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Consolidation Analysis of Peaty soil using Elasto-Viscoplastic Theory

Key words: Finite Strain Elasto-Viscoplastic consolidation analysis Amorphous peaty clay Structural Degradation 1. Introduction It has been long recognized that the consolidation behavior of peaty clay could not be fully explained by classical consolidating theory. This is mainly due to high compressibility, rapid change of permeability and occurrence of creep behavior during the consolidation process. Creep behavior is dominant in peat due to the presence of high organic content and these organic fibers get significant compression as well as get degradation with time, makes the consolidation process complicated. Therefore it is necessary to takes into account those properties in order to get better prediction in peat consolidation analysis. In the present paper effort is made to back analysis consolidation behavior of amorphous peaty clay, due to gradual placement of fill constructed in Sri Lanka using an Elasto-Viscoplastic constitutive model considering both infinitesimal and finite strain. The model used in the analysis is proposed by Adachi and Oka (1982) and it takes account of the main variables involved in the peat consolidation process as well as effect of structural degradation with the modification done by Kimoto and Oka (2004). 2. Elasto-viscoplastic constitutive model The elasto-viscoplastic constitutive model proposed by Adachi and Oka (1982) is based on the on the Perzyna's elasto-viscoplastic theory and Cambridge elasto-plastic theory together with empirical evidences. In this model total strain rate tensor consist of elastic strain rate tensor and viscoplastic strain rate tensor. Elastic strain rate is given by a generalized Hooke type law while viscoplastic strain rate tensor is calculated using following viscoplastic flow rule.

vp ij = ( f y )

Kyoto University Student member Asiri Karunawardena Kyoto University International member Fusao Oka Kyoto University International member Sayuri Kimoto peat consolidation. The parameter m and C /Cc concept proposed by Mesri(1997) to predict the secondary consolidation is interrelated by Oka (2005) as follows. - (6) where is secondary compression rate and =

m(1 + e)

vp under the condition v p = kk exist during the secondary creep. And in terms of coefficient of secondary consolidation (C ) above relationship can be expressed as

given by

p v p = ln(t / t0 ) + v0

m =

Cc - C s C

(7) often in peat soils C s 0.1C c , m =

0.9Cc (8) C

Mesri reported that C /Cc for amorphous peat varied from 2025 and according to the above relationship corresponding m becomes 18-23.

2.2 Relationship between viscoplastic parameter C and shape of the field compression Curve It is generally accepted that creep takes place under the constant effective stress as well as during the excess pore water pressure dissipation in peat consolidation process. As a result of that strain at the end of primary consolidation increases with the sample thickness and therefore it is necessary to describe relevant field compression curve when analyzing field consolidation behavior using the laboratory results. This important phenomenon can be simulated by correct evaluation of the viscoplastic parameter C as illustrated in Kimoto et al. (2006). 3. General description of the site A peat land was reclaimed for infrastructure development project near the Capital of Sri Lanka in the year 2000. The thickness of the peat layer is around 5m and it can be classified as amorphous type. Extend of the fill area is about 2.4 hectares and instrumentation were located around the centre of the fill area. Therefore one dimensional consolidation behavior is expected in the peat layer and analysis was done adopting a finite element mesh having element size 0.2m x 0.2m. The bottom boundary is assumed to be perfectly drained due the existence of medium dense to dense sandy silt layer below the peat layer. The investigation reveals that, compacted fill behave as impermeable material and therefore top boundary is assumed as impermeable in the analysis to simulate the field conditions. The field rate of consolidation was evaluated by independent field monitoring of pore water pressure and settlements. Pizometers were installed in the middle of the peat layer and settlement gauges were installed just above the peat layer. 4. Determination of soil parameters The parameters required for the analysis are determined as follows. Compression index and swelling index

= -de / d ln( v ) = 0.434C c = - de / d ln( v ) = 0.434C s

f p ij


f y = ( 0) + M * ln ms ) ( my



: Material function indicating strain rate sensitivity. f p and f y are

(s potential and static yield function based on Cam clay theory. my ) is

a hardening parameter and in order to account structural degradation effect, viscoplastic strain softening is introduced in addition to the strain hardening with viscoplastic volumetric strain as follows (Kimoto and Oka, 2004).

( s my ) = ma ( s ) 1 + e0 vp (3) = + - exp - z a (4) myi exp v ma maf mai maf mai -


) (


here mai and

maf are initial and final value of the ma .

of second invariant of viscoplastic strain rate. Both and a can be determined for curve fitting the strain softening part of undrained triaxial test. The concrete form of model together with finite element formulation is shown in Oka et al. (1982). The change of permeability is taken into account using the following empirical relationship given by Taylor(1948). where Ck is material parameter called k = k 0 exp( e - e0 ) / C k (5) permeability change index. 2.1 Relationship between viscoplastic parameter m and secondary compression rate C Secondary compression is often more significant in peat soils and therefore account for secondary compression plays an important role in

Consolidation Analysis of Peaty soils using Elasto-Viscoplastic Theory, University

Parameter denotes degradation rate of ma and z is an accumulation

Where C c and C s are compression and recompression index determined from oedometer test. The value of initial permeability ( k0 ) was determined by from field permeability test results and the permeability change index

Asiri Karunawardena, Fuaso Oka, Sayuri Kimoto ­Graduate School of Kyoto

( C k ) was deduced from the variations of permeability through oedometer test. Viscoplastic parameter m is determined using following relationship m = (Cc - Cs ) / C where all the symbols have their usual meanings. Viscoplastic parameter C, degradation parameter and initial shear modulus G0 is determined by curve fitting of the stress strain curve of undrained triaxial test done on peaty soils. Compression yield stress ( mbi ) is assumed to be equal to the preconsolidation pressure determined through the oedometer test and structural parameter ( maf ) is assumed to be 0.7 mbi . Initial vertical

effective stress ( 22 ) was determined based on the in situ density profile. The parameters used for the calculations are given in Table 1, Table 1. Soil Parameters used in the analysis # k0 =1.5x10-7m/s 22 =12.5kPa =1.7176 m =22 -10 -1 # C=5x10 s Ck=0.80 =0.1145 mbi =15kPa

e0 =6.28 G0 =800kPa

data even though it underestimates the actual settlement quantitatively. Similar to pore water pressure predictions OFS&SD model shows the qualitatively and quantitative better agreement with observed field data for the used parameters in the analysis.


M * =0.6304

# varied with the depth

5. Prediction of filed behavior, comparison with actual observation and discussions Observed field behavior, namely cumulative settlement and excess pore water pressure were compared with the calculated results. Analysis was carried out by considering both infinitesimal strain (IS) and finite strain (FS). In FEM analysis considering FS, updated Lagrangian method with the objective Jaumann rate of Cauchy stress for a weak form of the equilibrium equation is adopted. Biot type two-phase mixture theory is used with a velocity-pore pressure formulation. Effect of structural degradation considered only in the FS analysis and the corresponding model represent as OFS&SD. Original model without considering structural changes assuming the finite deformation referred as OFS and original model with IS represented by the symbol OIS. 5.1 Excess pore water pressure behavior. The predicted and observed excess pore water in the middle of peat layer (depth: 2.5m) are presented in Fig.1.Loading curve showing construction of the fill is also shown in the same figure. It shows that, field pore water pressure reached around 30kPa at the completion of the fill due to a load of 46kPa. After the completion of the fill, the quantity of excess pore water pressure dissipated was only about 10kPa during the following year. When this behavior is compared with predicted behavior, it shows that prediction made by the OIS model under estimate the excess pore water pressure, in contrast OFS model overestimates the same when it compared with observed filed data. Only the predictions made by OFS&SD model remarkably agreed with the observed filed behavior. The above results indicated that when predicting excess pore water pressure behavior in high compressible material like peat it is necessary to consider geometry change (decrease in soil layer height) in order to account correct drainage path. Moreover it emphasizes that, it is essential to consider the effect of structural degradation with other variables in order to simulate stagnated pore pressure observed after the construction. 5.2 Settlement behavior The comparisons of predicted and actual settlement are presented in the Fig.2. Field settlement data indicates that, settlements advance even though the existences of stagnated excess pore water pressure in filed. This behavior has been observed in many embankment constructions around the world. Many researches suggest that this behavior occurred due the effect of structural degradation of the compressible layer and Kimoto and Oka(2004) simulate this behavior numerically by considering degradation effect on consolidation process. Comparison shows that, as expected, predicted settlement assuming ID gives the higher value than the FD and in this case the difference is more significant due to the resultant large strain around 20% in the field. Predictions made by the OIS model overestimate the field settlement where as OFS Model shows qualitative agreement with the observed

Fig.1. Excess pore water Prediction

Fig.2. Settlement Prediction

6. Conclusion The results show that model which accounts main variables in peat consolidation such as finite deformation, secondary creep, change of permeability is capable of predicting consolidation behavior of the amorphous peaty clay once the effect of structure degradation is considered. Effect of structural degradation has significant on the current analysis and without considering it, it is almost impossible to simulate observed filed behavior. 7. Reference. 1.Kimoto, S. and Oka, F. (2005):An Elasto-Viscoplastic model for clay considering destructuralization and consolidation analysis of unstable behavior, Soil and Foundations, Vol.45, No.2, 29-42. 2.Kimoto, S. and Oka, F. (2006): Effect of initial strain rate on the consolidation of clay with different thickness, Proc.41st JGS conference (in Japanese). 3.Oka, F. (2005): Computational modeling of large deformations and the failure of geomaterials, Theme lecture, Proc.16th ICSMFE, Vol.1, 47-95. 4. Mesri, G., Stark, T.D. (1997): Secondary Compression of Peat with or without Surcharging, Journal of Geotechnical and Geoenvirmental Engineering, 411- 421. 5.O'Loughlin. (2001): Modeling the time-dependent compression of peat and organic soil, Soft Soil Engineering, Lee et el(eds), 369-375.


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