Effects of rarely analyzed soil parameters for FEM analysis of embedded retaining structures

V. Józsa1 Geotechnical Department, Budapest University of Technology and Economics, Hungary

ABSTRACT

Finite element modeling (FEM) is highly dependent on the reliability and the accuracy of the input data. The assigned Poisson'sratio is very dominant for the shear strength parameters in the case of the elastic and Mohr-Coulomb (MC) soil model. This value may vary between 0.25 and 0.45 (from gravel to clay). Using FEM analysis with MC soil model, the calculateddeformations obtained from the model are not realistic, meanwhile it is perfectly suitable for stability calculations. Moreaccurate displacement results can be obtained with the same software applying Hardening Soil (HS) model. In this case,additional factors are required for the model, such as unloading-reloading modulus of elasticity (Eur), and Over-Consolidated Ratio (OCR). The HS model is useable with dense and hard soils. The soil will behave 3-5 times ‘’stiffer’’ in unloading-reloading, which defines the choice of the value of the Eur. The above-mentioned factors are important in determining the behavior of soils, especially at the reactions of retaining structures and deformations. The influence of factors is illustrated by a trusted, embedded retaining structure. This study draws attention to the importance of parameter analysis. Keywords: retaining wall, Poisson’s ratio, overconsolidation, unloading-reloading modulus.

1 Budapest University of Technology and Economics, Geotechnical Department, Müegyetem rkp 3, Budapest 1111, Hungary. vjozsa@mail.bme.hu

1 INTRODUCTION

In general computer programs examine the stability of the excavation and the retaining structure. The necessary excavation area depends on the adjacent building, the retaining wall system, the traffic and transportation roads as well as the dewatering system. Large-scale works can be quite expensive if something goes wrong.

It is now essential to approximate the behavior as realistic as possible, for reasons of economy, time and safety. If the input parameters are sufficiently precise, then the output results of the FEM are usable.

This paper presents a parameter analysis, which will help us to see the impact of changing the input values.

2 DEFINITIONS

2.1 Poisson's ratio ν

When a material is compressed in one direction, it usually tends to expand in the other two directions perpendicularly to the direction of compression. This phenomenon is called the cross-contraction effect.

The Poisson's ratio ν is dominant for the shear strength parameters in the case of the elastic and

Mohr-Coulomb soil model. This value may vary between 0.25 and 0.45 (from gravel to clay) [6].

The Poisson's ratio in the unloading section has a lower initial value, but in general when using MC model the use of a higher value is recommended. K0 is the ratio of lateral (horizontal) pressure to vertical pressure (K = σh'/σv') [3]. We use the Poisson's ratio in the K0 calculation, as follows:

'/ ' / (1 )h vσ σ ν ν= − (1)

In granular soils and normally consolidated soils, the Jáky-formula is recommended:

0 1 sin 'K ϕ= − (2)

In many cases, the ν value is obtained for the range of 0.3 to 0.4 from the axial tests, but in unloading-reloading case this value is 0.15 to 0.25 [3]. If it is not known, whether the higher or the lower Poisson's ratio is safer, parameter analysis will be necessary [2]. The third case is the over-consolidated soil. The Plaxis program calculates with the following formula:

0.50, 0xOCRK K OCR= (3)

If you must give the value K0 in the computer program, you must check, that the calculation module is able to apply Poisson's ratio-independent K0 formula [2].

2.2 Unloading-reloading modulus

In the Hardening Soil model (Plaxis) the relationship is hyperbolic between the vertical strain, ε1, and the deviatoric stress q in the primary triaxial loading (see Figure 1) [3].

E50ref modulus is difficult to determine

accurately from triaxial tests, so that in general often the Oedometric modulus Eoed

ref is used. For oedometer conditions of stress and strain

the model uses the following relationship:

( / )ref ref moed oedE E pσ= (4)

where pref is the particular reference pressure (in generally 100 kPa), and m is the power of soil hardening. This m value may vary between 0 and 1 (gravel: 0.5; mud: 0.75; clay: 1.0).

Figure 1. Hyperbolic stress-strain relation in primary loading

for a standard drained triaxial test [3]

2.3 The initial pre-consolidation stress

When using advanced models (example: in Plaxis) an initial pre-consolidation stress has to be determined. In the practice the engineers calculate with Over-Consolidation Ratio (OCR), i.e. the ratio of the greatest effective (previously reached) vertical stress σp. and the in-situ effective vertical stress, 0' yyσ [3]:

0/ 'p yyOCR σ σ= (5)

If this value is less than 1, lower consolidated, if equal to 1, normally consolidated, and if greater than 1, then we are talking about over-consolidated soil.

Figure 2. Illustration of OCR and POP [3]

There is another opportunity to specify the

initial stress state. The Pre-Overburden Pressure (POP) is defined by:

0| ' |p yyPOP σ σ= − (6)

Figure 2 illustrates the two types of pre-

consolidation stress.

3 ANALYSIS METHOD

3.1 Soil models

The aim of this paper is to compare the effect of different soil parameters. Two different material models were investigated: the Mohr-Coulomb model and the Hardening Soil model.

3.1.1 The Mohr-Coulomb model The Mohr-Coulomb model is usable as a first approximation, because of the constant stiffness, the calculation is very fast and the model is ideal for the stability test, but the displacements obtained are not realistic [6]. Parameters of linear-elastic perfectly-plastic (MC) model with their standard units are listed below: - E: Young’s modulus [kN/m2] - ν: Poisson’s ratio[-] - φ: Friction angle [°] - c: Cohesion [kN/m2] - ψ: Dilatancy angle [°] In general the secant modulus is used at 50% strength E50 instead of the tangent modulus (E0) (see Figure 3), except in the case of dynamic loads [5].

Figure 3. Definition of E0 and E50 [3]

3.2 The Hardening Soil model

In this model the primary load creates both elastic (recoverable by unloading) and plastic (irrecoverable by unloading) deformations.

The model uses the unloading-reloading modulus (see Figure 1) and also the compression modulus. The relationship is hyperbolic between the vertical strain, ε1, and the deviatoric stress. There are five important parameters:

- E50ref: secant modulus 50% strength [kN/m2]

- Eoedref: Oedometric modulus [kN/m2]

- Eurref: Unloading-reloading modulus [kN/m2]

- νur: Unloading-reloading Poisson’s ratio [-] - m: Exponent of the stress-stiffness function Basic characteristics of MC model: - φ: Friction angle [°] - c: Cohesion [kN/m2] - ψ: Dilatancy angle [°]

3.3 Settings of the analysis

In the analysis plane strain conditions and 15 node triangle elements were used. The boundary conditions were built up with the “box model”.

The upper 3 m is gravelly sand and below 20 m has been defined as sandy clay. Table 1 represents the fixed soil characteristics. The retaining wall is 18 m long and the excavation is 10 m deep. The strut supports the wall at 1m below the top.

External groundwater is found 3 m below the surface, the internal water level is reduced by pumping to 2 m below the bottom of the excavation. The aim of the study is to present the effect of changing 3 parameters, which are the Poisson's ratio, the Unloading-reloading modulus and the Over-consolidated ratio.

Figure 4. Excavation with retaining wall (Plaxis)

In the Table 2-3 and 4, the gray shading value

changes in the calculations with the sandy clay soil, these are Poisson's ratio (0.25; 0.3; 0.35) with the Mohr-Coulomb model, Eur (30MPa; 45MPa; 75MPa; 150MPa) and OCR (1; 2; 3; 4; 5) in the Hardening Soil model.

Table 1. Fixed soil characteristics

Table 2. Settings to the Poisson's ratio analysis

Table 3. Settings to the Unloading-reloading modulus analysis

Table 4. Settings to the Over-consolidation ratio analysis

Before the calculations we have to define the construction stages: - There is no excavation, the wall is active - Excavation is 1 m deep - The strut is active and the excavation is 10

m deep (short term/plastic analysis) - φ/c reduction (stability analysis) - Consolidation analysis (long term analysis).

4 RESULTS

4.1 Parameter analysis of ν

During the short term analysis and consolidation calculation the same effect is found, which is the following: due to the increasing Poisson-ratio the displacements increase also. The increase from 0.25 to 0.30 in the first calculation changed the displacement from 15.6 cm to 20.0 cm (+25%) (see Figure 5)

For the bending moments the experience was the same. The maximum increase is 40% (short term calc.) and 30% (Consolidation calc.) (see Figure 6).

In the consolidated state there is almost no difference between the case of ν = 0.25 and 0.30.

Figure 5. Parameter analysis of υ (1)

Figure 6. Parameter analysis of υ (2)

4.2 Parameter analysis of Eur

Due to the increase of the Eur the displacement and the bending moments decreased. If we change the value of the Eur from 45MPa to 150MPa, then the displacement appears minus 40% (short term analysis), minus 20% (consolidation calc.), and at the bending moments minus 25% (short term calc.), minus 15% (consolidation calc.), see Figure 7.

This observation is (in the case of bending moment) true both for the negative and positive site of the wall (in absolute value) (see Figure 8). In the case of Eur = 30 MPa in the short term calculation a stability problem occurred.

Figure 7. Parameter analysis of Eur (1)

Figure 8. Parameter analysis of Eur (2)

4.3 Parameter analysis of OCR

When we used OCR=1 and 2 there were some stability problems in the short term analysis.

After the calculations the effect was the following: the increase of the OCR from 1 to 5 at the short term analysis is minus 25% and in the consolidation state minus 35% (displacement), see Figure 9. For the bending moments these values are minus 30% and minus 15%, see Figure 10.

Figure 9. Parameter analysis of OCR (1)

Figure 10. Parameter analysis of OCR (2)

5 CONCLUSIONS

5.1 General conclusions

When we use FE-modeling for engineering tasks, there are many important circumstances. The calculation result cannot be more reliable than the data and theories used, the reliability of approximations and generalizations [2].

We can determine how accurately the results are that are obtained, but the origin of errors lies in the modeling. The reliability of the material characteristics of engineering structures (steel, concrete) is substantially higher, than the geotechnical parameters [2].

Mechanical material models and computer programs must be selected, that fit the data well. If it is possible to follow the construction stages, the granular (non-cohesive) soil must be defined drained, the cohesive soil undrained and also follow the consolidation phases. If the FE program is able to handle the Hardening Soil model, the unloading-reloading parameters must be defined.

The computers solve the tasks without thinking, so we have to be aware of the input parameters and output results.

5.2 Conclusions of analysis

The effect after the small change of physical soil parameters can be cumulative, causing up to 2 to 3-fold difference in results. It is now essential to approximate the reality as close as possible, for reasons of economy, time and safety. The advanced models give more possibilities, but are also more prone to error. The Mohr-Coulomb model is usable as a first approximation, because of the constant stiffness, the calculation is very fast and the model is ideal for the stability test, but the displacements obtained are not realistic. The increase of the soil-ordered Poisson's ratio also increases displacements and bending moments.

The Hardening Soil model can present more precise displacement results when the correct values are chosen for the Over-Consolidated Ratio, unloading-reloading modulus, etc.

If you are not sure of behavior of the soil use the value Eur=3*E recommended by the program (Plaxis) [1].

When we remove the soil mass near the retaining structure, the soil will unload and the wall will move in. With low values of Eur we will get large surface displacements, which cannot be handled by generally used strut systems [1].

ACKNOWLEDGEMENT

I would like to thank Zoltan Czap of the Geotechnical Department at the, Budapest University of Technology and Economics, for the helpful advice and support.

REFERENCES

[1] J. Farkas, Z. Czap, Deep Excavations and Retaining Structures, Problems with the deep excavaions p.86-88, Budapest, 2009.

[2] Gy. Greschik, About the geotechnical dates of tunneling calculations K+F p.24-28

[3] Plaxis V.9 Material Models Manual, 2010 [4] R. Szepesházi, Modern Soil models (web note) p.4-6 [5] R. Szepesházi, Surface displacements in the case of

deep excavations (web note) [6] Z. Czap, G. Varga, Cuttings and fillings, Methods of

the FE analysis, MTM (2003/5. okt.)