Collapsible Soil:
and Marcio de Souza Soares de Almeida Graduate School of Engineering, COPPE, |

ABSTRACT

This paper presents the results of recent experimental and theoretical studies of a colapsible soil. Suction controlled oedometer tests under different stress paths have been performed on a colapsible soil with the purpose to get a better understanding on the compressibility and collapsibility of this soil.

KEYWORDS: Unsaturated soil, Collapse, Elasto-plastic model.

INTRODUCTION

Alonso et al. (1990) using a 4-D space extended elasto-plastic critical state concepts to unsaturated soils. The four variables of Alonso et al’s models are the mean net stress p, the deviator stress q, the suction *s* and the specific volume v. A number of constitutive models (e.g, Josa et al, 1992; Wheeler and Sivakumar, 1995) have subsequently been proposed following these concepts.

The present paper further extends the fundamental points proposed by Alonso and his co-workers to a collapsible soil. Results of suction controlled oedometer tests on a natural collapsible soil are provided and the fundamentals of the proposed model are briefly presented. Model predictions of oedometer tests are performed and the maximum collapse is evaluated.

SOIL DESCRIPTION

The soil presently studied consists of a porous silty clay found in the State of Mato Grosso, in Central Brazil. Studies with this soil have already been reported (e.g. Futai et al., 1998) and the main features of this soil are presented in Table 1. It is seen that as far as grain size is concerned, the soil consists mainly of clay particles. Electron microscopy studies show that this soil has a sort of granular fabric with sand and silt particles linked by bunches of clay particles, as shown in Figure 1. In other words, the clay particles work simply as connectors and the available suction induces a meta-stable structure to this soil.

**Figure 1.** Fabric of the collapsble soil tested (schematic)

When wetted, the soil collapse occurs due to the decrease in the soil stiffness caused by the suction decrease and also by the washing of the clay cementation. The interest in the study of this soil has arisen due to foundation problems experienced by silos constructed on this soil.

**Table 1.** Proprieties of the tested soil

Property | value |

Natural water content, w | 25 - 40% |

in situ suction, s | 10 - 45 kPa |

Average voids ratio, e | 1.9 |

Plasticity index, I_{p} | 22.6% |

Clay content | 74% |

Silt content | 16% |

Sand content | 10% |

EXPERIMENTAL STUDY

Tests performed

Undeformed cubic blocks with 20cm sides have been collected and suction controlled oedometer tests were carried out in samples trimmed directly from the block. The initial conditions of the tested specimens, the applied suction and the vertical stress *svi* in which the soil specimen was flooded (saturated) are given in Table 2.

**Table 2.** Tested specimens: initial conditions

Test | e_{o} |
w_{o} (%) |
Suction (kPa) | svi (kPa) |

Saturated | 1.90 | 30.10 | 0 | - |

NS-01 | 1.70 | 30.09 | 50 | - |

NS-02 | 1.91 | 33.16 | 100 | - |

NS-03 | 1.98 | 31.76 | 120 | - |

NS-04 | 1.99 | 31.85 | 138 | - |

NS-05 | 1.98 | 32.28 | 195 | - |

C1-01 | 2.12 | 30.89 | 120 | 2.2 |

C1-02 | 2.01 | 31.25 | 120 | 22.2 |

C1-03 | 2.14 | 31.13 | 120 | 88.8 |

C1-04 | 2.11 | 30.85 | 120 | 355.3 |

C1-05 | 1.96 | 30.65 | 120 | 1509.9 |

D-01 | 1.90 | 30.84 | see Figure 5 | |

D-02 | 1.90 | 30.84 | see Figure 6 | |

Tests with constant suction

For the test series NS the suction was kept constant and the vertical stress was applied in increments. Some of the results of the NS series tests are shown in Figure 2 together with the result of the saturated specimen.

For the range of applied stress, both the virgin compression index l(*s*) and the yield stress *svm*(*s*) tend to increase with the suction *s*, as shown in Figure 2 and Table 3. The unloading compression index k(*s*) is also presented in Table 3. However, this does not show a clear variation with the suction *s*. The yield stress *svm*(*s*) was determined following Casagrande’s method. The compression indexes l(*s*) and k(*s*) are defined by:

(0) |

** **

**Figure 2.** Suction controlled oedometer test results

**Table 3.** Soil parameters

Suction (kPa) | svm(s) (kPa) | l(s) | k(s) |

0 | 20 | 0.24 | 0.0072 |

50 | 60 | 0.28 | 0.0066 |

100 | 110 | 0.34 | 0.0057 |

120 | 120 | 0.36 | 0.0064 |

138 | 130 | 0.42 | 0.0065 |

195 | 140 | 0.48 | 0.0057 |

As far as the variation of l versus suction *s* is concerned, a number of experimental results (Aguilar, 1990; Wheller and Sivakumar, 1995; Araki and Carvalho, 1995; Futai, 1997; Machado and Vilar, 1998), have yielded data similar to those presented here. These results contradict Alonso et al. (1990) model predictions of l decreasing monotonically with suction.

These results suggest that at low stress levels the suction has greater influence than at greater stress levels, where the compressibility of the soil skeleton governs and the meta-stable soil structure is broken under the applied stresses. It appears that as the soil is compressed the deformation behaviour less dependent on the suction and voids ratio and more dependent of the compressibility of the soil skeleton. At very high stress levels where the soil structure has been broken, the voids are reduced and the suction becomes negligible.

Tests with variable suction

For the test series C1 and C2 the suction was initially kept constant at 120 and 75kPa, respectively. Then vertical stresses were applied in increments up to a stress level *svi*. At stress level *svi* suction was decreased in stages until saturation of the specimen, thus inducing collapse to the soil. Results of these tests are shown in Figures 3 and 4.

**Figure 3.** C1 test series, si = 120 kPa

(Comma is used in this figure for decimal separator)

**Figure 4.** C2 test series, si = 75 kPa

Tests C1 e C2 show that the collapse increases with the applied stress up to a point beyond which vertical strains start to decrease and become negligible, due to the decrease in suction (*svi* = 1500 kPa).

Test D-01 had three steps of suction decrease, coupled with increase in vertical stress, as shown in Figure 5a. The stress-strain curve of this test is shown Figure 5b.

**Figure 5.** (*a*) Suction stress path and; (*b*) Stress-strain curve for test D –01

The imposed *s* - *s*_{v} stress path for test D-02. in which the suction was slowed decreased, is shown in Figure 6. The yield curve is shown in dashed line in the same figure.

**Figure 6.** Stress path for D–02 test

The stress-strain curve and the suction-strain curve for test D-02 is seen in Figures 7. It is noticed that the strains due to the decrease in suction are initially very small. However, beyond *s* = 50 kPa (point E) a sudden change in the curve clearly defines yielding.

**Figure 7.** Results for test D-02

(Comma is used in this figure for decimal separator)

PROPOSED MODEL

Futai (1997) and Futai et al (1998) have described a finite element model, which is also the proposed model here. Silva Filho (1998) implemented the model in CRISP finite element code (Britto and Gunn, 1987) and carried out a number of validations against laboratory tests and field tests. Futai et al (1998) and Silva Filho (1998) have concluded that model predictions were very close to measured values, not only in laboratory for natural and compacted soils, and different stress paths, but also for field tests.

Model parameters

The model parameters are dependent on the suction represented by functions.

The elastic volumetric strain is computed by:

(1) |

where

(2) |

In most models k(*s*) is constant, thus the bulk modulus decreases with suction, as *v* decreases, which is inconsistent. The present model adopts the following function to represent the variation of k(*s*) with the suction:

(3) |

where k(*s*), k(0), k(¥) are the values of k at suction *s*, at the saturated condition and at a very high (infinite) suction, respectively;

c is the parameter controlling stiffness with suction for the elastic condition.

The function proposed for l(*s*) permits modelling of decrease or decrease of l(*s*) with suction, as given by the equation:

(4) |

where l(*s*), l(0), l(¥) are the values of l at suction *s*, at the saturated condition and at a very high (infinite) suction, respectively, and b controls the soil stiffness with the suction variation.

The parameter *N*(*s*) is the specific volume at *p* = 1 atm. It was also assumed a point of convergence (*pf*, *Nf*) at which there is no more collapse, as seen in Figure 8. Thus, it is possible to obtain:

(5) |

**Figure 8.** Idealization of the compressibility behaviour

The yield surface can be obtained by stress path shown in Figure 9 and one obtains

(6) |

Triaxial behaviour

The triaxial behaviour (*p* : *q* : *s*) has been modelled following Alonso et al. (1990)’s proposal:

(7) |

where

(8) |

*k* is the parameter describing the increase of cohesion with suction and *M* is the slope of the critical state line. The flow rule is associated.

Collapse calculation

The collapse strains are computed by the change in the saturated yield stress, as this characterises the change in the yield stress given by:

(9) |

The new *po* position is determined in the stress state (*p* : *s*), but can also be activated by the deviator stress. The suction path can occur in three positions:

*a* - fully elastic, there is no collapse, but elastic expansion under unloading, *p* < *po*(o);

*b* - initially elastic, the LC is crossed, then elasto-plastic, *po*(*s*)<p<*po*(o);

*c* - initially on the yield surface, and therefore elasto-plastic *p* = *po*(*s*).

**Figure 9.** Stress path and change in specific volume

According to the present formulation the maximum collapse takes place at the initial yield surface LC. Therefore, it is simpler to compute the maximum collapse directly from the curves:

(10) |

(11) |

These equations are valid only for isotropic or oedometric conditions.

MODEL PREDICTIONS

For the present paper the predictions have been carried out by a finite element code (Silva Filho, 1998) in which loading and boundary conditions of each test were imposed. The soil parameters for the studied soil for the proposed model are (Futai et al., 1998):

l(0) = 0.24 | l(¥) = 0.54; |

k(0) = 0.0072 | k(¥) = 0.005; |

ks = 0.004 | c = 0.006; |

b = 0.006 | po* = 18 kPa; |

N(0) = 2.45 | pf = 1000 kPa. |

The closeness of the functions to experimental values can be seen in Figures 10 and 11.

**Figure 10.** Predicted and measured k(*s*) and l(*s*)

Oedometer tests

Rigorously, the parameters obtained in the oedometer are not directly applicable to the model as the correct stress state to obtain the model parameters is the isotropic. However, the values of k(*s*) and l(*s*) obtained in the oedometer test can be directly used in the model as the slopes of oedomer and isotropic curves are usually assumed to be the same. However, the preconsolidation or yield stress has to be converted for the isotropic condition using the equation of the yield function, as shown in Figure 11.

**Figure 11.** Yield surface

Test D-02 provides a typical example of collapse. Measured and predicted vertical strain values for test D-02 are shown in Figure 12 and the good agreement obtained is quite noticeable.

Predicted and measured results for test D-01 are shown in Figure 13 and again a good agreement is obtained in most of the test, with exception for the early part. The yield took place during increase of vertical under constant suction (CD, *s*=100 kPa). Therefore, the collapse (DE) was for elasto-plastic conditions.

** **

**Figure 12.** Measurements (squares) and prediction for test D-02

**Figure 13.** Measured (circle) and predicted for test D-01

Evaluation of the maximum collapse

The methodology of the double oedometer test has also been independently used. Neglecting the variations of the initial state in each specimen (see Table 2) collapse strains have been obtained by the difference between unsaturated and saturated compressibility curves (Figure 2), and these values are shown in Figure 15.

The data of Figure 14 was generated from tests shown in Figures 3 and 4 for the tests with variable suction. It is noticed that the values are quite similar to those obtained by the double oedometer test technique.

It can be seen in Figure 15 that the predictions made by the model follow the test trend with close agreement between predicted and measured values.

**Figure 14.** Estimated collapse strains by double oedometer tests

**Figure 15.** Predicted and measured collapse strains

CONCLUSIONS

This paper has presented results of suction controlled oedometer tests on an unsaturated collapsible soil. Some of the tests have undergone unconventional stress paths that illustrated important aspects of the studied soil.

A new constitutive model has been proposed and implemented in a finite element program. Comparisons have been made between model predictions and test results and good agreement was generally observed. It was noticed that the collapse increases up to a maximum value close to the initial soil yield, beyond which it starts to decrease. The maximum collapse is larger for larger suction values and it tends to a limit value.

The *K*_{0} value for saturated soils is a function of the friction angle. In the case of unsaturated soils the *K*_{0} value is also dependent on the suction and during collapse on the stress state, elastic or elasto-plastic.

REFERENCES

- Aguilar, S. E. S., 1990. Compressibility of a collapsible unsaturated clay soil under isotropic compression with controlled suction, MSc thesis (in portuguese), Catholic University, Rio de Janeiro, Brasil.
- Alonso, E. E., Gens, A. & Josa, A., 1990. A constitutive Model for Partially Saturated Soils. Géotechnique, vol. 40. N. 3. 405 - 430.
- Araki, M. S. & Carvalho, J. C., 1995. Study of a Collapsible Porous Soil of Brazil. I International Congress on Unsaturated Soil, Paris.
- Futai, M. M., 1997. Suction controlled oedometer tests in a collapsible unsaturated clay soil, MSc thesis (in portuguese), COPPE, Federal Univ. of Rio de Janeiro, Rio de Janeiro, Brasil.
- Futai, M.M., Almeida, M.S.S. & Soares, M.M., 1997. Evaluation of collapse by means of laboratory tests (in portuguese), XI Brazilian Conference on Soil Mechanics and Geotechnical Engineering, Brasília, p. 1023-1030.
- Brito, A. M. & Gunn, M. J. (1987) Critical State Soil Mechanics Via Finite Elements. John Wiley & Sons
- Josa, A., Balmaceda, A., Gens, A. & Alonso, E. E. (1992) An Elastoplastic Model for Partially Saturated Soils Exhibiting a Maximum of Colapse. Proc. 3th Int. Conf. Computational Plasticity, Barcelona, 815-826.
- Machado, S. L. & Vilar, O. M., 1998. Estudo da Compressibilidade e Resistência de Solos não Saturados ao Longo de um Perfil da Cidade de São Carlos – SP, XI COBRAMSEG, Brasília.
- Silva Filho, F. C., 1998. Numerical analysis of Análise Numérica de Problemas em Solos Não Saturados: Modelagem, Implementação e Aplicações Práticas. Tese de Doutorado, COPPE/UFRJ.
- Wheeler, S. J. & Sivakumar, V., 1995. An elasto-plastic Critical State Framework for Unsatureted Soil. Géotechnique, vol. 45. N. 1. 35 - 53.

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