Numerical Analysis of Seepage Induced Earthern Slope Failures

Numerical Analysis of Seepage Induced Earthern Slope Failures 5

Numerical Analysis of Seepage Induced Earthern Slope Failures

침투가 고려된 토사사면파괴의 수치해석

Seo, Young-Kyo1서 영 교

요 지

침투에 의한 토사사면의 붕괴는 기상학적인 현상과 더불어 많은 양의 지하수의 유입에 의하여 발생한다 토사사면.

속에존재하는지하수의흐름은심각한재산및인명손실의잠재적인요인으로작용한다 이러한침투에의한토사사면.

의 안정성 문제는 지반공학에서 중요한 문제로 인식되어져 오고 있다 본 연구는 기존의 유체 및 고체의 상호 작용에.

대한 수치모델링 기법을이용하여 침투에 의한 토사사면붕괴의 이해및 이를 예측하기 위하여 수행되었다 본 연구는.

지반공학에서 중요히 다루는 사면안정화기법 연구에 효과적인 기술적 기여에 중점이 있다.

Abstract

Seepage induced earthern slope failures occurs in concert with meteorological events when large quantities of

groundwater are channeled into slopes through infiltration. The presence of flowing groundwater in earthern slopes can

induce ground failures that result in significant property damage and potential loss of life. Seepage induced earthen

slope failures represent a serious problem in geotechnical engineering. This research applies existing fluid-solid numerical

modeling capabilities to the study and prediction of seepage induced earthen slope failures. Study of the targeted application

holds potential for much needed advances in geotechnical engineering analysis technology which could be used to design

more effective engineering slope stabilization interventions.

Keywords : Finite element method, Numerical method, Seepage, Slope stability

1 Assistant Prof., Div. of Ocean Development Engrg., Korea Maritime Univ., [email protected]

Jour. of the KGS, Vol. 24, No. 9. September 2008, pp. 5 11～

1. Introduction and Motivation

Pore water in soils can strongly influence the physical

interactions between soil grains. Changes of pore press-

ures can directly impact the effective stresses which in

turn impact both the shear strength and consolidation

behaviors of soils. Moreover, the water in the void spaces

of soils is not static, particularly in slopes. Therefore, the

analysis of pore fluid seepage plays an important role in

the solution of many geotechnical problems, especially

those concerning the stability analysis of slopes and

retaining structures. Stability analysis of slopes in which

seepage is occurring involves solving boundary value pro-

blems for coupled field equations on spatial domains part

of whose boundaries (the so called free surface or phreatic

line) are unknown and remain to be determined as a part

of the solution. The major difficulty in solving free-

boundary problems numerically is associated with the

nonlinearity introduced by the unknown free surfaces.

Solving stability analysis problems for slopes in which

unconfined seepage occurs involves mainly two

difficulties. The first involves the fact that the soil can

undergo inelastic deformation under gravity and seepage

forces, while the second involves locating the equilibrium

6 Jour. of the KGS, Vol. 24, No. 9, September 2008

free boundary of fluid in the soil. In the slope stability

analyses considered in this paper only steady state seepage

effects are considered, but transient effects could also be

considered if one knew the changing hydrologic conditions.

The objective of this paper is first to develop a general

methodology for solving the coupled slope stability

analysis problem, which involves simultaneously solving

the fluid pressure and velocity fields as well as the

phreatic surface, and also the stress and deformation fields

in the slope including the limit state failure mechanism.

As an approximation to the fully coupled problem, a

simplified two-step decoupling is then introduced, im-

plemented and solved. The first step involves solving the

unconfined seepage problem in the soil while assuming

that the soil skeleton is rigid and does not deform. The

fluid pore pressure field is then imposed on the slope and

fixed while the slope stability problem is solved using the

‘Strength Reduction Method’ introduced in Swan and Seo

(1999). The de-coupled procedure is then applied to assess

the stability of slope systems in which steady state,

unconfined seepage is occurring.

2. Literature Survey

Fluid flow through porous media occurs and plays an

important role in many geotechnical problems. Due to the

intrinsically irregular geometries associated with most of

real problems, analytical solutions can be obtained only

for relatively simple situations (Harr, 1962). The analysis

of more complex cases can be carried out through numerical

procedures based on various discretization techniques

which are becoming increasingly popular and are replacing

traditional procedures like hand-drawn graphical flow nets

(Cedergren, 1967). Among numerical techniques, the

finite element method and the boundary integral equation

method are those most widely used. Confining attention

here to the finite element approaches, Zienkiewicz et al.

(1966) first presented the solution of confined seepage

flow problems. Thereafter, adaptive mesh methods (Desai,

1972; Chen et al., 1973) and fixed domain methods

(Desai, 1976; Lancy et al., 1987; Cividini et al., 1989)

have been widely used to find free surfaces.

The adaptive mesh methods solve the seepage problem

with a trial free surface, iteratively modifying the geometry

of the saturated soil mesh so that the free surface coincides

with element boundaries until a sufficient approximation

of the correct shape of the flow domain is reached. In

the first step, the mesh is usually defined between given

physical boundaries and an assumed location of free

surface, then the Laplace equation is solved for the

domain below the trial free surface, then the flow domain

is modified based on computed velocities at the free

surface. With the modified flow domain and free-surface,

the problem is then re-meshed and solved again. The

iterative procedure continues until the flow domain con-

verges. While this method is general and can define the

free surface very accurately (Isaacs, 1980), it requires

significant amounts of computational effort and potential

human intervention in the re-meshing at each iteration.

Moreover, this method, as pointed out by Oden and

Kikuchi (1980), often presents stability problems during

the iterative solution process, which in some cases leads

to apparently non-uniqueness of solutions. Difficulties have

also been encountered in problems involving inhomo-

geneous permeabilities. In order for these methods to work

reliably, one must typically start with a mesh that very

closely approximates the actual flow domain.

In order to overcome these difficulties, progress has

been made in formulating and solving the problems on

the entire domain. These so-called fixed domain methods

do not change the geometry of the finite element mesh

during the iterative solution process. Instead, the conditions

on the free boundary are observed in the field quantities,

which are then enforced within the spatial problem domain.

Once a trial pressure field is computed, the free surface

is then computed a posteriori as some suitable level set

within this fixed domain. For the spatial region above the

trial phreatic surface the permeability is then decreased

(penalized) to model the lack of flow in this region.

3. Problem Statement for Unconfined Seepage

in a Coupled Porous Medium

The description of the problem is shown in Figure 1.


Let ⊂ represent the porous medium domain in

3-dimensional space. Let ⊂ represent the saturatedpart of which is the flow region, and let the com-

plementary part, represent a dry region. Withcapillarity, partial saturation and evaporation effects

neglected, the soil domain is decomposed strictly into

fully saturated () and fully dry () regions. Theexternal boundary of the porous medium domain consists

of three parts: is the impermeable part, is the part

in contact with the air, and is the part in contact with

water reservoirs. The boundary of the saturated region

is assumed to have four parts; ⊂ is the impermeable

part; ⊂ is the internal free surface boundary; is the boundary with the water reservoir; and ⊂ is

the seepage face [Refer from (Borja, 1991)].

3.1 Strong Form

With steady state seepage of an incompressible fluid

assumed, the coupled boundary value problem is stated

as follows: Find the skeletal displacement field ×

and the pressure field ×→ such that thefollowing equations are satisfied:

Balance of linear momentum of the fluid and solid

media moving together;

∇∙′ in , and (3.1)

Conservation of mass for the fluid phase;

∇∙

∙∇

∇∙

(3.2)

where ′ is the effective stress tensor, is the pore

pressure, is the permeability tensor, is the body force

vector, is the total density of the soil mass, is the

second order unit tensor and is a fluid source term.

The displacement and force boundary conditions for

theis problem are stated as following:

on (3.3)

∙′ on ∪ (3.4)

where and are prescribed displacements and surface

tractions, respectively, and is the outward unit normal

to .

The pressure and fluid flow boundary conditions in and

on are as follows;

in ; elsewhere (3.5)

∙ on (3.6)

and ∙ on (3.7)

on (3.8)

and ∙ ≤ on (3.9)

where, as an example associated with Figure 1,

on the right side of the damon the left side of the dam

(3.10)

The fluid velocity field is determined from Darcy’slaw as

∙

(3.11)

where is the permeability tensor, is unit weight of

water and is elevation head.

3.2 Penalized Problem and Matrix Equations

To define the weak form, a collection of trial solid dis-

placement and fluid pressure solutions satisfying the two

respective differential equations and boundary conditions

are required, in addition to trial weighting functions which

vanish on the regions where essential boundary conditions

are imposed. Trial solutions for the skeletal displacement

field, and the fluid pressure field, satisfy the fol-

lowing requirements

∈ (3.12)

⊂ ⊂

Fig. 1. The problem geometry


∈ (3.13)

The virtual skeletal displacement functions and the

virtual pressure function satisfy the following requirements

∈ (3.14)

∈ (3.15)

Using these quantities, the variational equation of linearmomentum balance (Eq. 3.1) can be written as follows

′

′

∪

(3.16)

where

∪

In addition, the variational equation for mass balanceof the fluid (Eq. 3.2) takes the form

≤ (3.17)

where the inequality implies that the pore fluid may beseeping outward across the unknown seepage face . The

domain of integration for the third term in Eq. (3.17) canbe extended to the entire region using Heavysidefunction, .

≤ (3.18)

where

lim→

≤

≥

(3.19)

the above inequality can be converted into equality using

penalty function, .

(3.20)

where and is defined by

∗ (3.21)

In the above equation, represents a small penalty

parameter which smooths the step function. It is generally

chosen as a function of mesh discretization size.

These coupled equations can be re-written in matrix

form as follows

(3.22)

where

(3.23)

′

(3.24)

While the coupled field equations of equations (3.22)-(3.24) can be in principle be solved, such transient coupledproblems are characterized by singular and non-symmetricstiffness matrices. To overcome such difficulties, directsimultaneous time integration of the coupled semi-discreteequation has been used (Prevost, 1983; Zienkiewicz, 1985)and the resulting algorithms have been shown to beunconditionally stable. However, such implementationshave several limitations (Charbal et al., 1991). First, theyrequire the development of special software modules tosolve the coupled field equations. Second, result in verylarge matrix problems, especially for three-dimensionalcases. For these reasons, staggered solution algorithms(Park et al., 1980; Zienkiewicz, 1988) have been suggestedin which the skeletal displacement and pore pressure fieldequations are solved separately assuming that the fieldvariables of the other subsystems are known (via a predictor)and temporarily frozen. There are many advantages to such


staggered procedures: (1) modularity features which allowthe coupled equations to be processed by separate programmodules taking full advantage of specialized features anddisciplinary expertise built into independently developedsingle-field analyzers; (2) resulting algorithmic structurewhich allows the set of analyzers to be synchronized tooperate in sequential or parallel fashion. However, simple,straight forward implementations of staggered proceduresare known to be at best only conditionally stable. Implicitintegrations are used for the individual modules. To dealwith this, various stabilization procedures have beenproposed (Park et al., 1983; Park, 1983).

4. Problem Statement for De-coupled Seepage

Analysis

In the previous section, the fully coupled seepage pro-blem with free boundaries and the skeletal equilibriumproblem with pore fluid pressure effects were developed,culminating in Eq. (3.22). While such a fully coupledsystem of equation can indeed be solved in principle, itwould require the development of special purpose solutionalgorithms such as those noted. To avoid such com-plexities, a simplification is proposed here. First, the porefluid pressure field equations are solved, including locationof the free-surface, while assuming that the soil skeleton

is rigid and does not deform ( ). Once the porepressure field is found in this manner, it is applied tothe slope domain and used in finding the equilibriumdeformation state of the slope. During the limit statestructural analysis of the slope, it is assumed that defor-mations of the slope do no result in changes of the porepressure field.

With the assumption that , the strong form ofthe uncoupled equation governing conservation of the pore

fluid is;

∇

∙∇

(4.1)

which results in the following matrix systems ofequations.

(4.2)

Brezis et al (1978) showed the existence and uniqueness

of the pressure field to the penalized problem, in the

limit as tends to zero. In the first iteration of the solution

procedure, the penalty function is assumed to be

unity throughout the entire domain. In regions of negative

pressure the step function is applied, and the problem

re-solved. In subsequent iterations, the stiffness matrix and

forces vectors are pressure dependent. The iterative

solution procedure terminates when the pressure field

satisfies Eq. (4.2).

4.1 Slope Stability Analysis with De-coupled Seepage

In the following, de-coupled slope stability problems

are solved with pore pressure fields resulting from seepage

analysis by the strength reduction methods discussed in

Swan and Seo (1999). The basic equilibrium field

equations solved are

∇∙′ in (4.3)

where the pressure field is solved from de-coupled

seepage analysis and imposed on the slope domain; ′denotes the effective stress in the soil; and denotes the

mass density of the soil (dry density above the phreatic

surface and saturated density below the phreatic surface).

In the examples that follow the intention is to compare

the stability characteristics of slopes both with and without

seepage. The example problems include earthen slopes

having both purely cohesive soils and purely frictional

soils. The soil strength parameters used are the same as

those listed in Table 1.

Table 1. Clay and sand material parameters used in slope analysis

Material

ParameterClay Values Sandy Values

× ×


Non-Frictional, Purely Cohesive Soils

In this analysis of a purely cohesive soil slope, the free

surface of the headwater is taken to be below the

ground surface and tailwater level corresponds to the toe

level of the slope. The calculated free surface and pore

pressure field are shown in Figure 2a. Slope stability

analysis is then preformed and the deformed shape of the

slope at the limit state is shown in Figure 2b. An analysis

of the same slope was considered in Swan and Seo (1999)

without seepage effects. While the mechanisms of failure

are virtually the same, stability analysis without seepage

yielded while in this analysis .

This represents a reduction of thirty three percent in the

factor of safety.

Analysis with Purely Frictional Soils

In these examples for various heights of frictional sandy

slopes, the free surface is also calculated from a certain level

of the slope as shown in Figure 3. The free surface head

water was also taken as the same with non-frictional, purely

cohesive soil. The deformed shapes and compared factor of

safeties are shown in Figure 4. In general, the results indicate

that the presence of flowing water in the slopes modeled

can reduce the stability factors by between 18% and 22%,

with the larger reductions corresponding to higher slopes.

5. Summary and Closure

The strength reduction method was applied to the

earthern slopes, in which active, unconfined steady state

seepage is occurring. As an approximation, the problem

is de-coupled from the fully coupled problem of slope

stability analysis. In the first step of analysis, the

unconfined seepage was performed for the pressure field

in the slope. Then the fluid pore pressure field is imposed

on the slope stability problem. In the example of the

boundary problem some of published problems were

computed and compared. The seepage induced slop

analysis was then performed to compare the results of

dry slope which was done in Swan and Seo (1999). The

results show that the presence of water can reduce the

factors of safety.

(a)

(b)

Fig. 2. Undeformed configuration with free surface and deformed

failure mechanisms for 30 meter clay slope with a response

angle of 49°

Fig. 3. Undeformed configuration of a 20° slope with free surface

and piezometric head distribution

Dry slope Seepage effects included

Fig. 4. Limit state mechanisms and stability factors computed for

a 20° purely sand slope of varying heights and saturated

conditions with seepage.


References

1. Borja R. I. and Kishnani, S. S. “On the solution of ellipticfree-boundary problems via Newton’s method”, Comp. Meth. Mech.Eng. 88, pp.341-361, 1991.

2. Brezis, H. D. Kinderlehrer and G. Stamppacchia, “Sur une nouvelleformulation du problem de 1’ecoulement a travers une digue”, C.R. Acas. Sci. Paris 287 (ser. A) pp.711-714, 1978.

3. Cedergren, H, R. (1967), “Seepage, drainage and flow nets”, NewYork: Willey.

4. Chen, R. T. S. and Li, C. Y. (1973), “On the solution of transientfree-surface flow problems in porous media by the finite elementmethod”, J. Hydrol. 20, pp.49-63.

5. Cividini, A. and Gioda, G. (1989), “On the variable mesh finiteelement analysis of unconfined seepage problems”, Geotechnique,London, England, (2) pp.251-267.

6. Desai, C. S. (1972), “Seepage analysis fo earth banks underdrawdown”, J. Soil Mech. Found. Div., A.S.C.E., 98(SM11), pp.1143-1162.

7. Harr, M. E. (1962), “Groundwater and seepage”, New York:McGraw-Hill.

8. Isaacs, L, T. (1980), “Location df free surface in finite elementanalyses”, Civil Engineering Transaction (Australia), CE-22(1) pp.9-16.

9. Lacy, S. J. and Prevost, J. H. (1987), “Flow through porous media:a procedure for locating the free surface”, Int. J. Numer. Anal.Methods Geomech. 11, No.6, pp.585-601

10. Oden, J. T. and Kikuchi, N. (1980), “Recent advances: theory ofvariational inequalitied with applications to problems of flowthrough porous media”, Int. J. Eng. Sci., 18, pp.1173-1284.

11. Park, K. C. (1983), “Stablization of partitioned solution procedurefor pore fluid-soil interaction analysis”, Int. J. Num. Mech. Eng.19, pp.1669-1673.

12. Park, K. C. and Felippa, C. A. (1983), “Partioned analysisprocedures for coupled systemed”, in Computational methods fortransient analysis, Eds T. Belytschko and T. J. R. Hughes,North-Holland, Amsterdam. pp.158-219.

13. Park, K. C. and Felippa, C. A. (1980), “Partitioned transient analysisprocedures for coupled field problems: accuracy analysis”, J. Appl>Mech., 47, pp.919-926.

14. Prevost, J. H. (1983), “Implicit-Explicit schemes for nonlinearconsolidation”, Comp. Mech. Appl. Mech. Eng., 39, pp.225-239.

15. Swan, C. C. and Seo. Young-kyo (1999), “Limit Analysis ofEarthern Slopes using dual continuum/FEM approaches”, Int. J.Numer. Anal. Methods Geomech. 3, No. 12, pp.1359-1371.

16. Zienkiewicz, P., Mayer, P. and Cheung, Y. K. (1966), “Solutionof anisotropic seepage by finite element method”, J. Eng. Mech.Div., A.S.C.E., 92(EMI), pp.111-120.

17. Zienkiewicz, O. C., Paul, D. K., and Chan, A. H. C. (1988),“Unconditionally stable staggered solution procedure for soil-fluidinteraction problems”, Int. J. Num. Mech. Eng., 26, pp.1039-1055.

18. Zienkiewicz, O. C. and Taylor R. L. (1985), “Coupled problems-asimple time stepping procedure”, Comm. Appl. Num. Mech., 1, pp.233-239.

(received on Jun. 18, 2008, accepted on Jul. 23, 2008)

The Interference of Organic Matter in the Characterization of Aquifers Contaminated with LNAPLs by Partitioning Tracer Method 13

The Interference of Organic Matter in the Characterization ofAquifers Contaminated with LNAPLs by Partitioning Tracer Method

오염 지반에 분배성 추적자 시험법 적용 시LNAPLs

유기물질의 영향에 관한 연구

Khan, Sherin Momand1칸 쉐 린

Rhee, Sung-Su2이 성 수

Park, Jun-Boum3박 준 범

요 지

분배성 추적자 시험법은 로 오염된 지반을 조사하는데 아주 유용한LNAPLs(light nonaqueous phase liquids)방법이다 하지만 토양 내 유기물질로 흡착되는 분배성 추적자는 잠재적으로 분배성 추적자 시험법의 정확성에.영향을 끼칠 수 있다 연구 결과 추적자의 액상 간 분배 계수는 선형 관계를 보였다 토양의 흠착능력을. , -LNAPL .평가하기 위해 흡착 등은 실험을 수행한 결과 흡착 등은 양상과 거의 일치하였고 추적자의 흡착, Freundlich ,정도는 토양 내 유기물질 함량이 증가함에 따라 증가하였다 또한 토양 유기물의 흡착능에 따른 잠재적 영향을. ,판단하고 추적자 시험법에 의한 예측의 오차를 수정하기 위해 서로 다른 유기물 함량을 가진 개의, LNAPLs 4컬럼 실험을 수행하였다 컬럼 실험 결과 오염물질이 없더라도 주문진 표준사와 유기물질이 섞인 컬럼에서는. ,추적자의분리현상이발생하였다 오염물질로케로진을주입한이후에다시추적자시험법을수행하여파괴곡선.을구한결과 토양유기물질에대한추적자의흡착으로인해추적자의지연계수 가커졌고 의오염도가, (R) LNAPLs과대평가되었다 또한컬럼실험결과를바탕으로유기물함량과 의예측도사이의관계식을제안하였다. LNAPLs .

Abstract

Partitioning tracer method is a useful tool to characterize large domains of the aquifers contaminated with lightnonaqueous phase liquids (LNAPLs). Sorption of the partitioning tracers to the organic matter content of soil canpotentially influence the efficacy of partitioning tracer method. LNAPL-water partitioning coefficients of tracers(Knw), measured by static method, showed linear relationship. Sorption isotherm tests were conducted to evaluatethe sorption capacity of the soils packed in the columns and the results were appropriately represented by Freundlichsorption isotherm. The sorption of tracers proportionally increased with the increase of the organic matter contentof the soil. Laboratory experiments were conducted in four columns each packed with soils of different organicmatter contents to determine the potential interference effects of sorption to soil organic matter content and correctionfactors for the errors in estimation of LNAPLs by partitioning tracer method. Though there were no contaminantsadded, breakthrough curves from columns packed with mixture of Jumunjin standard sand and organic matter showedseparation of tracers. Columns were then contaminated to residual saturation with kerosene and breakthrough curveswere obtained. The results show that sorption of tracers to soil organic matter leads to an increase in the retardationfactor (R) and hence, to an overestimation of the saturation of LNAPLs. A relation between the percentage oforganic matter content and the corresponding percentage error in the estimation of NAPLs has been developed.

Keywords : Column Test, LNAPLs Monitoring, Partitioning Tracer Test, Soil Organic Matter, Sorption Test, Tracer Test

1 Graduate Student, Dept. of Civil and Environmental Eng., Seoul National Univ.2 Member, Graduate Student, Dept. of Civil and Environmental Eng., Seoul National Univ.3 Member, Prof., Dept. of Civil and Environmental Eng., Seoul National Univ., [email protected], Corresponding Author



1. Introduction

Sub-Surface contamination by light nonaqueous phase

liquids (LNAPLs) has proven to be a formidable challenge

for environmental engineers and its presence is often the

single most important factor limiting remediation of sites

contaminated by organic compounds (National Research

Council, 1994). Potential for further contamination is also

a concern when considering the presence of LNAPLs

sources in the subsurface (e.g. underground storage tanks

and oil/gas pipelines). Proper characterization, which

involves the location, composition and quantification of

LNAPLs, is required for accurate risk assessments and

effective remediation (Jacksons and Pickens, 1994). As

many LNAPLs are both sparingly soluble and highly

mobile, assessing their time-varying concentrations and

sub-surface distribution can be extremely difficult, particularly

in complex, near-surface industrial environment. Furthermore,

considering the various constraints to mass transfer and

the generally low maximum contaminant levels, LNAPLs

are now widely accepted to be a long-term source of both

vapor phase and ground water contamination (National

Research Council, 1994).

Light NAPLs remain floating on the top of the capillary

fringe but the fluctuation of the water table creates a smear

zone of LNAPLs at the residual saturation within the

upper portion of the saturated subsurface. It is due to these

unusual behaviors that make the detection and quantifi-

cation of LNAPLs extremely difficult in the subsurface

with the point sampling techniques of site characterization

like core sampling, cone penetrometer, and geophysical

logging (Cain et al., 2000). The sample of these methods

has relatively small volume of the subsurface and thus,

accurate characterization of the given domain is very

difficult without a cost prohibitive amount of sampling.

Thus, partitioning tracer method has been proposed as a

means to characterize the sites contaminated with

LNAPLs. This method, with a particular advantage over

the point sampling techniques covers large volume of the

subsurface, produces more reliable estimates of the

quantity and distribution of LNAPLs (Jin et al., 1995).

Partitioning tracer method is based on performing a tracer

test in the subsurface of the site, potentially contaminated

with LNAPLs. Chemical tracers with known NAPL-water

partition coefficients are injected into the subsurface to

detect the presence of LNAPLs and to estimate LNAPLs’

saturation within the zone swept by the tracers. The

LNAPLs reversibly retain the partitioning tracers with

respect to nonpartitioning tracers causing the former to

lag behind the later. The extent of separation depends on

the residence time of tracers, which are a function of its

partition coefficient and the saturation of LNAPLs. Thus, the

magnitude of measured separation of the partitioning tracers

can be translated into quantifying NAPLs present within

the zone swept through by the tracers (Jin et al., 1995).

The partition tracer method can be used as an

innovative and effective technique for the detection and

quantification of LNAPLs’ contamination in the subsurface

as well as to evaluate the remediation performance.

However, the results can be affected by many factors such

as rate limited transfer, subsurface heterogeneities, multiphase

retention, biochemical degradation, and sorption on to the

soil organic matter of chemical tracers, which leads to

inappropriate characterization of the site under conside-

ration (Brusseau et al., 2003). Hence, partition tracer

method needs to be evaluated to determine the effect of

influencing factors. The purpose of this paper is to present

the effect of sorption of the chemical tracers to the soil

organic matter on partition tracer method from column

scale experiments in laboratory. A comparison of the

saturation of LNAPLs determined from partition tracer

test conducted in a column packed with Jumunjin standard

sand and columns packed with different weight ratios of

Jumunjin standard sand and organic matter provided a

measure of the effect of sorption.

2. Theory and Analysis Techniques

2.1 Method of Moments

It has been shown that the method of moment’s theory

can be used to determine LNAPLs’ saturations in a

subsurface, given the difference in mean residence times

between two different tracers by using partitioning tracer

method (Jin et al., 1995). Partitioning tracer method is


based on the chromatographic separation of two or more

selected tracers as they flow with ground water through the

LNAPLs’ contaminated aquifer. The partition coefficient

(Knw, unitless) of a partitioning tracer quantifies the

fraction of tracer in LNAPLs’ phases and water phase

at equilibrium (Jin et al., 1995). It is defined as the ratio

of the concentration of tracer in the LNAPLs phase (Cn,

unit: mg/L) to the concentration of tracer in the water

phase (Cw, unit: mg/L), or

Knw=Cn/Cw (1)

Nonpartitioning tracers have a partition coefficient of

zero with respect to LNAPLs, whereas the partitioning

tracers have partition coefficients with non zero positive

value. A set of partitioning and nonpartitioning tracers is

selected to get the greatest degree of separation between

tracer pairs in a reasonably short period of time. The

magnitude of retardation is a function of LNAPLs saturation

and partition coefficient (Brusseau et al., 2003). The R

value (unitless) determined from the tracer test is equated

to the mass-balance definition of R, given for aqueous-

phase transport as:

　( )

11 nw

p b nd

n w n

t SR K K

t Sρθ

⎡ ⎤⎛ ⎞= = + + ⎢ ⎥⎜ ⎟ −⎢ ⎥⎝ ⎠ ⎣ ⎦

(2)

Where, tp is the travel time of the partitioning tracer, tnis the travel time for the nonpartitioning tracer, ρb is bulk

density of porous media (unit: g/cm3), θw is the water-

filled porosity (unitless), Kd is the water-aquifer solids

partition coefficient (unit: cm3/g), and Sn is the effective

LNAPLs’ saturation (unitless) degree.

The previous researchers have neglected the second

term on the right side of the equation (2) assuming that

liquid-liquid partitioning is much greater than the

liquid-solid partitioning. It was further supported that the

large volume of the LNAPLs in the subsurface would

cause the liquid - liquid partitioning to dominate tracers’

retardation (Cain et al., 2000). No previous research has

been carried out to support this assumption. We have

considered the second term i.e. sorption, in our calculations

to evaluate the authenticity of this assumption. The

sorption can occur with organic matter or clay material.

But, this study focuses on the effect of organic matter.

The detailed procedure for the quantification of LNAPLs

using partitioning tracer theory can be found in Jin et al.

(1994, 1995).

The total volume of LNAPLs in subsurface may often

be underestimated using partitioning tracer method because

of factors such as rate-limited transfer, bypass flow and

mass loss, but the contrary can be true in case of sorption

of the tracers to soil organic matter (Hatfield and Stauffer,

1993). We have demonstrated how the saturation of

LNAPLs is an overestimate of the true value because of

sorption to the soil organic matter using columns packed

with selected soils of known sorption capacities.

3. Material and Methods

3.1 Composition of Soil

Jumunjin standard sand was packed in column 1 and

mixture of Jumunjin standard sand and organic fertilizer

in columns 2~4 in ratios 19:1, 9:1, and 4:1 respectively.

Organic fertilizer, passing No. 10 sieve (0.200 mm

opening size) and retained by No. 40 sieve (0.420 mm

opening size), was used to represent the soil organic

matter. The organic matter content in the organic fertilizer

and Jumunjin standard sand was determined by the

loss-on-ignition method (Veres, 2002) and was found to

be 5.35% and 0.50% respectively. X-Ray Fluorescence

(XRF) analysis and X-ray Diffraction (XRD) analysis of

Jumunjin standard sand and organic fertilizers were

conducted and are given in Table 1. Jumunjin standard

sand and its mixture with organic fertilizer in different

ratios were used to ascertain the effect of concentration

of the organic matter content on tracers’ breakthrough

curves. Jumunjin standard sand was used in column

marked as number “1” and the columns marked as “2,

3 and 4 were packed with the mixture of organic fertilizer

and Jumunjin standard sand with organic matter content

of 2.64, 5.29 and 10.58, respectively.

3.2 Tracers

Methanol and chloride ions were used as non-


partitioning tracers while 2-ethyl-1-butanol, 4-methyl-2-

pentanol, 1-pentanol, 1-hexanol, and 2,3-dimethyle-2-

pentanol were used as partitioning tracers in the column

experiments and were chosen to yield breakthrough curves

in a reasonably short time, and yet they ensured good

separation of the partitioning and nonpartitioning tracers

(Varandarajan and Garry Pope, 1998). Kerosene dyed

with Sudan IV was used as a representative LNAPLs in

columns packed with selected soils.

3.3 Batch-Partitioning Experiments

Batch-partitioning experiments were conducted todetermine kerosene-water partition coefficients (Knw) forthe group of selected tracers. Batch partitioning tests, in20 mL septa-capped vials with equal volumes of keroseneand water (10 mL each), were conducted with methanol,2-ethyl-1-butanol, 4-methyl-2-pentanol, 1-pentanol, 1-hexanol,and 2,3-dimethyle-2-pentanol ranging in concentrationfrom 50 to 800 mg/L. Vigorous mixing on an orbital mixerfor thirty one hours equilibrated the vials. Followingequilibration, a 2 mL aqueous sample was collected viasyringe after centrifuging the sample in the centrifuge for30 minutes at 3500 rmp, and placed into a 2 mL septavial for alcohol analysis with a Hewlett-Packard (HP)6890 gas chromatograph (GC). The GC was equippedwith a 30.0 m long by 0.25 mm PAG capillary column(Supelco 2-4223) and a flame ionization detector (FID).The FID signal was acquired and integrated with personal

computer (PC) using HP Chemstation software.

3.4 Sorption Isotherm Experiments

Sorption isotherm experiments were conducted to

determine soil-water partition coefficients of tracers and

the sorption capacity of the selected soils. The tests were

conducted in 20 mL, septa-capped vials with 4 grams of

the selected soil and measured amount of the tracer

solution to make the head space almost zero. Vigorous

mixing on an orbital mixer for 48 hours equilibrated the

vials. Following equilibration, a 2 mL aqueous sample

was collected via syringe after centrifuging the sample

in the centrifuge for 40 minutes at 3800 rmp, and placed

into a 2 mL septa vial for alcohol analysis with GC.

3.5 Column-Scale Experiments

Figure 1 shows the schematic diagram of the equipment

setup for column experiment. Jumunjin standard sand and

its mixture with organic fertilizer were packed under

dynamic compaction in the glass columns, each 40 cm

long and with an inner diameter of 3.5 cm.

Packed columns were saturated with DI (deionized)

water at a constant flow rate of 0.1 ml/min after purging

by CO2 gas to remove the air bubbles and get full

saturation of the packed soils. The flow rate was slow

enough to give sufficient time for reversible reaction to

occur between tracers and the other media. Sodium azide

Table 1. Composition of Jumunjin standard sand and organic fertilizer from XRF and XRD analysis

Jumunjin standard sand Organic fertilizer

XRF analysis XRD analysis XRF analysis XRD analysis

Weight (%) Weight (%) Weight (%) Weight (%)

SiO2 88.50 Quartz 74.70 SiO2 60.04 Quartz 43.80

Al2O3 6.59 Plagioclase 7.20 Al2O3 11.85 Plagioclase 7.70

TiO2 0.08 K-feldspar 18.10 TiO2 0.57 K-feldspar 14.10

Fe2O3 0.04 Muscovite 0.00 Fe2O3 6.55 Muscovite 16.40

MgO 0.02 Calcite 0.00 MgO 1.98 Calcite 2.70

CaO 0.21 Goethite 0.00 CaO 7.34 Goethite 15.10

Na2O 0.12 Na2O 0.54

K2O 3.81 K2O 3.78

MnO 0.03 MnO 0.37

P2O5 0.02 P2O5 1.33

Loss on ignition 0.50 Loss on ignition 5.35


solution was injected to kill the bacteria in the packed

columns as they may biodegrade the chemical tracers.

Tracer test in the columns was conducted before and after

contamination with kerosene. A known volume of dyed

kerosene was injected as a representative of the LNAPLs

contamination. Residual contamination was insured by

continuously injecting DI water until there was no

movement of the dyed kerosene. The method of volume

measurement was adopted to determine the volume of

residual kerosene saturation in the columns which

involves the measurement of the volume of the injected

kerosene and the volume produced during the DI water

flood (Jin et al., 1995). The tracers’ pulse was 0.15 pore

volume for all the columns. Effluents were collected every

hour and were analyzed with GC.

4. Results and Discussions

4.1 Batch Tests and Tracer Screening

The results of batch-partitioning experiments conducted

to determine kerosene-water partition coefficients for the

selected group suite of alcohol tracers are shown in Table

2. The Results in Figure 2 indicate that kerosene-water

partitioning is linear with respect to alcohol tracers’

concentrations employed in this study. Measured partition

coefficients, reflected as the slope of the linear trend, are

constant with increasing aqueous tracer concentration. The

retention times from our GC analysis for methanol,

2-ethyl-1-butanol, 4-methyl-2-pentanol, 1-pentanol, 1-hexanol,

and 2,3-dimethyl-2-pentanol were 1.64, 7.13, 4.76, 4.78,

7.14, and 8.27 respectively. The results from batch tests

and a column test were screened to determine the most

suitable group of tracers for producing breakthrough

responses in a reasonably short time and yet ensuring good

separation of tracers. 1-Pentanol and 2,3-dimethyl-2-

pentanol were discarded because of its similar retention

time with 4-methyl-2-pentanol and 2-ethyl-1-butanol

respectively and hence, their peaks cannot be differentiated

in the GC. Another reason for discarding 2,3-dimethyl-2-

pentanol was that it was restrained for unreasonably long

Fig. 1. Schematic diagram of column setup and sampling

Table 2. Kerosene-water partitioning coefficients of tracers

Tracer Formula Molar mass (g/mol) Knw R2

Methanol CH3OH 32.04 0.003 0.9204

1-Pentanol CH3(CH2)4OH 88.15 2.276 0.9233

1-Hexanol CH3(CH2)5OH 102.17 4.293 0.9958

2-Ethyl-1-butanol (C2H5)2CHCH2OH 102.18 3.656 0.9987

4-Methyl-2-pentanol (CH3)2CHCH2CH(OH)CH3 102.18 2.677 0.9713

2,4-Dimethyl-3-pentanol (CH3)2CHCH(OH)CH(CH3)2 116.20 11.257 0.9996

0

100

200

300

400

500

600

0 100 200 300 400 500 600 700The concentration of tracer in water, mg/L

The

con

cent

ratio

n of

trac

er in

kero

sene

, mg/

L

MethanolPentanol2-Ethyl-1-butanol4-Methyl-2-pentanol2,4-Dimethyl-3-pentanolHexanol

Fig. 2. Partitioning of tracers between kerosene and water


time in the columns packed with mixture of selected soils.

Measured partition coefficients were used in conjunction

with measured partitioning tracer retardations to predict

kerosene volume within zone swept by the tracers.

　4.2 Sorption Isotherm Experiments

The results of sorption isotherm experiments conducted

to determine soil-water partition coefficients for the

selected group of alcohols are shown in Table 3.

Freundlich sorption isotherm is used which is mathematically

expressed as below:

S=KCN (3)

Where, S is the mass of the tracers sorbed per unit dry

mass of solid in mg/kg, C is the concentration of the

tracers in solution at equilibrium in mg/L, and K is the

distribution coefficient in L/kg.

The equation (3) is linearized by plotting log of C

verses log S. The slope of the straight line is N and the

intercept is equal to log K. It is the most commonly used

isotherm in contaminant migration analysis and is

generally valid at low contaminant concentration ranges.

Results indicate the solute concentration sorbed onto the

soil and the concentration of the tracer in solution phase

in equilibrium. The capacity of the soil to remove the

traces i.e. solutes is a function of the concentration of

the solute within the same test soil. The sorptive process

is rapid initially but an equilibrium condition of solute

is reached with the amount sorbed onto the soil within

certain duration. The results clearly demonstrate that the

sorption capacity of Jumunjin standard sand is negligible

and that its mixture with organic fertilizer shows

considerable sorption capacity. The sorption of tracers

increased proportionally to the percentage of soil organic

matter content.

　4.3 Column Experiments

The breakthrough curves obtained from column 1

(packed with Jumunjin standard sand) show no separation

of tracers as given in Figure 3, which indicate that there

is no partitioning of tracers to the media swept through

Table 3. Results from sorption isotherm experiments using Freundlich isotherm

Column

number

Organic matter

content (%)Tracers Kf N R

2

1 0.00

4-Methyl-2-pentanol 1.7814 0.3011 0.7646

Hexanol 2.3799 0.1809 0.9765

2-Ethyl-1-butanol -0.9913 1.3293 0.9990

2 2.64

4-Methyl-2-pentanol 1.7814 0.3011 0.9773

Hexanol 2.3799 0.1809 0.6671

2-Ethyl-1-butanol -0.9913 1.3293 0.9187

3 5.29

4-Methyl-2-pentanol 1.7814 0.3011 0.9514

Hexanol 2.3799 0.1809 0.9351

2-Ethyl-1-butanol -0.9913 1.3293 0.9772

4 7.93

4-Methyl-2-pentanol 1.7814 0.3011 0.8518

Hexanol 2.3799 0.1809 0.9907

2-Ethyl-1-butanol -0.9913 1.3293 0.9845

0.0

0.2

0.4

0.6

0.8

1.0

0 100 200 300 400 500 600 700 800Cumulative volume, mL

Rela

tive c

oncentr

ati

on

Methanol

4-Methyl-2-pentanol

2-Ethyl-1-butanol

Hexanol

Chloride ion

Fig. 3. Breakthrough curves from pre-contaminated column 1

which has 0% organic matter content


by the tracers and hence no contamination was detected.

The breakthrough curves from the pre-contaminated

columns 3~5 which contain known percentage of organic

matter content, show significant separation of tracers and

a marked increase in the separation of tracers was

observed with the increase in the percentage of organic

matter content as shown in the Figures 4~6. It is evident

from this phenomenon that partitioning of tracers occurred

only between water and organic matter content of soil

as the columns were precontaminated and that Jumunjin

standard sand caused no separation of tracers. A situation

like this can be quite misleading as it can be taken for

contamination in the subsurface or, at least, exaggerate

the quantity of the contaminants.

The breakthrough curves from the post-contaminated

columns are given in Figures 7~10 and measured versus

predicted volumes of kerosene are shown for homo-

geneously distributed residual saturation of kerosene in

different columns in Table 4. The retardation factor is

0.0

0.2

0.4

0.6

0.8

1.0


Rela

tive c

oncen

trati

on

Methanol

4-Methyl-2-pentanol

2-Ethyl-1-butanol

Hexanol

Chloride ion


which has 2.64% organic matter content

0.0

0.2

0.4

0.6

0.8

1.0


Rela

tive c

oncen

trati

on

Methanol

4-Methyl-2-pentanol

2-Ethyl-1-butanol

Hexanol

Chloride ion



0.0

0.2

0.4

0.6

0.8

1.0


Rela

tive c

oncen

trati

on

Methanol

4-Methyl-2-pentanol

2-Ethyl-1-butanol

Hexanol

Chloride ion



0.0

0.2

0.4

0.6

0.8

1.0


Rela

tive

co

nce

ntr

ati

on

Methanol

4-Methyl-2-pentanol

2-Ethyl-1-butanol

Hexanol

Chloride ion

Fig. 7. Breakthrough curves from post-contaminated column 1

which has 0% organic matter content

0.0

0.2

0.4

0.6

0.8

1.0


Rela

tive c

oncen

trati

on

Methanol

4-Methyl-2-pentanol

2-Ethyl-1-butanol

Hexanol

Chloride ion




between 1.2 and 4 for all the partitioning tracers which

are desirable for partitioning tracer method to have

appropriate estimation of kerosene in the subsurface. The

magnitude of retardation is a function of the kerosene

saturation and the partition coefficients for column 1 as

the partioning of racer to the Jumunjin standard stand is

negligible but in the cases of columns 2~4, sorption of

the tracers to the soil organic contents also contributes

to the magnitude of retardation. To get appropriate

estimation of the kerosene saturation, it is imperative

to determine the appropriate correction factor. The

hexanol breakthrough curve was retarded more with

4-methyl-2-pentanol and 2-ethyl-1-butanol. The methanol

and chloride ions were used as nonpartitioning tracers and

were not retarded at all. The predicted values by

partioning tracer method vary linearly from under

estimation to overestimation with the increase in organic

matter contents of the soil as shown in Figure 10. This

significant difference is due to the sorption of tracers to

the organic matter in the columns. Based on these results,

the error in the estimated values of kerosene can be

corrected for the known percentage of the organic matter

content. From this data we have been able to express the

error estimation as a function of organic content of the

soil.

Estimation Error (%) = 13.7 × [Organic Matter

Contents] – 37.5 (4)

Thus, knowing only the organic content in the soil will

enable us to determine the error estimation from now on.

0.0

0.2

0.4

0.6

0.8

1.0


Rela

tive c

oncen

trati

on

Methanol

4-Methyl-2-pentanol

2-Ethyl-1-butanol

Hexanol

Chloride ion



0.0

0.2

0.4

0.6

0.8

1.0


Rela

tive c

oncen

trati

on

Methanol

4-Methyl-2-pentanol

2-Ethyl-1-butanol

Hexanol

Chloride ion



y = 13.671x - 37.142R2 = 0.9995

-100

-50

0

50

100

150

0 2 4 6 8 10 12 14Organic Matter Content (%)

Esti

mati

on

Err

or

(%)

Fig. 11. The error in estimation of kerosene by partition tracer

method caused by the organic matter content in the soil

Table 4. The percentage error in predicted values of kerosene by partitioning tracer method

Column

Number

Organic matter

content (%)

Measured

contamination (ml)

Average estimated

contamination (ml)

Percentage

error

1 0.00 28.01 17.97 -35.83

2 2.64 29.35 28.87 -1.65

3 5.29 34.72 46.33 33.44

4 10.58 27.48 57.30 108.51


5. Conclusions

Most of the current subsurface characterization methods

provide measurements for very small spatial domains,

even for point values. While such methods can provide

accurate data for small scales, their use for characterizing

larger domains is generally constrained by sample-size

limitations. Thus, partition tracer method that provides

measurements at larger scales has been developed to

complement the point-sampling methods. The experimental

and theoretical basis for these tracer techniques is well

established. However, there is a major concern about its

application in the subsurface organic soil to provide

reliable in-situ measures of the relative quantities of

LNAPLs due the sorption of tracers to the organic matter.

In our study, we only test with the mixture of organic

fertilizer and Jumunjin standard soil to evaluate the

interference of organic soil in partitioning tracer method.

The tracers tests conducted in the pre-contaminated columns,

with known amount of organic matter, demonstrate that

tracers can be retarded with marked separation. Thus, the

accurate quantity estimation of LNAPL using partitioning

tracer test should be considered by conducting partitioning

tracer test without soils containing organic matter. The

presence of organic matter caused a linear increase in the

overestimation of the predicted values and thus can be

corrected for the known percentage of the organic matter

in the subsurface soil under given conditions.

Acknowledgement

The authors wish to acknowledge the financial support

by SNU SIR BK21 Research Program funded by Ministry

of Education, Science and Technology.

References

1. Brusseau, M.L., Zhihui Zhang, Nelson, N.T., Cain, R.B., Geoffrey,R.T., and Oostrom, M. (2002), “Dissolution of Nonuniformly

Distributed Immiscible Liquid: Intermediate-Scale Experiments andMathematical Modeling”, Journal of Environmental Science andTechnology, Vol.36, No.5, pp.1033-41.

2. Cain, R.B., Johnson, G.R., McCray, J.E., Blanford, W.J., andBrusseau, M.L. (2000), “Partitioning Tracer Test for EvaluatingRemediation Performance”, Journal of Ground Water, Vol.38, No.5, pp.752-761.

3. Deed, N.E. (2000), “Laboratory Characterization of Non-AqueousPhase Liquid/Tracer Interpretation in Support Of Vadose ZonePartitioning Interwell Tracer Test”, Journal of contaminant hydrology,Vol.41, pp.193-204.

4. Harvey, C.F. and Gorelick, S.M. (1995), “Temporal Moment-Generating Equations: Modeling Transport and Mass Transfer inHeterogeneous Aquifers”, Journal of Water Resources, Vol.31,No.8, pp.1895-911.

5. Hatfield, K. and Stauffer, T.B. (1993), “Transport in Porous MediaContaining Residual Hydrocarbon”, Journal of EnvironmentalEngineering, Vol.119, No.3, pp.540-58.

6. Jacksons, R.E. and Pickens, J.F. (1994), “Determining Location andComposition of Liquids Contaminants in Geologic Formations.”U.S. Patent 5,319,966, U.S. Pat. Off., D.C.

7. Jin, M., Delshad, M., Dwarakanath, V., McKinney, D.C., Pope,G.A., Sepehrnoori, K., Tilburg, C., and Jackson, R.E. (1995),“Partitioning Tracer Test for Detection, Estimation and RemediationPerformance Assessment of Subsurface Nonaqueous Phase Liquids.”Journal of Water Resources Research, Vol.31, No.5, pp.1201-11.

8. Jin, M., Butler, G.W., Jackson, R.E., Mariner, P.E., Pickens, J.F.,Pope, G.A., Brown, C.L., and McKinney, D.C. (1997), “SensitivityModels and Design Protocol for Partitioning Tracer Tests in AlluvialAquifers”, Journal of Ground Water, Vol.35, No.6, pp.964-972.

9. Mayer, A.S. and Miller, C.T. (1992), “The Influence of PorousMedium Characteristics and Measurement Scale on Pore-ScaleDistributions of Residual Nonaqueous-Phase Liquids”, Journal ofContaminant Hydrology, Vol.11, pp.189-213.

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11. Rao, P.Suresh C., Annable, M.D., and Kim, H. (2000), “NAPLSource Zone Characterization and Remediation Technology Perfor-mance Assessment: Recent Developments and Applications ofTracer Techniques”, Journal of Contaminant Hydrology, Vol.45,pp.63-78.

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(received on Jul. 21, 2008, accepted on Sep. 23, 2008)

Global Stability of Geosynthetic Reinforced Segmental Retaining Walls in Tiered Configuration 23

Global Stability of Geosynthetic Reinforced Segmental RetainingWalls in Tiered Configuration

계단식 블록식 보강토 옹벽의 전체 안정성

Yoo, Chungsik1유 충 식

Kim, Sun-Bin2김 선 빈

요 지

본논문에서는계단식형태로시공되는블록식보강토옹벽의전체안정성이고려된설계에관한내용을다루었

다 다양한제원과이격거리로설계된네가지설계사례에대해현재통용되고있는 및 설계기준에. FHWA NCMA근거하여내 외적안정해석을수행하고그결과를토대로두설계기준의차이점을검토하였다 아울러대상옹벽.･에대해한계평형해석에근거한사면안정해석과연속체역학기반의강도감소기법해석을수행하여계단식옹벽의

설계를지배하는파괴메카니즘을고찰하였다 그결과내 외적안정성공히 에서채택하고있는설계기준. FHWA･이 보다 보수적인 결과낮은 안전율를 주는 것으로 나타났다 또한 계단식 옹벽의 보강재의 소요 포설NCMA ( ) .길이는 전반적으로 전체 안정성에 좌우되는 것으로 검토되었으며 상부 옹벽의 보강재의 길이는 현 설계기준

보다 현저히 증가시켜야 하는 것으로 검토되었다.

Abstract

This paper presents the global stability of geosynthetic reinforced segmental retaining walls in tiered configuration.Four design cases of walls with different geometries and offset distances were analyzed based on the FHWA andNCMA design guidelines and the discrepancies between the different guidelines were identified. A series of globalslope stability analyses were conducted using the limit-equilibrium analysis and the continuum mechanics basedshear strength reduction method with the aim of identifying failure patterns and the associated factors of safety.The results indicated among other things that the FHWA design approach yields conservative results both in theexternal and internal stability calculations, i.e., lower factors of safety, than the NCMA design approach. It wasalso found that required reinforcement lengths are usually governed by the global slope stability requirement ratherthan the external stability calculations. Also shown is that the required reinforcement lengths for the upper tiersare much longer than those based on the current design guidelines.

Keywords : Geosynthetic-reinforced segmental retaining Wall, Geosynthetics, Global stability, Limit equilibrium,

Finite element analysis, Shear strength reduction

1 Professor, Dept. of Civil & Envir. Engrg, Sungkyunkwan Univ.2 Graduate Student. Dept. of Civil & Environ. Engrg., Sungkyunkwan Univ., [email protected], Corresponding Author

1. Introduction

Geosynthetic reinforced segmental retaining walls (GR-

SRWs) have been well accepted in practice as alternatives

to conventional retaining wall systems due to several

benefits such as sound performance, aesthetics, cost and



expediency of construction. This is especially true in Korea

since its first appearance in the early 1990’s. Recently

the application of the GR-SRWs has been extended to

public sectors such as roadway and railway constructions,

especially in Japan as well as north America. For example,

GR-SRWs are frequently adopted in bridge construction

in public sectors, as the form of geosynthetic-reinforced

soil (GRS) abutments in bridge applications (Lee and Wu,

2004).

There are many situations where GR-SRWs are constructed

in tiered configuration for a variety of reasons such as

aesthetics, stability, and construction constraints, etc. Yoo

and Kim (2002), however, reported that the interaction

between the upper and lower tiers is not insignificant for

walls with an intermediate offset distance as per the

FHWA design guideline (Elias and Christopher 1997),

thus yielding larger wall deformation and reinforcements

forces than what might be anticipated. In addition, the

currently available design guidelines such as the NCMA

(Collins, 1997) and FHWA design guidelines are somewhat

empirical and geometrically derived.

Surprisingly, studies concerning GR-SRWs in tiered

configuration are scarce. For example, Yoo (2003), Yoo

and Jung (2004) reported the instrumentation results of

a full-scale, 5 m high two tier segmental retaining wall

that was constructed to investigate the short and long term

performance of the segmental retaining wall. Leshchinsky

and Han (2004) performed a series of finite difference

analyses on multi-tiered segmental retaining walls in order

to examine the failure mechanisms and to assess the

required tensile strength as a function of reinforcement

length, stiffness, offset distance, among others. Later, Yoo

and Kim (2006) conducted a numerical investigation on

two-tier segmental retaining walls with different offset

distances. More recently, Yoo et al. (2005) investigated

the deformation behavior of two-tier segmental retaining

walls on competent foundation having different wall

geometries as well as reinforcement layouts. Yoo and

Song (2006) later extended the work by Yoo et al. (2005)

for cases constructed on yielding foundation. Although

these studies provided valuable information as the subject

relevant to this study, in-depth studies are warranted in

order to accumulate required data for improving the

currently available design guidelines.

In this study four design case histories of geosynthetic

reinforced segmental retaining walls in tiered configuration

were considered, intending; 1) to highlight inherent

differences between the currently available design guidelines,

2) to demonstrate the governing failure mechanism that

yields the smallest factor of safety is the global failure,

3) to highlight the importance of carrying out the global

stability analysis as part of design. This study presents

the results of a series of analyses conducted in parallel

using two independent type of analyses: one based on

limiting equilibrium (LE) and the other based on

continuum mechanics. This paper is intended to be an

extension of the previous work done by Yoo and Kim

(2006).

2. Review of Design Guidelines

2.1 NCMA (National Concrete Masonry Association)

The NCMA design approach basically replaces the

DH 2

q

αα

qeq = f (D)

H1

L1

L1

H1

Fig. 1. Equivalent surcharge model (NCMA)


upper tier with an equivalent surcharge of which the

magnitude is determined according to the offset distance

D (Figure 1). External and internal stability calculations

of the lower tier are performed assuming the lower tier

being a single wall under the equivalent surcharge (qeq).

The upper wall is designed as if it were a single wall

without taking into consideration of the possible interaction

between the upper and the lower tiers. As for a single

wall, the local stability calculations for the connection

failure, local overturning, and internal sliding should be

performed for both tiers. Details of the design procedure

are available in Collin (1997).

2.2 FHWA (Federal Highway Association)

In the FHWA design guideline, the required reinforcement

lengths for the upper and lower tiers are determined based

on the maximum tension line criteria given in Figure 2.

For example, no interaction is assumed and each tier is

designed independently when D＞ H1 tan(90 – ). When

D≤ 1 / 20(H1 + H2), on the other hand, the wall is

designed as if it were a single wall with a height of H =

H1 + H2. For walls with an intermediate offset distance

of 1 / 20(H1 + H2)＜ D≤ H1 tan(90 – ), the lower and

upper tier reinforcement lengths are taken as L1≥ 0.6H1

and L2≥ 0.6H2, respectively. Where, H1 = lower tier

height, H2 = upper wall height, L1 and L2 = reinforcement

length of lower and upper tier, respectively, and =

internal friction angle of backfill.

For internal stability calculations, additional vertical

stresses at depths due to the upper tier are computed based

on the criteria shown in Figure 3. Note, however, that

these criteria are geometrically derived and empirical in

nature. As for the NCMA approach, no provision is made

to take into account the possible interaction between the

upper and the lower tiers when designing the upper tier.

The connection failure should also be checked for both tiers

as part of internal stability check based on the procedure

for a single wall (Elias and Christopher, 1997).

As discussed, the external and internal stability calculation

models adopted in the two design guidelines are somewhat

different, thus yielding different stability calculation results

in terms of the factors of safety for most of the cases.

In addition, although the two aforementioned design

guidelines require to perform a global stability analysis

to ensure overall stability, it is general practice that no

global stability analysis is usually carried out in routine

designs. Further study is warranted to fill the gap between

the two design guidelines.

Note that in the FHWA and NCMA design guidelines

Fig. 2. Maximum tension line (FHWA)


outlined above, same minimum factors of safety for

internal and external failure modes for a single wall are

applicable for a multi-tiered wall. In addition, for the

minimum factor of safety for global slope stability, a

typical value used in a geotechnical project can be used.

3. Field Walls Considered

Figure 4 shows four field walls considered in this study.

As summarized in Table 1, the total exposed wall heights

range from 4 to 12 m with the offset distance ranging

0.23~0.45 times the total wall height (H). The reinforce-

ment lengths vary as (0.38~0.56)H. Note that the walls

are designed based on either NCMA or FHWA design

approaches with the design parameters given in Table 2.

4. Stability Analysis

4.1 Internal and External Stability Analysis

The above field walls were re-analyzed by NCMA and

FHWA design approaches with the aiming of demonstrating

the inherent differences in the stability calculations. Table

2 summarizes the design parameters for the backfill and

the reinforcement used in the stability analyses. Note that

these parameters reflect the practice adopted in Korea.

The results of the external and the internal calculations

are summarized in Table 3. Importance findings can

H1

H2

D

σf

φγH2ζj

γi

ζ1

ζ2

σi

γH2

φς tan1 D= ⎟⎠⎞

⎜⎝⎛ +=

245tan2

φς oD

212

1 Hjf γ

ςςςς

σ−

−=

⎟⎠⎞

⎜⎝⎛ −≤

245tan1

φoHD

( )φ−> o90tan1HD 0=iσ

2Hi γσ =

( )φφ−≤<⎟

⎠⎞

⎜⎝⎛ − oo 90tan

245tan 11 HDH

σj

where: ,

245 φ

+o

Fig. 3. Calculation model for vertical stress increase due to upper tier (FHWA)

Table 1. Summary of wall geometry and reinforcement length

Wall

Height (m)Offset distance

D (m)

Reinforcement length (m)

Lower

Tier, H1

Upper

Tier, H2

Total

H1

Lower tier

L1

Upper tier

L2

A 3.8 5.4 8.8 2.5(0.34H) 4.9(0.56H) 3.5(0.7H2)

B 5.6 5.6 10.5 2.5(0.23H) 5.3(0.50H) 3.8(0.8H2)

C 8.8 4.4 12.4 5.0(0.40H) 7.0(0.56H) 5.0(1.3H2)

D 2.6 2.2 4.6 2.0(0.45H) 1.6(0.38H) 1.6(0.8H2)

Note) 1exposed height

Table 2. Design parameters for backfill and reinforcement used in stability analysis

Wall BackfillReinforcement

Reduction factor1

Tall (kN/m)2

A

c=0,

RFD RFID RFCR FS 6T=16, 8T=21.5, 10T=27

B

1.05 1.1 2.15 1.5

6T=16, 10T=27

C TYPE1=15, TYPE2=22 TYPE3=30

D N/A

Note)1Reduction factors represent general practice;

2Tall=allowable strength


10T L=4.9M10T L=4.9M

10T L=4.9M

8T L=4.9M

8T L=5.9M8T L=3.5M8T L=3.5M

8T L=3.5M

8T L=3.5M

6T L=3.5M6T L=3.5M

6T L=3.5M

6T L=4.0M

2500

1:0.12

800

3400

5000

q=10 kPa

PG 6T H=0.2 L=5.28M

PG 10T H=0.8 L=5.28M

PG 10T H=1.4 L=5.28M

PG 10T H=2.0 L=5.28M

PG 6T H=2.6 L=5.28M

PG 6T H=3.2 L=5.28M

PG 6T H=4.0 L=5.28M

PG 6T H=4.8 L=5.28MPG 6T H=0.2 L=3.78M

PG 6T H=1.0 L=3.78M

PG 6T H=1.6 L=3.78M

PG 6T H=2.4 L=3.78M

PG 6T H=3.2 L=3.78M

PG 6T H=4.0 L=3.78M

PG 6T H=4.8 L=3.78M

5000

500

5100

400

2500

q=13.0 kPa

q=100.0kPa

150

150

116

116

(a) Wall A (b) Wall B

*All numbers are in mm unless otherwise indicated

300

L1 TYPE3 H=0.6M L=7.0ML1 TYPE3 H=1.2M L=7.0ML1 TYPE3 H=1.8M L=7.0ML1 TYPE2 H=2.4M L=7.0ML1 TYPE2 H=3.0M L=7.0ML1 TYPE2 H=3.6M L=7.0ML2 TYPE2 H=4.2M L=7.5ML2 TYPE2 H=4.8M L=7.5ML2 TYPE2 H=5.6M L=7.5ML2 TYPE1 H=6.4M L=7.5ML2 TYPE1 H=7.2M L=7.5M

L1 TYPE1 H=0.6M L=5.0ML1 TYPE1 H=1.2M L=5.0ML1 TYPE1 H=1.8M L=5.0M

L1 TYPE1 H=3.8M L=5.0ML1 TYPE1 H=3.0M L=5.0ML1 TYPE1 H=2.4M L=5.0M

18

18

400

4000

8000

2000

30050

028

0012

400

6000 500 6850

300

650

2000

2000

4650

G.L

2000

L1 TYPE H=1.6M L=1.6M




(c) Wall C (d) Wall D

Fig. 4. Field walls considered

Table 3. Results of external and internal stability calculations for field walls

Wall

External Internal

FSbsl FSot Ti,max (kN/m) Le (m)

NCMA FHWA NCMA FHWA NCMA FHWA NCMA FHWA

A 3.13 1.27 8.87 2.13 19.7 30.5 3.4 4.1

B 2.19 1.23 4.53 1.76 19.8 36.9 1.5 2.5

C 2.79 2.02 6.09 5.01 16.0 37.5 2.4 3.9

D 1.28 1.67 3.54 1.65 9.9 19.7 0.3 0.3

Note) 1) FSbsl = factor of safety against base sliding 2) FSot = factor of safety against overturning 3) Ti,max = maximum reinforcement

force within lower tier 4) Le = embedded length beyond active zone for top-most reinforcement in lower tier 5) For Wall D, FHWA design

guideline assumes no interaction.


be summarized as follow. As seen in Table 3, the FHWA

design guideline tends to give smaller factors of safety in

the external analysis except for the wall D. For example,

according to the NCMA design approaches walls A, B,

and C satisfy the requirement for base sliding while the

opposite is true according to the FHWA design approach.

Additional global stability analyses in fact support the

instability against base sliding as the factors of safety

against global/compound stability for all the walls are less

than the minimum of 1.2 (to be shown later), which

suggests that the global/compound stability analysis should

be conducted as required in the two design approaches.

In terms of the internal stability calculations, the FHWA

design approach gives significantly larger maximum rein-

forcement loads and the embedment lengths beyond active

failure line than the NCMA design approach giving larger

pullout capacities. Apart from the different design earth

pressures adopted in these design approaches, the differences

in the calculation models (i.e., the way in which the upper

tier is treated) adopted in the two design approaches may

also be responsible for the discrepancies. Note that the

NCMA and the FHWA design guidelines adopt the

Coulomb and Rankine active earth pressures, respectively.

Such differences may give designers confusion to some

extent in selecting proper reinforcements in terms of

strength. Further study is warranted to fill the gap between

the two design approaches.

4.2 Global Slope Stability Analysis

A series of global slope stability analyses were additionally

performed on the field walls, aiming at examining if the

reinforcement layouts of the walls also satisfy the global

stability requirement. The limit-equilibrium (LE) as well

as the continuum mechanics based slope stability analyses

were performed using, MSEW ver. 1.0 (Leshchinsky 1999)

and Phase2 (Rocscience, 2005), respectively. Note that the

finite element analysis in conjunction with the shear

strength reduction method (Griffths and Lane 1999) was

employed as the continuum mechanics based approach.

Two different approaches were adopted in this study to

see if the two independent types of analyses would yield

similar results so that an acceptable level of confidence

in the results can be afforded. One of the advantages of the

finite element analysis with the shear strength reduction

(FEM-SSR) over traditional limit equilibrium approach is

that no assumption needs to be made a priori regarding

the shape or location of the failure surface.

In the finite element analysis with the shear strength

reduction method (FE-SSR), the factor of safety (FS) of

a slope can be defined as the number by which the original

shear strength parameters must be divided in order to

bring the slope to the point of failure (Griffths and Lane,

1999) so that the factored shear strength parameters (c'f,

'f) can be defined as:

FScc f'' = (1)

(a) LEM, FS=1.05 (b) FE-SSR, FS=0.92

Fig. 4. Global stability analysis : Wall A


FSf'' φφ = (2)

Note here that this definition of FS is the same as that

adopted in the traditional LE methods. When adopting the

shear strength reduction approach, there are several possible

definitions of failure, e.g., non-convergence of the solution

(Zienkiewicz and Talyor, 1989) or acceleration of slope

displacement, etc. Details of the FE-SSR can be found

in Griffths and Lane (1999).

The results of the global stability analyses, in terms

of the minimum factors of safety and the corresponding

failure surfaces, are given in Figures 4~7. The factors of

safety values for each wall are summarized in Table 4.

Note that the LE slope stability analyses were conducted

based on the modified Bishop method. Salient features

that can be observed in these figures are two-fold. First,

for a given wall, the minimum factors of safety computed

by the LE and the FE-SSR analyses are in good agree-

ment, although the factors of safety from the FE-SSR are

somewhat smaller (less than 10%) than those from the

LE approach. Second, the potential failure surfaces from

the two approaches are also similar in shape. These results

demonstrate that the FE-SSR approach can also be effec-

tively used in the global stability analysis of reinforced

earth structures with an acceptable level of confidence.

Another important observation is that for all the walls

investigated, the minimum global factor of safety is smaller

than those of the external stability calculations for the base

sliding and over turning failure modes. Such a trend

implies that the governing failure mechanism in terms of

external stability is the global slope failure for walls in

tiered configuration with an intermediate offset distance.

A global stability check must be performed in addition

(a) LEM, FS=0.96 (b) FE-SSR, FS=0.93

Fig. 5. Global stability analysis : Wall B

(a) LEM, FS=1.01 (b) FE-SSR, FS=0.98

Fig. 6. Global stability analysis : Wall C


to the external stability check when determining the

reinforcement lengths.

4.5 Reinforcement Distribution to Meet Global Stability

Requirement

Another series of global stability analyses were performed

to determine the reinforcement distributions that meet the

global stability requirement, taking the required minimum

factor of safety as FSmin = 1.20. The results are given

in Table 5 and Figure 8.

The results indicate that both the upper and lower tier

reinforcement lengths need to be increased as great as

by 50% to meet the global stability requirement. The

results also show that the lower and upper parts of the

upper and lower tiers, respectively, require much longer

reinforcement lengths than those satisfying the external

stability. Such a trend stresses that the global stability

analysis is not an option but a requirement when

designing GR-SRWs in tiered configuration with an

intermediate offset distance. Another important observation

is that the revised reinforcement lengths for the upper tiers

in all walls are significantly longer than those required

by the design guideline in which the upper tier is designed

as an independent wall. The fact that both tiers’ reinforce-

ment lengths need to be increased to ensure the global

stability requirement suggests that the interaction between

the upper and lower tiers can be explicitly accounted for

by performing the global stability analysis.

5. Summary and Conclusions

This paper presents the results of stability analyses on

geosynthetic reinforced segmental retaining walls in tiered

(a) LEM, FS=0.90 (b) FE-SSR, FS=0.82

Fig. 7. Global stability analysis : Wall D

Table 4. Summary of global stability analysis

Factor of Safety

Wall A Wall B Wall C Wall D

LE 1.05 0.96 1.01 0.90

FEM-SSR 0.92 0.93 0.98 0.82

Table 5. Summary of revised reinforcement lengths to meet global stability

WallOffset distance

D (m)

FSReinforcement length (m)

Lower tier (L1) Upper tier (L2)

as-designed1

revised as-designed revised2

as designed revised2

A 2.5(0.34H) 0.92 1.20 4.9(0.55H) 7(0.80H) 3.5(0.65H2) 6(1.11H2)

B 2.5(0.23H) 0.93 1.20 5.3(0.50H) 8(0.76H) 3.8(0.68H2) 6(1.07H2)

C 5.0(0.40H) 0.98 1.20 7.0(0.56H) 12(0.97H) 5.0(1.13H2) 7(1.49H2)

D 2.0(0.45H) 0.82 1.26 1.6(0.35H) 3(0.65H) 1.6(0.73H2) 2(0.91H2)

Note)1based on FE-SSR;

2maximum length


configuration. Four design cases of walls with different

geometries and offset distances were considered. Based

on the results of stability analyses using the FHWA and

NCMA design guidelines, the discrepancies between the

two different guidelines were identified. A series of global

slope stability analyses were conducted using the limit-

equilibrium analysis and the continuum mechanics based

shear strength reduction method aiming at investigating

governing mode of failure for walls with an intermediate

offset distance.

The results indicated among other things that the FHWA

design approach yields conservative results both in the

external and internal stability calculations, i.e, lower factors

of safety, than the NCMA design approach. In addition

to the different design earth pressures, the differences in

the calculation models (i.e., the way in which the upper

tier is treated) adopted in the two design approaches may

also be responsible for the discrepancies. Also found is

that required reinforcement lengths are usually governed

by the global slope stability requirement rather than the

external stability calculations, thus demonstrating the global

stability analysis should be part of design calculations in

addition to the internal and external stability checks. It

is shown that when considering the global stability

requirement, the required reinforcement lengths for the

upper tiers are much longer than those based on the

10T L=6.0M

10T L=6.0M

10T L=6.0M

8T L=7.0M

8T L=7.0M

8T L=4.0M

8T L=6.0M

8T L=5.0M

8T L=5.0M

6T L=4.0M

6T L=5.0M

6T L=4.0M

6T L=4.0M

2500

1:0.12

800

3400

5000

87

q=1.0 ton/m2

PG 6T H=0.2 L=6.0M

PG 10T H=0.8 L=6.0M

PG 10T H=1.4 L=6.0M

PG 10T H=2.0 L=6.0M

PG 6T H=2.6 L=8.0M

PG 6T H=3.2 L=8.0M

PG 6T H=4.0 L=8.0MPG 6T H=4.8 L=8.0M

PG 6T H=0.2 L=6.0M

PG 6T H=1.0 L=6.0M

PG 6T H=1.6 L=6.0M

PG 6T H=2.4 L=5.0M

PG 6T H=3.2 L=5.0M

PG 6T H=4.0 L=5.0M

PG 6T H=4.8 L=5.0M

5000

500

5100

400

2500

q=13.0kN/m2

q=100.0kN/m2

속채움 잡석구간

유공관 150φ

(a) Wall A (FS=1.20) (b) Wall B (FS=1.20)

L1 TYPE3 H=0.6M L=10.0ML1 TYPE3 H=1.2M L=10.0ML1 TYPE3 H=1.8M L=10.0ML1 TYPE2 H=2.4M L=10.0ML1 TYPE2 H=3.0M L=10.0ML1 TYPE2 H=3.6M L=10.0ML2 TYPE2 H=4.2M L=10.0ML2 TYPE2 H=4.8M L=10.0ML2 TYPE2 H=5.6M L=12.0M

L2 TYPE1 H=6.4M L=12.0M

L2 TYPE1 H=7.2M L=12.0M

L3 TYPE1 H=7.8/8.0/8.2M L=12.0ML1 TYPE1 H=0.6M L=7.0ML1 TYPE1 H=1.2M L=7.0ML1 TYPE1 H=1.8M L=7.0M

L1 TYPE1 H=3.8M L=7.0M

L1 TYPE1 H=3.0M L=7.0ML1 TYPE1 H=2.4M L=7.0M

1

8

18

400

4000

8000

2000

30050

0

2800

1240

0

6000 500 6850

650

2000

2000

4650

G.L

F.L

2000





(c) Wall C (FS=1.20) (d) Wall D (FS=1.26)

Note) All numbers are in ‘mm’ unless otherwise indicated.

Fig. 8. Reinforcement distributions to meet global stability requirement


current design guidelines in which the upper tier is treated

as an independent wall. These results warrant that a global

stability based design approach needs to be developed for

geosynthetic reinforced segmental retaining walls in tiered

configuration.

Acknowledgements

This work was supported by Grant No. R01-2004-000-

10953-0 from the Basic Research Program of the Korea

Science & Engineering Foundation and by Korea Ministry

of Construction and Transportation under Grant No.

C06A0300-01511.The financial supports are gratefully

acknowledged.

References

1. Collin, J. (1997), “Design Manual for Segmental Retaining Walls”,2nd Ed. 1997, National Concrete Masonry Association (NCMA),Virginia, USA.

2. Elias, V. and Christopher, B.R. (1997), “Mechanically StabilizedEarth Walls and Reinforced Soil Slopes, Design and ConstructionGuidelines”, FHWA Demonstration Project 82, FHWA, Washington,DC, FHWA-SA-96-071.

3. Lee, K.Z.Z. and Wu, J.T.H. (2004), “A synthesis of case historieson GRS bridge-supporting strucutres with flexible facing”, Geotextileand Geomembranes, 22(4), 181-204.

4. Leshchinsky, D. (1999), Putting Technology to Work: MSEW andReSlope for Reinforced Soil-Structure Design. Geotechnical FabricsReport, Vol.18, pp.34-39.

5. Leshchinsky, D. and Han, J. (2004), “Geosynthetic ReinforcedMultitiered Walls”, J. of Geotech. and Geoenvir. Engrg, ASCE,Vol.230, No.12, pp.1225-1235.

6. Yoo, C. (2003), “Instrumentation of Geosynthetic ReinforcedSegmental Retaining Wall in a Tiered Configuration”, InternalReport, Sungkyunkwan University.

7. Yoo, C. and Kim, J.S. (2002), Behavior of Soil-ReinforcedSegmental Retaining Walls in Tiered Arrangement. Journal ofKorean Geotechical Society, KSGE, Vol.18, No.3, pp.61-72.

8. Yoo, C. and Jung, H.S. (2004), “Measured behavior of a geosynthetic-reinforced segmental retaining wall in a tiered configuration”,Geotextiles and Geomembranes, Vol.22, No.5, pp. 359-376.

9. Yoo, C. and Kim, S.B. (2006), “A Comparative Study on Designof Geosynthetic Reinforced Modular Block Wall in TieredArrangement”, Proceedings of 8th International Conference onGeosynthetics, Yokohama, Japan, in-print.

10. Yoo, C., Jung, H.Y., and Song, A.R. (2005), “Numerical Investigationon Behavior of Geosynthetic Reinforced Modular Block Walls ina Tiered Arrangement”, Journal of Korean Geotechnical Society,21(10):1-12.

11. Yoo, C. and Song, A.R. (2006), “Effect of foundation yielding onperformance of two-tier geosynthetic reinforced segmental retainingwalls A numerical investigation”,– Geosynthetics International,20(30): 110-120.

12. Griffiths, D.V. and Lane, P.A. (1999), “Slope stability analysis byfinite elements”, Géotechnique 49, No.3, 387-403.

13. Rocscience Inc. (2005), Phase2 v6.0 Two dimensional finite elementslope stability analysis.

14. Zienkiewicz, O.C. and Taylor, R.L. (1989), “The finite elementmethod”, Vol.1, 4th edition. London, New York, McGraw-Hill.

(received on Jul. 24, 2008, accepted on Sep. 26, 2008)

Prediction and Assessment on Consolidation Settlement for Soft Ground by Hydraulic Fill 33

Prediction and Assessment on Consolidation Settlement forSoft Ground by Hydraulic Fill

준설매립 연약지반에 대한 압밀침하 예측 및 평가

Jeon, Je-Sung1전 제 성

Koo, Ja-Kap2구 자 갑

Oh, Jeong-Tae3오 정 태

요 지

본연구에서는해안준설매립지반에대한연약지반개량사례를이용하여연직배수공법적용시의현장계측및압밀침

하해석을실시하였다 대상현장은원지반위에대략 의준설매립을통해조성된부지로서고함수비및고압축성의. 10m

해성점토로구성되어있다 년동안의현장계측결과 당초설계시의예측침하량에비해매우큰압밀침하가발생하였. 1 ,

고 이 조건에서의 향후 침하거동을 예측하기 위한 추가 압밀침하 해석 및 계측결과를 이용한 역해석을 실시하였다, .

상부시공 영향 등에 의해 준설매립지반에는 과다한 전단변형이 발생하였으며 이에 대한 현장 계측결과의 평가 및,

보정을실시하였다 압밀해석및원지반조건을평가하기위해실내시험결과를이용한물질함수분석을실시하였으며. ,

최종적으로부지인도후의잔류침하량및최종지반고를만족시키기위한추가성토고를산정하였다 추가성토이후의.

현장 계측결과와 당초 예측했던 압밀침하 거동을 비교하였으며 이를 통해 당초 예측내용에 대한 검증을 수행할 수,

있었다.

Abstract

This paper describes the performance of ground improvement project using prefabricated vertical drains of condition,

in which approximately 10 m dredged fill overlies original soft foundation layer in the coastal area composed of soft

marine clay with high water content and high compressibility. From field monitoring results, excessive ground settlement

compared with predicted settlement in design stage developed during the following one year. In order to predict the

final consolidation behavior, recalculation of consolidation settlements and back analysis using observed settlements were

conducted. Field monitoring results of surface settlements were evaluated, and then corrected because large shear

deformation occurred by construction events in the early stages of consolidation. To predict the consolidation behavior,

material functions and in-situ conditions from laboratory consolidation test were re-analyzed. Using these results, height

of additional embankment is estimated to satisfy residual settlement limit and maintain an adequate ground elevation.

The recalculated time-settlement curve has been compared with field monitoring results after additional surcharge was

applied. It might be used for verification of recalculated results.

Keywords : Consolidation analysis, Consolidation settlement, Dredged fill, Marine clay, Settlement monitoring

1 Member, Principal Researcher, KIWE, Korea Water Resources Corporation, [email protected], Corresponding Author2 Member, Prof., Dept. of Civil Eng., Hankyong National University3 Member, Construction Team Manager., Yeosu Regional Office, Korea Water Resources Corporation



1. Introduction

Increasing national necessity for expansion of industrial

site together with a general decrease in the number of

available areas have created the need for landfills using

fine-grained material dredged from the coastal area near.

For the construction of national industrial complexes, a

large scale reclamation and ground improvement project

involving about 20 million square m of soft ground

improvement has been under way on the south coast area

in Korea.

Land reclamation on the foreshore of existing coastlines

often overlies soft clays which require soil improvement

to ensure stability during and after construction and to

reduce or eliminate undesirable short and long term

settlement (Choa et al., 2001). The project is the case of

landfills on soft marine clay in the coastal area of Yeosu,

southern Korea, and involves ground improvement using

prefabricated vertical drains and surcharge. The consoli-

dation settlement of not only the surface reclamation layer

but also the original soft clay layer underneath has been

continuously measured since the beginning of the work.

The predicted results in design stage using various labora-

tory data are compared with the observed ones considering

construction effects, such as heaving and displacement,

caused by additional works near. From the field monitoring

results, excessive ground settlement has been developed

and compared with the value in design stage. This is a

serious issue for this project, in which the transfer date

of final improved is limited for further construction of

industrial facilities. In this study, the magnitude and the

rate of the consolidation settlement were reassessed by

back analysis of the observed settlement, and results from

laboratory consolidation test.

2. Improving Soft Ground

2.1 The Site and Ground Condition

The site for the study is located in the Yeosu national

industrial complexes project in Korea. The project com-

prises land reclamation and ground improvement works

to allow for the future construction of advanced chemical

and heavy industry complex. Land reclamation works

which involved the hydraulic placement up to 20 m of

soft marine clay for the formation of 7.8 km2 land has

been conducted from 1996 to 2003 on the original soft

ground. The ground consists of upper dredged fill which

contained very soft marine clay, up to 10 m in thickness,

having high compressibility and high moisture content and

lower original clay layer of 3-10 m thickness. The areas

for project were divided into 4 sections, and each section

was divided into appropriate blocks for efficient con-

struction. For block 3 in section 1, ground improvement

by vertical drain in combination with up to 3.5 m

thickness of surcharge commenced from September, 2006

is in progress after hydraulic filling of 8,300×103 m3 of

slurry completed in Dec. 2003.

2.2 Vertical Drains with Preloading

The use of prefabricated vertical drain with preloading

was considered in this project to accelerate the rate of

consolidation and to minimize future settlement of the

treated area under future load.

Construction procedure for improving soft ground is

shown in Fig. 2. Geotextile of PET mat was spread out

on the soft ground to get construction capability caused

by very low shear strength. With the same reason, rubble

mat of 0.8 m height was spread out using conveyer system.

Generally, the ground improvement works are carried out

in such a way that a specified degree of primary con-

solidation is attained within the desired time by improving

The South Sea

SEC. 1SEC. 2SEC. 3

Block 3The South Sea

SEC. 1SEC. 2SEC. 3

Block 3

Fig. 1. The site of national industrial complexes project


the soil drainage system. It should be required to satisfy

final ground level pre-designed for industrial facilities

after site transfer, and to limit residual consolidation set-

tlement within 10~30 cm in this project. It corresponds

to requirement of site transfer to client companies which

have plans to construct industrial facilities. The main

variables in design stage are the magnitude of preloading,

the spacing of vertical drains, the duration of preloading,

and the consolidation parameters of soft marine clay.

Prefabricated vertical drains in a width 10 cm were

installed at 0.8~1.5 m square spacing depending on the

duration of the preloading period. Preloading was subse-

quently placed to the design height of 2.35~3.5 m for 8~12

month after surcharge placement. In design stage, the

consolidation settlement that the requirements for site

transfer can be satisfied was expected to develop during

8~12 month. However, there was a great difference be-

tween the design value and estimated results from the field

monitoring.

2.3 Field Monitoring

In order to monitor the performance of ground

improvement and to verify the original design for

improving soft ground, several geotechnical instruments

were installed to monitor the degree of consolidation and

final settlement. The surface settlement plates were install-

ed just before the installation of vertical drain on the

geotextile to ensure construction capability. The multilevel

settlement gauges and piezometers were installed at various

levels in order to monitor the settlement of various sub-

layers and pore pressure dissipation.

Surface settlement and pore pressure were monitored

at close intervals of 1~3 days during the first three months,

and at the wider intervals of 7~10 days during the later

part of monitoring. Fig. 3 shows the surface settlement

results of P1-2-4, P1-2-5, and P1-2-6 together with the

construction activities. These three surface settlement

plates were installed in a typical zone with a space of

25 m in order to verify each result by cross review. As

shown in Fig. 3, surface settlement of each point shows

big differences due to construction events in which large

shear deformation may occur by installation of PVD and

continuous embankment in the early stages of consolidation.

However, from results after 33 days of PVD installation,

PET Mat-2(15TON)

Embankment-1 ( Rubble Mat for horizontal drainage) 0.80m(0.3+0.5m)

PET Mat-1(20TON)

Embankment-2

Installation of PVD

0.70m(0.4+0.3m)

0.85m

Embankment-3

(a) Spread PET Mat-1 (20T) (b) Rubble Mat-1, 0.8 m

(c) Spread PET Mat-2 (15T) (d) Embankment-2, 0.7 m

(e) Installation of PVD (f) Embankment-3, 0.85 m

Fig. 2. Construction procedure for improving soft ground

-100

0

100

200

300

400

5000 50 100 150 200 250 300 350 400

Elapsed Time (day)

Set

tlem

ent

(cm

)

P1-2-4

P1-2-5

P1-2-6

2006.09.11Instruments installation

06.09.14~09.18Embankment 1Final H=0.8m

06.11.02Installation of

PVD

06.11.20Embankment 3Final H=2.35m

06.09.30~10.16Embankment 2Final H=1.5m

Fig. 3. Monitoring results of surface settlement for zone-1


surface settlements of three points show a good agreement

as shown in Fig. 4. It is important to note that settlement

up to the present has developed over 4.5 m although

ultimate consolidation settlement in design stage was

predicted as about 3.0 m at zone-1. These disagreements

between predicted consolidation settlement in design and

monitored results made big trouble for this project, in

which the transfer date of final improved site is limited

for further construction of industrial facilities.

Fig. 5 shows results of consolidation settlements on

surface with surcharge period of 250 days for zone-2.

Monitoring period of zone-2 after installation of PVD and

continuous embankment is under 3 months. For zone-2,

field monitoring results of surface settlement could not

be used for the prediction of consolidation behavior and

ultimate settlement.

3. Characteristics of the Marine Clay

3.1 Sampling Methods

The most important thing when unexpected excessive

settlement developed was to take a proper step for pre-

dicting ultimate consolidation settlement. It was required

to investigate consolidation parameters and material func-

tion by laboratory (Yoo, 2007) and in situ tests.

Undisturbed samples were taken from lower original

clay layer of 3-10 m thickness. All samples were carefully

sealed on site immediately after sampling. The fresh sam-

ples were carefully wire trimmed into specimens for testing

in the laboratory. For the upper dredged fill up to 10 m,

retrieval of undisturbed sample was impossible because

fill material of marine clay was in the state of slurry with

high moisture content up to 150%. Disturbed clays were

taken from field and remolded samples for laboratory tests

were made by large consolidation apparatus under certain

effective stress.

3.2 Soil Properties

In accordance with KS standards, natural unit weight,

specific gravity, grain size distribution, and Atterberg

limits of marine clay at Yeosu were determined as shown

in Table 1. For upper layer of dredged fill, test results

of disturbed sample taken from in-situ show that average

values of the specific gravity, liquid limit and plasticity

index are 2.72, 86.3% and 56.5, respectively. Maximum

natural water content which is determined by disturbed

clay of SPT sampler is 117.9%. For lower layer of original

0

100

200

300

4000 30 60 90 120 150 180 210 240 270 300

Elapsed Time (day)

Set

tlem

ent

(cm

)

P1-2-4

P1-2-5

P1-2-6

Zero reading time : 2006.12.05

- 33 days have elapsed since installation of PVD

- 15 days have elapsed since final embankment

Fig. 4. Monitoring results after zero reading for zone-1

-200

-150

-100

-50

0

50

1000 50 100 150 200 250 300

Elapsed Time (day)

Set

tlem

ent

(cm

)

P2-28

P2-29

P2-30

07.01.05Instrument installation

(P2-29)


(P2-28)


(P2-30)

Final EmbankmentH = 3.0m

Fig. 5. Monitoring results of surface settlement for zone-2

(a) preparation of clay slurry (b) setup consolidation apparatus

(c) consolidation (d) sampling for laboratory tests

Fig. 6. Remolded sample of disturbed clays taken from dredged

fill (Yoo, 2007)


marine clay, laboratory tests were conducted using undis-

turbed sample.

3.3 Consolidation Parameters

The preconsolidation pressure, the compression index,

vertical coefficient of consolidation and permeability were

determined by conventional oedometer tests as well as

150 mm diameter CRS (Constant Rate of Strain) tests using

both undisturbed and remolded samples. With the use of

vertical drain, the horizontal coefficient of consolidation

becomes one of the most important consolidation pa-

rameters. Laboratory tests with 60 mm, 100 mm, 150 mm

diameter were also performed to measure coefficient of

consolidation in horizontal direction, . In-situ test,

conepenetrometer dissipation tests (CPTu) were used to

measure as well as pore water pressure. Results of

consolidation parameters are shown in Table 2.

3.4 Material Function

The most important parameters governing the primary

consolidation calculations are the void ratio-effective stress

and void ratio-coefficient of permeability relationships

obtained from laboratory consolidation tests (Stark et al.,

2005).

Cargill (1985) and Poindexter (1988) describe the rec-

ommended laboratory testing procedure to obtain these

relationships. These relationships may be used to assess

initial effective stress at each sub-layer for consolidation

calculation and coefficient of consolidation at each effec-

tive stress. Defining these relationships from low effective

stress level requires two different laboratory consolidation

tests of self-weight consolidation and conventional oedo-

meter. Stark et al. (2005) used results of self-weight con-

solidation test to find the void ratio-effective stress and

void ratio-permeability relationships at effective stresses

less than about 0.96 kPa. Also, results of conventional

oedometer test were used to find the void ratio-effective

stress and void ratio-permeability relationships at effective

stresses greater than about 0.96 kPa. In this research, con-

ventional oedometer, Rowe cell and CRS tests were per-

formed for these relationships.

Fig. 7 presents the void ratio-effective stress and void

ratio-permeability relationship measured using self-weight

Table 1. Soil properties of marine clay

Soil properties

Upper dredged fill layer

(remolded sample except for

water content)

Lower original clay layer

(undisturbed soil)

Min. Max. Min. Max.

Natural water content (%) 88.1 117.9 65.1 82.5

Passing No.200 sieve (%) 95.8 99.9 97.9 99.1

Specific gravity 2.71 2.73 2.70 2.73

Liquid limits (%) 76.3 96.2 54.5 88.9

Plasticity index 50.8 62.2 31.9 60.3

USCS CH CH

Table 2. Consolidation parameters of marine clay

Soil properties

Upper dredged fill layer

(remolded sample)

Lower original clay layer

(undisturbed soil)

Min. Max. Min. Max.

Initial void ratio, eo 2.3 2.9 1.6 2.3

Compression index, cc 0.83 1.22 0.79 1.07

Vertical coefficient of consolidation,

cv(cm2/s)

5.0E-04 9.2E-04 3.0E-04 3.5E-04

Horizontal coefficient of consolidation,

ch(cm2/s)

6.0E-04 9.7E-04 4.6E-04 6.5E-04


consolidation and typical oedomenter tests for 19 dredged

material types from 17 placement sites (Stark et al., 2005)

Fig. 8 presents material function for void ratio-effective

stress and void ratio-permeability from Lab. tests in this

study. For void ratio-effective stress relationship, material

function shows a good agreement with empirical rela-

tionship of high void ratio, e > 2.3. A series of results

that describe effective stress and permeability with void

ratio less than 2.3 show difference of a considerable margin.

4. Prediction of Consolidation

As mentioned above, settlement after 350 days has de-

veloped over 4.5 m although ultimate consolidation set-

tlement in design stage was predicted as about 3.0 m at

zone-1. These disagreements between predicted consoli-

dation settlement in design and monitored results made

big trouble for this project, in which the transfer date of

final improved site is limited for further construction of

industrial facilities. In this particular situation, overriding

concern was to predict the consolidation settlement with

time including magnitude of ultimate settlement.

In conventional consolidation theory, strains are assumed

to be small or in a mathematical sense, infinitesimal

(Gibson et al., 1981; Mesri et al., 1974).

This is a background to use constant coefficient of

compressibility, and the coefficient of volume compress-

ibility, when calculating consolidation settlement. Pri-

mary consolidation settlements in design stage of this

project were calculated by . However, this method has

limitations for considering large strain problem associated

with a great change of effective stress because of its

nonlinear stress-strain relationship (Gibson et al., 1981;

Terzaghi et al., 1996).

The primary consolidation settlements of upper dredged

fill and original clay layer were recalculated using com-

0

2

4

6

8

10

12

14

1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03

Effective Stress(kPa)

Voi

d R

atio

New Haven(PI=68) Port Authority(PI=65)

Lower Passaic(PI=63) Port Elizabeth(PI=49)

Stamford(PI=46) Red Hook(PI=43)

Duwamish(PI=39) PI=40 (relationship)

PI=50 (relationship) PI=60 (relationship)

PI=70 (relationship)

PI=40PI=50 PI=60

PI=70

0

2

4

6

8

10

12

14

1.0E-10 1.0E-09 1.0E-08 1.0E-07 1.0E-06 1.0E-05 1.0E-04

Permeability(m/s)

Voi

d R

atio

New Haven(PI=68)

Port Authority(PI=65)

Lower Passaic(PI=63)

Port Elizabeth(PI=49)

Stamford(PI=46)

Red Hook(PI=43)

Duwamish(PI=39)





PI=70

PI=60

PI=50

PI=40

Fig. 7. Void ratio-effective stress and void ratio-permeability

relationship for inorganic clays of high plasticity (Stark et

al., 2005)

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0001 0.001 0.01 0.1 1 10 100Vertical effective stress (kgf/cm2)

Voi

d r

atio

, e

Zone-1 (No.1) Zone-1 (No.2)



Zone-2 (CRS)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

1.0E-9 1.0E-8 1.0E-7 1.0E-6 1.0E-5 1.0E-4

Permeability, k (cm/sec)

Voi

d ra

tio,

e




Zone-2 (CRS)

Fig. 8. Void ratio-effective stress and void ratio-permeability

relationship from Lab. tests


pression index, . Initial effective stresses of sub-layers

were estimated from both void ratio-effective stress rela-

tionship and natural water content-void ratio relationship.

The magnitude of settlement was calculated on several

subdivided layers in order to be able to predict the ultimate

settlement accurately. The and values basically were

derived from material function of laboratory tests, and

different values were applied to calculation by effective

stress level.

Field monitoring results gave a good agreement with

time-settlement relationship although it shows fluctuation

in initial part caused by shear deformation with upper

construction activities. At first, consolidation settlement

with time was recalculated using material function from

Lab. tests. There were a some differences between recal-

culated value and real field monitoring results during 350

days. The back analysis was conducted by modifying

material function until recalculated curve fits to field

monitoring results. The recalculated and monitored

surface settlements for zone-1 are shown in Fig. 9.

Major contract terms for site transfer in this project are

that residual settlement after site transfer should be less

than 10 cm, and final ground elevation should be the same

as the original design value. For satisfying ground elevation

in design stage, additional surcharge was required to

compensate excess ground settlement.

However, additional surcharge may act as an external

load, and this may give rise to more settlement. In

instances when it appears that too much consolidation

settlement is likely to occur, it may be desirable to apply

some additional surcharge loading in order to eliminate

or reduce the post-construction settlement. It was important

to estimate how much additional surcharge was required

to satisfy all contract terms for site transfer. Essential facts

related with estimation of settlement, such as settlement

history, final ground elevation, date of site transfer, load

condition after completion, and allowable residual

settlement, were considered carefully. Fig. 10 shows the

consolidation settlement with time in case of applying

additional surcharge at time elapse of 429 days. The

additional surcharge with the height of 3.2 m was applied

for satisfying residual settlement limit and final ground

level.

The recalculated time-settlement curve shown in Fig. 9

has been compared with field monitoring results from 85

to 350 days. Fig. 11 includes some monitored results after

additional surcharge with the height of 3.2 m was applied.

It might be used for verification of recalculated results.

0.0

1.0

2.0

3.0

4.0

5.0

6.00 50 100 150 200 250 300 350 400

Elapsed Time (day)

Set

tlem

ent

(m)

Prediction of settlement

Monitoring relusts - Part1

Field monitoring resultsfor assessment

2006.09.11 2006.12.20 2007.03.30 2007.07.08 2007.10.16 2008.01.24 2008.05.03

2006.11.02Installation of PVD

Fig. 9. Recalculated and monitored time-settlement curve for

zone-1

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.00 100 200 300 400 500 600 700

Elapsed Time (day)

Set

tlem

ent

(m)

No additional surchargeSurcharge h=1.0mSurcharge h=2.0mSurcharge h=3.0m

Embankment H=2.35m

Additional Surcharge

Fig. 10. Prediction of time-settlement for each surcharge height

0.0

1.0

2.0

3.0

4.0

5.0

6.00 100 200 300 400 500 600 700

Elapsed Time (day)

Set

tlem

ent

(m)

Prediction of settlement



2006.11.02Installation of PVD

Field monitoring resultsfor assessment

Field monitoring resultsfor verification

2006.09.11 2006.12.20 2007.03.30 2007.07.08 2007.10.16 2008.01.24 2008.05.03

Fig. 11. Additional field monitored time-settlement curve for

zone-1


5. Conclusion

The project of landfills on soft marine clay including

ground improvement using prefabricated vertical drains

and surcharge was carried out on the foreshore of southern

Korea where a significant thickness of highly compressible

soils existed on the seabed. Ground improvement works

were required for both upper dredged fill layer and lower

seabed soils. Excessive settlements, which could not be

expected in design stage have been developed. It was

required to reassess monitoring results because it showed

large fluctuations in magnitude of settlement due to shear

deformation. The material functions related to consolidation

and permeability characteristics of the marine clay were

investigated from laboratory and in situ tests. Application

of different consolidation parameter by effective stress

level from material function gives a good result for

prediction of settlements with time for very soft marine

clay.

The primary consolidation settlements with time of

upper dredged fill and original clay layer were recal-

culated, and the back analysis was conducted by modifying

material function until recalculated curve fits to field mon-

itoring results. Method of additional surcharge loading

was adapted as a technical measure to reduce the post

construction settlement, and speed up consolidation

process before site transfer. Amount of additional surcharge

loading was evaluated carefully in consideration of final

ground elevation, date of site transfer, and allowable

residual settlement.

References

1. Arulrajah, A, Nikraz, H, and Bo, M.W. (2004), “Observational methodof assessing improvement of marine clay”, Ground Improvement,Vol.8, No.4, pp.151-169.

2. Cargill, K.W. (1984), “Prediction of Consolidation of Very Soft Soil”,J of Geotechnical Engineering, ASCE, Vol.110, No.6, pp.775-795.

3. Cargill, K.W. (1985), Mathematical model of the consolidation/desiccation processes in dredged material, Technical Rep. D-85-4,U.S. Army Engineering Waterways Experiment Station.

4. Choa, V, Bo, M.W., and Chu, J (2001), “Soil improvement worksfor Changi East Reclamation Project”, Ground Improvement, Vol.5,No.4, pp.141-153.

5. Chu, J, Bo, M.W., Chang, M.F., and Choa, V (2002), “Consolidationand Permeability Properties of Singapore Marine Clay”, J Geotech-nical and Geoenvironmental Engineering, Vol.128, No.9, pp.724-732.

6. Cousens, T.W., and Stewart, D.I. (2003), “Behavior of a trialembankment on hydraulically placed pfa”, Engineering Geology,Vol.70, pp.293-303.

7. Gibson, R.E., Schiffman, R.L. and Cargill K.W. (1981), “The Theoryof One-dimensional Consolidation of Saturated Clays II. FiniteNonlinear Consolidation of Thick Homomgeneous Layers”, CanadianGeotechnical Journal, Vol.18, pp.280-293.

8. Hansbo, S. (1981), “Consolidation of fine-grained soils by prefab-ricated drains”, 10th Int Conf Soil Mechanics and Found Engineering,Stockholm, Sweden, Vol.3, pp.677-682.

9. Mesri, G., and Rokhsar, A. (1974), “Theory of Consolidation forClays”, Journal of the Geotechnical Engineering Division, ASCE,Vol.100, No.GT8, pp.889-904.

10. Poindexter, M.E. (1988), Behavior of subaqueous sediment mounds:Effect on dredged material disposal site capacity, Ph.D. Thesis,Texas A&M Univ., College Station, Tex.

11. Stark, T.D., Choi, H., and Schroeder, P.R. (2005), “Settlement ofDredged and Contaminated Material Placement Areas. II: PrimaryConsolidation, Secondary Compression, and Desiccation of DredgedFill Input Parameters”, J Waterway, port, coastal, and ocean engi-neering, Vol.131, No.2, pp.52-61.

12. Tan, S.A. (1993). “Ultimate Settlement by Hyperbolic Plot for Clayswith Vertical Drains”, J Geotechnical Engineering, Vol.119, No.5,pp.950-956.

13. Terzaghi, K, Peck, R.B., and Mesri, G. (1996), Soil Mechanics inEngineering Practice, 3nd Edition, John Wiley & Sons, New York,pp.71-121.

14. Yoo, N.J. (2007), Consolidation Characteristics of Dredged FillMaterial Including Centrifuge Test, Research Rep., KSCE, pp.1-117.

(received on Aug. 22, 2008, accepted on Sep. 17, 2008)

A Graphical Method for Evaluation of Stages in Shrinkage Cracking Using S-shape Curve Model 41

A Graphical Method for Evaluation of Stages in Shrinkage CrackingUsing S-shape Curve Model

형 곡선 모델을 적용한 수축 균열 단계 평가S

Min, Tuk-Ki1민 덕 기

Vo Dai Nhat2보 다이 낫

요 지

본 연구에서는 수축균열 단계를 나타낼 수 있는 도해적인 방법을 제안하였다 우선 발생된 균열들을 균열.폭의크기순서대로나열하여균열분포를구하였다 다음에균열폭을정규화하여 에서 사이의값으로나타내었. 0 1다 마지막으로 와 와 이 제안한바 있는 형 곡선. Brooks Corey(1964), Fredlund Xing(1994), van Genuchten(1980) S모델에 실험 결과를 적용시켰다 분석 결과 의 식이 와 식보다 정확도가 크게 높은. van Genuchten Brooks Corey것으로 나타났으며 와 식보다도 높게 나타나 의 식을 적용하였다 결과적으로 수축, Fredlund Xing van Genuchten .균열의 단계는 정규화된 균열폭 분포가 개의 직선부로 나누이는 도해적인 방법으로 나타낼 수 있었다 제안된3 .방법의적용성을보기위해시료의두께에변화를주며시험을실시하였다 측정된데이터를제안된모델에적용하.여본 결과높은 상관성을보여 주었다 따라서수축 균열은 초기수축단계 이차수축단계그리고잔류수축단계의. ,단계로 모사할 수 있었다 또한 각 단계에서의 균열 폭의 범위를 제시하였다3 . .

Abstract

The aim of this study is to present a graphical method in order to evaluate stages in shrinkage cracking. Firstly,the distribution of crack openings is established by sorting the openings of individual cracks in the soil crackingsystem. Secondly, it is normalized in a range of 0 to 1 to obtain the normalized crack opening distribution. Thirdly,three S-shape curve models introduced by Brooks and Corey (1964), Fredlund and Xing (1994) and van Genuchten(1980) are chosen to fit the normalized crack opening distribution using a curve fitting method. The accuracy offitting which is described through fitting parameters by the van Genuchten equation is much higher than that bythe Brooks and Corey equation and slightly higher than that by the Fredlund and Xing equation; thus the vanGenuchten model is used. Finally, the stages of shrinkage cracking are graphically evaluated by drawing three separatestraight lines corresponding to three linear parts of the fitted normalized crack opening distribution. The proposedmethod is tested with different sample thicknesses. The measured data are fitted by the selected model with thefairly high regression coefficient and small root mean square error. The results show graphically that shrinkagecracking comprises three stages; namely, primary, secondary and residual stages. Subsequently, the ranges of evaluatedcrack opening for each of these stages are presented.

Keywords : Curve fitting method, Fitting parameters, Graphical method, Normalized crack opening distribution,

Shrinkage cracking stages, S-shape curve

1 Member, Prof. Dept. of Civil & Environ. Engrg., Univ. of Ulsan., [email protected], Corresponding Author2 Researcher, Dept. of Civil & Environ. Engrg., Univ. of Ulsan

Jour. of the KGS, Vol. 24, No. 9. September 2008, pp. 41 48～ Technical Note


1. Introduction

Soil cracking has been the subject of investigation formany years since it is a natural phenomenon andfrequently observed in many natural and man-madestructures such as buildings, dams, etc. Analysis methodsfor soil cracking during drying have been introduced anddeveloped based on (i) elasticity theory, (ii) transitionbetween tensile and shear failure, and (iii) linear elasticfracture mechanics (Morris et al., 1993). A numerical andphenomenological study has been based on the linearhygro-elasticity (Hu et al., 2006). Several theoreticalproblems and challenges have been summarized andintroduced by Fredlund (2006). Subsequently, manyresearchers have attempted to study the criteria ofshrinkage cracking (Horgan and Young, 2000; Kodikaraet al., 2000; Konrad and Ayad, 1997; Lecocq andVandewalle, 2003; Mal et al., 2005; Min and Vo-Dai,2007; Peng et al., 2006; Tay et al., 2001; Velde, 1999;Velde, 2001; Vogel et al., 2005; Wijeyesekera andPapadopoulou, 2001; Yesiller et al., 2000). As waterevaporates from the soil surface, the tensile stressdevelops in the soil system. The soil tends to crack whenthe tensile stress exceeds the tensile strength. Theyreported that cracking of clay generally depends onexperiment conditions such as base material, soil density,the desiccation rate, and thickness of the sample.Conditions that govern the characteristics of soil crackingmay be categorized as two separate terms: extrinsic andintrinsic conditions (Wijeyesekera and Papadopoulou,2001). Extrinsic conditions include fundamentally thetemperature, relative humidity, and wind velocity whereasmoisture condition, structure of material, degree ofpacking, physical and chemical composition, etc. belongto intrinsic conditions.

Furthermore, soil cracking also influenced soil structure

and behavior (Kodikara et al., 1999); volumetric shrinkage

strain, compaction water content and hydraulic con-

ductivity (Albrecht and Benson, 2001); and water infiltration

(Liu et al., 2004). The results showed that cracking led

to a considerable increase of hydraulic conductivity.

However, the development of soil cracking has been

known as a complex process consisting of several stages.

Thus it is important to understand the behavior of soil

in the cracking process characterized by how many stages

it includes. There are many different ways to describe

evaluation of stages in soil cracking. In this study, we

propose a graphical method to evaluate the stages of

shrinkage cracking for Kaolinite clay using a S-shape

curve equation based on the normalized distribution of

crack opening. The proposed method is examined with

several sample thicknesses. The results obtained by the

proposed method provide the ranges of crack opening

values for each of stages in the shrinkage cracking

process.

2. Fundamentals of Shrinkage Cracking

Evaporation appears from the soil surface. Con-sequently, the mass of the soil for motion will bedecreased by a loss of water as drying continues. Theevaporation rate is affected by conditions such astemperature, relative humidity, and wind velocity and soon. The flux of soil water upward to the soil surface ismainly controlled by the hydraulic properties of the soilsuch as unsaturated hydraulic conductivity, water potentialgradient, and thermal gradient in soil. The evaporationrate computed from the water loss is determined by boththe external conditions and the internal properties of thesoil system.

Shrinkage cracking is one of the most common typesof cracking found in the earth structures. As water is lostfrom the soil surface, tensile forces are established in thedrying surface layer and soil also loses its ability to relievethese tensile forces. These stresses are finally relieved bythe occurrence of cracks that grow up at the surface ofthe soil. As the drying process develops continuously,cracks are formed successively. An individual crackpropagates until it contacts with the other cracks or theborders of the container. Consequently, a network ofcracks is established.

3. Graphical Method

3.1 Establishment of Crack Opening Distribution

In a network of cracks, for simplicity, a crack is defined


by a set of pixels limited by two ends (diamond symbols)

as illustrated in Fig. 1 for a sample thickness of 0.01 m

as an example. The openings of individual cracks are

automatically calculated by applying a program written

in Matlab.

Due to the occurrence of cracks, the shrinkage potential

in the soil system will be reduced. Consequently, we

assume that this leads to a decrease of crack opening with

an increase of drying time. That means the later crack

will give smaller opening than the previous one. The

assumptions are appropriately verified with the results of

crack opening reported by Lecocq and Vandewalle (2003)

and Mal et al. (2005). Therefore, the values of crack

openings (presented in Fig. 1) are sorted as shown in Fig.

2 by a dot line. In this figure, the abscissa is crack opening

and the ordinate is number of crack.

3.2 Normalization of Crack Opening Distribution

Recently, S-shape curve models have been used widely

to describe the relationships between soil parameters such

as soil suction and volumetric water content, degree of

saturation and hydraulic conductivity (Jian and Jian-lin,

2005; Kamiya et al., 2006; Sharma et al., 2002; Sharma

and Mohamed, 2003; Sillers and Fredlund, 2002;

Sriboonlue et al., 2006; Zhang and Chen, 2005). Each

models is characterized by its parameters determined by

experiment.

The crack opening distribution is normalized in a range

of 0 to 1 as shown in Fig. 3 by dot line. The equations

for normalizing are given as follows:

minmax

min

minmax

min

WWWWW

NNNN

N

normalized

normalized

−−

=

−−

=

(1)

where and are minimum and maximum crack

openings corresponding to the minimum and maximum

number of crack and , respectively. is the

measured opening corresponding to the number of crack, .

3.3 Comparison of Three S-shape Curve Models

Based on the normalized distribution of crack opening

given in Fig. 3, three S-shape curve models are used and

compared to select the best model to fit the measured

data. They are given as follows:Fig. 1. Illustration of the individual cracks limited by two diamond‐

ends in case of 0.01 m in thickness as an example

0

30

60

90

120

0.0 0.5 1.0 1.5 2.0 2.5 3.0Cr ack opening [mm ]

Num

ber o

f cra

ck

Fig. 2. The distribution of crack opening for individual cracks

presented in Figure 1

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0(W-Wmin) /(Wmax-Wmi n)

(N-N

min)/(

N max

-Nm

in)

Fig. 3. The normalized distribution of crack opening obtained from

Figure 2


Brooks and Corey (1964) y = a - bxm (2)

Fredlund and Xing (1994)mn

axe

y

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛+

=

ln

1

(3)

van Genuchten (1980) ( )( )mnaxy

+=

1

1(4)

where a, b, n, and m are fitting parameters determined

through the curve fitting method.

These models are used to fit the measured data by using

the curve fitting method. The results are illustrated in Fig.

4. The normalized experiment data are denoted by dot

points (by the dash dot line for the Brooks and Corey

model, the dash line for the Fredlund and Xing model,

and the solid line for the van Genuchten model). The

Brooks and Corey model show worse fitting than the

others. The fitting parameters infer that van Genuchten

model is the best one consisting of the lowest values of

the sum of squares due to error (SSE, i.e. 0.0484) and

root mean squared error (RMSE, i.e. 0.0207), and the

highest value of R-square (i.e. 0.9950). They are summarized

in Table 1. Therefore, van Genuchten model is selected

for fitting the experiment data in this study.

3.4 Evaluation of Shrinkage Cracking Stages

According to the S-shape normalized distribution of

crack opening fitted by the van Genuchten model in Fig.

4 (solid line), we propose a graphical method for

estimating the stages in shrinkage cracking. The method

is presented in Fig. 5. Three regions from the S-shape

curve (solid line) are outlined separately by drawing three

straight components (dot lines). The first component is

determined by drawing a line tangent to the top curve

through the maximum value on the ordinate; the second

one is constituted by drawing a line tangent to the curve

through the point of maximum slope; and the third one

is a line tangent to the bottom part of the S-shape curve

through the minimum value on the ordinate. The first and

third straight components intersect the second one at two

separate points. These two transition points evaluate the

stages of cracking process described by the S-shape

equation. Three shrinkage cracking stages are illustrated

in Fig. 5. They are outlined by dash dot lines: namely,

primary, secondary and residual stages.

From these stages of shrinkage cracking, the corres-

ponding ranges of crack opening can be estimated by

projecting two transition points to the abscissa drawn by

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0(W-Wmi n)/(Wmax-Wmin)

(N-N

min

)/(N m

ax-N

min

)

Normalized data

Brooks and Corey

Fredlund and Xing

Van Genuchten

Fig. 4. The normalized distribution of crack opening (dot points)

fitted by three S shape curve models of Brooks and Corey‐(dash dot), Fredlund and Xing (dash line), and van

Genuchten (solid line)

Table 1. Fitting parameters for three S shape curve models‐Fitting Model

parameterBrooks

and Corey

Fredlund

and Xing

van

Genuchten

SSE 0.4307 0.0543 0.0484

R square‐ 0.9554 0.9944 0.9950

RMSE 0.0617 0.0219 0.0207

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0(W-Wmin)/(Wmax-Wmin)

(N-N

min

)/(N

max

-Nm

in)

Secondarystage

Residualstage

Primarystage

Fig. 5. Graphical method for evaluation of shrinkage cracking stages

by drawing three straight components corresponding to

three linear parts of the normalized crack opening

distribution fitted by van Genuchten equation


the arrows as shown in Fig. 5.

4. Soil Material Properties

For the laboratory measurements, Kaolinite clay is

used. The properties of Kaolinite are as follows: liquid

limit, LL = 42.07%; plastic limit, PL = 25.40%; plasticity

index, PI = 16.67%; specific gravity, Gs = 2.646; coefficient

of uniformity, Cu = 40.75; and coefficient of curvature, Cc= 2.33.

The experiments were performed in a rectangular steel

tray. Firstly, the soil was carefully mixed with water and

stirred for half an hour to make a paste. An initial water

content of the mixture was about 65%, 1.5 times higher

than the liquid limit. Secondly, the mixture was poured

in the tray and uniformly spread to make the surface flat.

We vary the thickness of sample with 0.005, 0.006, 0.007,

0.008, 0.009, 0.01, 0.015 and 0.02 m. Finally, the

specimen was balanced and allowed to dry naturally in

laboratory at room conditions. The drying process

continued for several days. When cracking processing

finished completely, images of the specimens were

captured by a digital camera. Image analysis with an

application of the control point selection technique is used

to analyze the images. The proper region of image is

selected to compute the opening of cracks by using a

numerical program written in Matlab.

5. Experimental Results

5.1 Shrinkage Cracking Stages Evaluated by the

Graphical Method

Fig. 6 presents the images of eight sample thicknessestested. Applying the proposed method for these images

resulted in the crack opening distributions as shown inFig. 7. The experiment data are plotted by dot lines; thenormalized values are denoted by dash dot lines; and

continuous lines present the fitted values correspondingto the normalized ones. The resulted fitting parametersare summarized in Table 2.

As seen in Table 2, for all the cases of sample thickness,the regression coefficients are extremely high, more than0.99; except in the case of 0.02 m (only 0.9724).

Correspondingly, the values of RMSE are really small,that is, less than 5% including the case of 0.02 m thicksample. This concludes that the proposed model is properly

adopted for describing the distribution of crack opening.As shown in Fig. 7, the distributions of measured crack

opening represent proximately S-shape curves with the

fairly high regression coefficients as well as low RMSEsshown in Table 2. By applying the graphical methodpresented in this paper to each of the crack opening

distributions, the ranges of shrinkage cracking stages -namely primary, secondary and residual - are tabulatedin Table 3 for both the normalized and real ranges of

crack opening.

0.5 0.6 0.7 0.8

2.01.51.00.9

Fig. 6. Images of soil cracking with different sample thicknesses (cm)


5.2 Additional Considerations

As reported by Kodikara et al. (2000), the measure-

ments of soil cracking depend on the sample thickness.

An observation of images with different sample thicknesses

as shown in Fig. 6 indicates that the number of cracks

and that of crack opening are dependent on the sample

thickness. In detail, the variations of crack opening with

0

100

200

300

400

0.0 0.5 1.0 1 .5 2 .0C rack o pen ing [m m ]

Num

ber o

f cra

ck

0.0

0 .2

0 .4

0 .6

0 .8

1 .00.0 0 .2 0.4 0 .6 0.8 1 .0

(W- Wmi n)/(W max -Wm in)

(N-N

min)/(

N max

-Nm

in)

D = 0.5 cm

0

100

200

300

0.0 0.5 1.0 1.5 2.0C rack o pen ing [m m ]

Num

ber o

f cra

ck

0.0

0.2

0.4

0.6

0.8

1.00.0 0.2 0.4 0.6 0.8 1.0

(W- Wmi n)/(W ma x-W min)

(N-N

min)/(

N max

-Nm

in)

D = 0.6 cm

0

50

100

150

200

250

0.0 0 .5 1.0 1.5 2.0 2.5C rack o pen ing [m m ]

Num

ber o

f cra

ck

0 .0

0 .2

0 .4

0 .6

0 .8

1 .00.0 0 .2 0.4 0.6 0.8 1.0


(N-N

min)/(

N max

-Nm

in)

D = 0.7 cm

0

50

100

150

200

0.0 0.5 1.0 1.5 2 .0 2 .5 3.0C rack o pen ing [m m ]

Num

ber o

f cra

ck0 .0

0 .2

0 .4

0 .6

0 .8

1 .00.0 0 .2 0.4 0 .6 0.8 1.0

(W- Wm in)/(W ma x-W min)

(N-N

min)/(

N ma

x-Nm

in)

D = 0.8 cm

0

50

100

150

200

0.0 0.5 1.0 1 .5 2 .0 2 .5 3.0C rack o pen ing [m m ]

Num

ber o

f cra

ck

0.0

0 .2

0 .4

0 .6

0 .8

1 .00.0 0 .2 0.4 0.6 0.8 1.0

(W- Wm in)/(W ma x-W min)

(N-N

min)/(

N ma

x-Nm

in)

D = 0.9 cm

0

30

60

90

120

0.0 0.5 1.0 1 .5 2 .0 2.5 3.0C rack o pen ing [m m ]

Num

ber o

f cra

ck

0.0

0.2

0.4

0.6

0.8

1.00.0 0 .2 0.4 0.6 0.8 1.0

(W- Wm in)/( Wma x-W min)

(N-N

min)/(

N ma

x-Nm

in)

D = 1.0 cm

0

20

40

60

80

0 .0 1.0 2.0 3 .0 4.0C rack o pen ing [m m ]

Num

ber o

f cra

ck

0.0

0.2

0.4

0.6

0.8

1.00 .0 0.2 0.4 0 .6 0.8 1.0

(W- Wmi n)/(W max -Wm in)

(N-N

min)/(

N ma

x-Nm

in)

D = 1 .5 cm

0

10

20

30

40

50

0 .0 1.0 2.0 3 .0 4.0 5.0C rack o pen ing [m m ]

Num

ber o

f cra

ck

0.0

0.2

0.4

0.6

0.8

1.00 .0 0.2 0.4 0 .6 0.8 1.0


(N-N

min)/(

N max

-Nm

in)

D = 2 .0 cm

Fig. 7. Crack opening distributions for several different sample thicknesses: the dot lines are experiment data, the dash dot lines are

normalized values, and the continuous lines are the evaluated values using the van Genuchten S shape equation based on the‐normalized values


sample thickness for the cases of maximum and minimum

crack openings are shown in Fig. 8.

In case of the maximum, crack opening varies increasingly

with an increase of sample thickness. That is because of

higher shrinkage potential of larger thickness sample. This

variation of crack opening can be described proximately

by power law as presented in Fig. 8 with solid line.

It is verified that as cracks appear, the shrinkage

potential of the soil system decreases. Hence, the opening

of the generated cracks is smaller than that of the previous

cracks. Particularly, the minimum crack openings in the

cases of sample thickness appear to be the same as shown

in Fig. 8. It can be explained that the minimum values

of crack openings are obtained as the shrinkage potential

of the soil system reaches to zero. Therefore, the minimum

crack openings appeared to be independent of the sample

thickness. Consequently, the minimum crack openings

become much smaller than the maximum crack openings

as the sample thickness increases as given in Fig. 8.

Similarly, it is expected that there is a fitted relationship

between the number of crack and sample thickness as

thickness increases. The result is given in Fig. 9 by power

law with the fairly high regression coefficient, more than

0.99. However, the number of cracks decreases drastically

from 0.005 to 0.01 m in thickness but it decreases slowly

from 0.01 to 0.01 m in thickness. This implies that with

enough relative thin samples, the number of cracks

decreases considerably compared with the relative thicker

samples.

Table 2. Fitting parameters in the cases of sample thickness

Fitting Thickness (cm)

parameter 0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.0

a 0.7071 2.03 1.059 0.0646 0.0729 0.2224 0.1399 0.054

m 15.63 2.12 5.726 545.7 338.5 402.1 310.1 861.9

n 2.195 2.188 2.093 1.67 1.679 2.803 2.214 1.944

R square‐ 0.9951 0.9949 0.9975 0.9966 0.9963 0.9950 0.9955 0.9724

RMSE 0.0203 0.0207 0.0144 0.0171 0.0177 0.0207 0.0198 0.0494

Table 3. Ranges of crack opening for shrinkage cracking stages in the cases of sample thickness (cm)

Cracking stageThickness (cm)

0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.0

PrimaryNormalized 0.58~1.00 0.52~1.00 0.58~1.00 0.50~1.00 0.61~1.00 0.68~1.00 0.67~1.00 0.70~1.00

Crack opening [mm] 1.15~1.63 1.14~1.78 1.55~2.36 1.60~2.62 1.85~2.75 2.15~2.94 2.61~3.64 3.32~4.49

SecondaryNormalized 0.10~0.58 0.08~0.52 0.11~0.58 0.08~0.50 0.07~0.61 0.23~0.68 0.18~0.67 0.16~0.70

Crack opening [mm] 0.59~1.15 0.56~1.14 0.65~1.55 0.74~1.60 0.60~1.85 1.04~2.15 1.08~2.61 1.21~3.32

ResidualNormalized 0.00~0.10 0.00~0.08 0.00~0.11 0.00~0.08 0.00~0.07 0.00~0.23 0.00~0.18 0.00~0.16

Crack opening [mm] 0.47~0.59 0.46~0.56 0.44~0.65 0.58~0.74 0.43~0.60 0.48~1.04 0.52~1.08 0.58~1.21

0.0

1.0

2.0

3.0

4.0

5.0

0 5 10 15 20 25Thickness [mm]

Cra

ck o

peni

ng [m

m]

Max

M in

Fig. 8. The variations of crack opening with sample thickness in

the cases of max and min values

R2 = 0 .9919

0

100

200

300

400

0 5 10 15 20 25Thickness [mm]

Tota

l num

ber o

f cra

ck

Fig. 9. The variation of total number of crack with sample thickness


6. Summary

A graphical method for evaluation of shrinkage

cracking stages based on the normalized crack opening

distribution represented as S-shape curve is presented. The

experimental data tested with different sample thicknesses

are fitted by van Genuchten model, which shows good

correlation with the fairly high regression coefficient and

low RMSE. Three stages in shrinkage cracking - primary,

secondary and residual stages - are evaluated graphically

by drawing three separately straight lines corresponding

to three linear parts of the fitted normalized crack opening

distribution. Consequently, the corresponding ranges of

crack opening for each of stages are represented for the

studied soil.

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(received on Jan. 8, 2008, accepted on Aug. 13, 2008)

Numerical Analysis of Seepage Induced Earthern Slope Failures

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