Ground Improvement Techniques Optimization

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ECCM 2010IV European Conference on Computational Mechanics

Palais des Congrs, Paris, France, May 16 -21, 2010

Optimization of Ground Improvement Techniques in Tunnelling

Using Genetic Algorithms

M. A. Eid1, M.Zaki Abd Elrehim

2, F. El-kashef

3and G. Swoboda

4

1Civil Engineering Department, Minia University, Minia, Egypt, [email protected]

2Civil Engineering Department, Minia University, Minia, Egypt, [email protected]

3Civil Engineering Department, Minia University, Minia, Egypt. [email protected]

4Department of Structural Analysis, University of Innsbruck, Innsbruck, Austria, [email protected]

Abstract:

With recent developments in efficient deterministic numerical algorithms, coupled with the rapid

improvement of computer performance, probabilistic finite element methods that use more realistic

soil and physical models are now feasible . The genetic algorithms (GAs) are one of such probabilistic

search methods which are well suited to solve large combinational design problems. The primary

reasons for their success are their broad applicability, ease of use, and global perspective. Being a

stochastic method, the GA does not need specific information to guide the search, and requires only an

evaluation of the objective function value for each decision variable set in order to proceed.

Tunnelling through difficult ground needs, in addition to face subdivision, effective solutionsbased on soil strengthening and reinforcement techniques. These different techniques and solutions

aim to improve the soil around the tunnel to minimize the ground deformation, to have longer

tunnelling free span and to maintain face stability. The layout and design of these techniques mainly

depend on experience. So, there is an increasing need for tools to help in more understanding and

more optimization of ground improvement techniques.

In the present paper, it is shown how a genetic algorithm can be incorporated into the displacement

finite element method to solve the optimization problem. Deterministic Finite Element program,

FINAL package, is used to simulate tunnelling operations under different loads with different initial

profiles and parameters values for ground improvement process. A Genetic algorithm program is

coded and linked to FINAL results to perform the evolution procedures (crossover, selection, mutationetc.). Repeating these stages for many generations, results in the optimum values and parameters

used for the ground improvement technique in both of its quantity and material properties.

1. Introduction:

Tunnelling work requires a proper attention of ground deformation. Depending on the method of

excavation and support, tunnelling may induce considerably different magnitudes of deformation to

the surrounding ground. These movements may cause damage to adjacent buildings and other surface

structures especially in soft soils. So, prediction and assig nment of control technique of surface and

subsurface settlement are very important parts of designers task to insure safe construction [1-3].

In some cases, using jet grout, as a soil strengthening technique, is selected as an economic

procedure to control surface settlement [4]. Determination of grouting parameters, dimensions and its


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material properties, is used to be previous experience dependent. Applying optimization process on the

determination of these parameters can help to get the best performance with minimum costs. The

search for a robust optimization algorithm, with good balance between efficiency and effectiveness

and able to survive in many different environments, has led to the use of Genetic Algorithms (GA s).

GAs have many advantages over traditional optimization techniques [5]. Among other considerations,

they do not need further additional information than objective function or fitness information. Its

ability to find out the optimum or quasi-optimum solution, even if the optimization function is non-

continuous, non-differentiable and with any kind of constraints, gives it a privileged position as a

powerful tool in non-conventional optimization problems. GA s have been successfully applied to

many branches in civil engineering optimization problems such as bridge construction management

[6], water network design [7], tunnel geometric design [8] and structural optimization [9].

In the present work, the grouting parameters properties optimization problem is treated as a

discrete problem using a GA. The GA is coded and combined with developed Finite Element program

to analyze NATM tunnel in grouted strengthened soil. The object of this new program is to get the

best values for grouting parameters. Best values are those values produce minimum cost within safety

limits for surface settlement. This article has been structured as follows: First a general description ofGAs is presented. Second, Tunnel structural modeling is demonstrated showing geometrical and

geotechnical parameters. Third, the optimization methodology has been presented with outlines about

the developed program. Finally, results are analyzed and discussed.

2. Genetic Algorithms:

Genetic algorithms are search and optimization procedures that are motivated by the principles of

natural genetics and natural selection. They are also referred to as stochastic optimization techniques

different from usual mathematical programming [10]. Being considered as stochastic methods, the

GAs do not need specific information to guide the search, and require only an evaluation of the

objective function value for each decision variable set in order to proceed. They typically work with a

coding of the decision variables, not with the decision variables themselves. They search

simultaneously using a population of decision variable sets, not a single set of decision variables.

Figure 1: A generic framework for genetic algorithm

Figure 1 illustrates the generic framework for genetic algorithm. As in a biological system

submitted to external constraints, the fittest members of the population are selected to survive and

given better chances of reproducing and transmitting part of their genetic heritage to the next

generation. A new population is then created by recombination of parental genes. It is expected that

some members of this new population will have acquired the best characteristics of both parents and,

being better adapted to the environmental conditions, will provide an improved solution to the

considered problem. After it has replaced the original population, the new group is submitted to the


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same evaluation procedure, and later generates its own offsprings. The process is repeated many times,

until elite members of a given generation share the same genetic heritage. These members, who are

often quite different from their ancestors, possess genetic information that corresponds to the best

solution to the optimization problem [11].

3. Structural Modelling of Tunnelling Problem

In this paper, conventional numerical model with plane-strain analysis is used. An optimal tunnel

profile is selected to induce minimum stresses on the lining [12]. Figure 2 shows the finite element

mesh used for simulation, the applied boundary condition and soil parameters.

Figure 2: Finite element mesh

Where; E elasticity modulus, soil density,

Poissons ratio, C cohesion,

angle of internal friction

3.1 Geometrical and Geotechnical Parameters

The tunnel is constructed in a clayey layer at a depth of 14.0m with no existence for ground water

in the tunneling vicinity. The excavated cross section is divided into two parts, heading and invert.

Grout is assumed to be distributed in uniform arc shape above the tunnel. Thickness and length of this

arc differ according to the grouting amount.

3.2 Finite Element Simulation

For the modelling process in the Finite Element program, FINAL package [13], the soil media is

modeled using a six node linearly varying strain triangular finite elements (L.S.T) and the shotcrete

lining by a six node curved boundary beam elements (Beam6). A half-section mesh is used in the

analysis to reduce computation time. Sufficient mesh depth and width, to model soil infinite body, are

used. For boundary condition, vertical and horizontal movements are prevented at the bottom of the

model while only the horizontal movements are prevented at both sides.


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3.3 Construction Sequences

For simulating the excavation sequences and shotcrete installation, 2D plane strain model with

different loading cases is employed. The initial loading case is the geostatic stat of stresses and the

existing surface loads. Then modulus of elasticity and soil parameters of clay are increased in

specified area to indicate the application of grouting strengthening technique in this area beforeexcavation. Each excavation step is simulated in two steps using stiffness reduction method. In the

first step, the stiffness of the soil in the excavated part is reduced by a factor accompanied with stress

redistribution at the tunnel zone. In the second step, the excavated part is removed and the temporary

lining is installed in its fresh state accompanied with a stress elimination of the excavated soil. Then,

the permanent shotcrete/concrete lining is installed after completing the whole cross section.

4. Grout Optimization Problem

The grout optimization problem addressed herein is to find out the optimal dimension for grouted

area and elastic modulus for grouting material those lead to pre-specified and safe surface settlement

to have minimum soil strengthening cost. Hence, the objective function can be stated as:

find X kR to

minimize f (X)

subject to gi (X) 0, i= 1, 2, . . . , n and

L U

j jX X , 1,2,...........,X j k =

where X is the vector of design variables; f (X) is the objective function; gi(X) is the performance

constraints; and

L

jX and

U

jX refer to the lower and upper bounds on the design variables respectively.The objective function here is the cost of the grout and can be expressed as:

( ) ( )min , ( ) 1,2,......c j i j iC M L T j i n= = (1)

where cM is grouting cost per cubic meter, ( )j iL is the length of grouting arc and ( )j iT is

grouting arc thickness taken from n trials.

The performance constraints include concern for surface settlement as:

0 , 1,2,........i i allg i n= = (2)

4.1 Design Variables

First design variable is grouting arc length. Grouting arc length is limited to two-third tunnel

perimeter as a practical value. This length is divided into 19 segments of 0.5 m length each. Thus we

have 20 possible values for this length by adding zero length value from the case of no-grout. So, the

length ranges from 0 to 9.5 m with 0.5 m step. Second design variable is thickness of grouting arc.

Clay layer extends for about 7.5 m above tunnel crown. So, this distance is divided into 15 layers of

0.5 m thickness each. This means that we have 15 possible values for thickness ranges from 0.5 m upto 7.5 m. By adding the case of no-grout, thickness equal zero, we got 16 possible values. These

variables are illustrated in Figure 3.


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The third variable is the elastic modulus for grouting material. As clay layer has an elastic

modulus of 50 MPa, the grouting modulus range starts from double of this value and increase with 50

MPa increment. A binary integer of 5-bit length is used to present all variables. So, 32 values range

from 100 to 1650 MPa are used as search area for elastic modulus in this analysis. Elastic modulus

indicates grouting material quality which is related to grouting unit cost. This cost differs from one

country to another depending on raw materials prices and technical process costs. In this research,

costs are estimated according to prices in Egypt.

Figure 3: Dimensions and limits of grouting arc

4.2 Computation Procedure

According to the assumed alternatives for every variable, the total number of possible solutions

(chromosomes) = 20 * 16 *32 = 10240. An initial population of 20 chromosomes is considered. Initial

population and every new generation pass through three different phases. First, for every randomly

generated solution, the structural analysis package FINAL is called to analyze it and calculate

maximum surface settlement. Solutions with allowed safe settlement value are kept for intermediate

phase and other solutions are to be mutated and re-checked until reaching safe value. All solutions in

the new phase are safe and to be evaluated. Roulette selection is applied on these solutions to move to

the third and final phase. Each solution has a probability to be selected depends on its fitness

(evaluation) value. The final phase represents the generation form involved with other GA operators.Best values are copied to secure their coexisting in next generation according to elitism operator. One-

point crossover and mutation operators are applied on the binary coded solution in order to form a new

preliminary population.


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Processing optimization operators and repeating them through generated population leads to

convergence toward global optimum. Difficulty of having optimal or quasi optimal solution increases

as convergence rate increases. In final optimization step, looking for the very close best chromosome

through random mutation is a time consuming process. In this case, changing mutation to local

searching technique is more preferable. The algorithm changes its mutation technique at the final 10

generations of every 100 generations to avoid having local minima. Then, termination of the GA

process depends on the resulted design variables values stability for more additional 100 generations

after final convergence.

Figure 4: Elite members convergence progression

For example, the algorithm was applied to optimize grouting variables with 3cm allowable surface

settlement as constraint value. Figure 4 shows elite members fitness progression through generations.

The resulted optimal values for design variables are 1m, 9.5m and 1450MPa for grouting arc

thickness, length and modulus of elasticity respectively. By generation number 190, elite members

converged and reached design variables of 1m, 9.5m and 1600 MPa for grouting arc thickness, length

and modulus of elasticity respectively. Two steps far from the optimal values. Starting from the

second 100 generation, the program switches mutation to local search (uniform mutation) technique at

the last 10 generations of every 100 generations as stated before. This leaded elite members to reach

the optimal value at generation number 195. Another 100 generations are produced to check solutions

stability.

5. Constraints Value Effect

The algorithm was applied for different constraint values: 4, 3.5, 3, 2.5 and 2cm allowable surface

settlement, 50 attempts for each. The aim of these attempts is to check the algorithm reliability in

reaching global optimum and to study the effect of constraints value on convergence speed. Figure 5

summarize results of a ll performed attempts. It shows algorithms success percentage in reaching

optimal design variables and global optimum costs value every hundred generations. Dividinggeneration range into hundreds demonstrates the speed of the algorithm.


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For allowable surface settlement of 4, 3.5, 3, 2.5 and 2 cm, the percentages of reaching

global optimum in the first hundred generations were 58%, 20%, 10%, 0 and 2% respectively.

The percentages of reaching global optimum in the first two hundreds generations were 96%,

90%, 80%, 72% and 34% respectively. The percentages of reaching global optimum in the first

three hundreds generations were 98%, 92%, 100%, 72% and 60% respectively. Increasing

limitation, by reducing the allowable value, bind the algorithms searching freedom. This slows

down the algorithm but does not stop it from reaching the target. For further limitation, the

algorithm will get slower and it may be more visible to use deterministic searching algorithms.

Figure 5: Prospects percentage of reaching global optimum

due to different constraints values

6. Conclusions

The developed algorithm combining GA and FE has proven to be successful in grouting,

as an example of ground improvement techniques, optimization problem. The developedcomputer program can be easily used to handle optimal solution. Due to its simplicity and ease of

coding the GA procedure described here can be applied to a wide variety of optimization

problems. It has been shown that it can be used in jet grouting costs minimization. Despite the

relatively large space of permissible solutions, the procedure converged towards the best possible

solution. The work presented here can be considered as a step forward towards analysis and design

automation using soft computing.

References

[1]

Soil Movements Around Tunnel in Soft Soil, C. Lee, B. Wu and S. Chiou, Proceeding of National ScienceCouncil, Vol.23, No.2, 1999.

[2] Analysis of Settlement Damage to Masonary Structures, H.J. Burd, G. T. Houlsby, L. Chow, C. E.Augarde and G. Liu, Numerical Methods in Geotechnical Engineering, Smith(ed), Balkema, Rotterdam,

1994.


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[3] Ground and Building Settlement due to Tunnelling in Hong Kong, R. A. Forth and C. B. B. Thorley,Proceedings of the Fifth International Symposium on Land Subsidence, The Hague, October 1995.

[4] Chemical Grouting and Soil Stabilization,R. H. Karol, Marcel Dekker, 2003.[5] Genetic Algorithms in Search, Optimization, and Machine Learning, D. E. Goldberg, Addison Wesley,

1989.

[6] Application of Genetic Algorithm to Bridge Construction Management, Natsuaki, Y., H. Furuta, S.Mukandai and K. Yasuda, 3rd International Symposium on Uncertainty Modeling and Analysis, 1995.

[7] Genetic algorithms for least-cost design of water distribution networks, D. A. Savic and W. A. Walters, J.of Water Resources Planning and Management, ASCE, 123B, p67-71, 1997.

[8] A Genetic Algorithm for Tunnel Design Optimization, M. B. Reed, S. Schenk and G. Swoboda, Geneticand Evolutionary Computation Conference (GECCO), 2005.

[9] A Combined Finite Element-Genetic Algorithm for Structural Optimi zation, M. Z. AbdElrehim, F. A.Elkashef, M. A. Eid, Aion Shams Journal of Civil Engineering, Vol. 1, No.1, 2009.

[10]Adaptation in Natural and Artif icial Systems, J. Holland, The University of Michigan Press: Michigan,1975; MIT Press : Cambridge, MA, 1992.

[11]Discrete Optimizat ion of Structures Using a Float ing Point Genetic Algorithm, N. Turkkan, AnnualConference of the Canadian Society for Civil Engineering, Moncton, Nouveau - Brunswick, Canada,

GCM-134/1-8, 2003.

[12]Design Optimization of Urban NATM Tunnelling, M. Z. AbdElrehim, A. M. Marwan, 13th InternationalConference on Structural and Geotechnical Enginnering (IGSGE), Cairo, 2009.

[13]Programmsystem FINAL, Finite Element Analysis Linearer und Nichtlinearer Stukturen, Version 7.1, G.Swoboda, Druck Universitt Innsbruck, Austria, 2001.

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