution, and the less soil has to be treated or removed.
On this basis a set of four input variables was retained for the prevision of soil contamination: the hydraulic conductivity K and thickness Hc of the cover layer, the water table depth Hw and the soil–pollutant contact time tc
3. Construction of the database
The database was built using finite element modelling with input parameters K, Hc, Hw and tc varying in a range of representative values: 1×10−6 m/s, 1×10−7 m/s and 1×10−8 m/s for K; 0.5, 1, 3, 5 and 7 days for tc; 15 values between 0 and 20 m for Hc and 9 values between 0 m and 45 m for Hw. The database was subdivided in three subsets. A first subset (about 50% of the database) is used to train the networks. A second one (25% of the database) is used to test the ANN models to determine when to stop the training stage. The third subset is used to validate the performance of the selected model on new cases. It should be noted that the training subset should contain the widest variety of patterns, since ANN are more reliable if they are used as an interpolation tool for generalization on new cases. Note also that log(K) instead of K was considered in the database to avoid using data spanning over several orders of magnitude, and that each input or output parameter has been normalized relative to its minimum and maximum
values, allowing for faster training by preventing larger numbers from overriding smaller ones.
4. Construction of Artificial Neural Network models
A brief description of the model and program used in this study will be given in this section. For a detailed description, evaluation, and discussion on the overall performance of the model.ANN are composed of a set of elements of calculation (nodes) connected to each other. The most popular type of network is the multilayer backpropagation neural network (BPNN) which is used in the present study. The architecture of a typical 3-layer backpropagation neural network is shown in Fig. Mathematically, a 3-layer ANN with n,m, and p the number of input, hidden and output nodes respectively, is based on the following equation:
where Ok are the output values and Xi the input values of the network; Wi j , the connection weights between the input layer and the hidden layer; Wjk , the connection weights between the hidden layer and the output layer; S is a transferfunction. The sigmoidal function was used in the present study.
The input from each node in the previous layer (Xi ) is multiplied by an adjustable connection weight (Wi j ). At each node, the weighted input signals are summed and a threshold value (Wj ) is added. This combined input Ajis then passed through the non-linear transfer function S to produce the output of the node (0 j ). The output of one node contributes to the input to the nodes in the next layer. This process is illustrated The learning process of BPNN is based on a series of connection weight adjustments in order to minimize a global error between predicted outputs and target values. It relies on a search technique (e.g. gradient descent) of the connecting weights yielding a minimum error. Inputs are first propagated forward through each layer of the network. Errors between outputs and target values are then propagated backwards and the connection weights are modified according to a specific learning algorithm (delta rule) to reduce the overall error. This forward–backward process is carried out for each epoch (set of training patterns used to compute the global error), and is repeated until predicted outputs and target answers coincide within a given tolerance.
The most common convergence criterion is the average squared error (ASE) defined as:
whereOqkanttqk are respectively the predicted and target value of the output node k for the pattern q, s is the number of patterns, and p is the number of output nodes. It should be noted that any level of agreement between predicted
and target vectors can be achieved provided a sufficient number of training cycles is carried out. Such an overtraining
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5. Optimum network architecture
The overall performance of an ANN is very dependent on the number of hidden layers and of hidden nodes in each hidden layer. In the usual case of a 3-layer BPNN (one hidden layer), the optimum number of hidden nodes can be assessed by cross-validation in the same way as the optimum number of training cycles .
A neural network relating inputs {X1, X2, . . . ,Xn} to outputs {O1, O2, . . . , Op} and containing one hidden layer with m hidden nodes will be noted:
{O1, O2, . . . , Op} = ANNn−m−p{X1, X2, . . . ,Xn}. (4)
If D and Q are sought as a function of parameters K, Hc, Hw and tc, it is possible to compute D and Q separately by using two different BPNN models (namely models 1 and 2) each with one node in the output layer ,But it is also possible to estimate D and Q at the same time (model 3) by considering two nodes in the output layer As can be observed in the optimal value of ASE was calculated while using 29, 32 and 27 nodes in the hidden layer for models 1, 2 and 3 respectively
{D} = ANN4-29-1{K, Hc, Hw, tc} (model 1) (5)
{Q} = ANN4-32-1{K, Hc, Hw, tc} (model 2) (6)
{D, Q} = ANN4-27-2{K, Hc, Hw, tc} (model 3). (7)
Table 2 gives ASE values for the training, testing and validation phases for the above 3 models. Somewhat larger values of the ASE are logically obtained during the validation phases for all models. An interesting feature is that the ASE for model 3 are about the same as for models 1 and 2, when a single network was built and used for the prediction of both D and Q in the first case. Moreover, it should be noted that the optimum network for model 3 contains 27 hidden nodes, against 29 and 32 for models 1 and 2 respectively. Hence the simultaneous prediction of several output parameters in the same network does not necessarily require a greater network complexity. In this example the single network model even features less hidden nodes for a comparable global error. Physically the depth of contaminated soil D and the quantity of injected pollutant Q are linked together. This dependency has been captured somehow by the artificial neural network.
CONCLUSIONS
A metamodel based on artificial neural networks has been used to assess the contamination of an unsaturated soil by a trichloroethylene spill in a road accident. A parametric study using the finite element software NAPL-Simulator first allowed the identification of four key input parameters
· cover soil thickness Hc
· permeability K
· water table depth Hw and
· soil–pollutant contact time tc
for the selected output parameters:
· D soil contamination depth and
· Q quantity of infiltrated pollutant.
A database of vertical contamination examples in a two-layer unsaturated soil was then constructed. Three artificial neural network architectures were trained and validated, in order to generalize the prediction of contaminant migration to cases not included in the database. The validation showed excellent performance of this metamodel for the prediction of pollutant transfer in the unsaturated zone. The metamodel has then been used for a simplified risk analysis in a highway project in the north of France, where it proved powerful and effective in the evaluation of the pollution migration over a wide area, as compared to a purely mechanistic model. As far as risk analysis is concerned, the output of the metamodelcould rather consist in the probability for the pollutant concentration to reach a given level.
Praman Tyagi(MCA/4542/10), Ashok Kumar(MCA/4543/10)
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