modelling oedometer tests on biocemented soils …

Congresso de Métodos Numéricos em Engenharia

1-3 julho 2019, Guimarães, Portugal

Universidade do Minho

MODELLING OEDOMETER TESTS ON BIOCEMENTED SOILS

CONSIDERING BONDS PRESENCE

R. Cardoso1, I. Borges

2 e I. Pires

3

1: IST/CERIS, University of Lisbon, Portugal

e-mail: [email protected]

2: IST, University of Lisbon, Portugal


3: former IST, University of Lisbon, Portugal


Key-words: Biocementation, bonds, constitutive modelling, structured material,

elastoplasticity, damage

Abstract Biocementation is being used mainly to improve the mechanical and hydraulic

properties of soils. This technique consists in adding bacteria and feeding solution to soils

to produce calcium carbonate (biocement). When produced in enough quantity, calcium

carbonate formed around bacteria present in the soil pores create bonds connecting the

particles. The treated material is therefore a bonded material, also considered to be an

artificially structured material. In this paper oedometer tests performed on saturated

samples of a sandy soil treated with bacteria were simulated using an elastoplastic

constitutive model for bonded materials. The model is defined based on Cam Clay Model

considering the destructured state as reference case, and a bonding parameter which

increases the size of the yielding surface. This parameter is reduced during loading due to

bonds' progressive failure, simulating damage. In this study the results of similar tests

performed on identical samples not submitted to treatment were used as reference case.

Two different definitions of the bonding parameter were adopted: (i) the definition used

for soft rocks, in which bonding is defined mathematically; (ii) bonding is defined

considering explicitly the presence and number of connections. Model calibration is

discussed for the two definitions, being more simple for case (i). Nevertheless, case (ii) is

based on physical properties and is more realistic than case (i). Both cases are consistent

and the model is able to reproduce the behaviour of the biocemented material.

1. INTRODUCTION

Biocementation is being used mainly to improve the mechanical and hydraulic properties of

soils. It is a green technique with huge potential in geotechnical applications [1]. This

technique consists in adding bacteria and feeding solution to soils to produce calcium

carbonate, the biocement, which clogs the soil pores and bonds the grains, changing the

hydro-mechanical (HM) properties of the soil [2]. Several are the applications predicted for

this treatment, such as: prevention of internal erosion [3,4] and liquefaction [5,6], soil

strengthening for foundations, excavation or drilling [7], etc. Only few large scale tests were

R. Cardoso, I. Borges e I. Pires

performed in treated sands [8,9].

Calcium carbonate CaCO3 is precipitated after the hydrolysis of urea made by the

microorganisms, resulting in ammonium (NH4+) and carbonate ions (CO3

2-):

CO(NH2)2 + 2H2O 2NH4+ + CO3

2- (1)

Calcium carbonate results from the reaction between the carbonate ions and calcium ions

supplied in the feeding solution:

Ca2+

+ CO32-

CaCO3 (2)

When produced in enough quantity, calcium carbonate formed around bacteria present in

the soil pores create bonds connecting the particles. The treated material is therefore a

bonded material, also considered to be an artificially structured material.

Oedometer tests performed on saturated samples of a sandy soil treated with bacteria were

simulated using an elastoplastic constitutive model for bonded materials. The model used,

presented by Gens & Nova [10] is defined based on Cam Clay Model considering the

destructured state as reference case, and a bonding parameter which increases the size of

the yielding surface. This parameter is reduced during loading due to bonds' progressive

failure, simulating damage. This parameter is reduced during loading due to bonds'

progressive failure, simulating damage. The results of similar tests performed on identical

samples not submitted to treatment were used as reference case. Two different definitions

of the bonding parameter were adopted. The first considered the definition for soft rocks

proposed by Gens and Nova [10], in which bonding is defined mathematically. The

second follows the definition proposed by Gajo and co-authors [11], in which bonding is

defined considering explicitly the presence and number of connections.

2. NUMERICAL MODEL

2.1. General definition

In artificially cemented materials stiffness and strength depend on bonds presence, and it is

natural to assume that these mechanical properties will reduce as bonds break during loading.

In this case, the amount of active bonds (bonds contributing to stiffness and strength)

decrease. The limit case is when there are no active bonds, which is the fully destructured

case, or the reference case. In this paper two different definitions of the bonds are adopted, the

first following the definition proposed by Gens and Nova [10], and the second by Gajo et al.

[11]. They are described as follows.

2.2. Bonding parameter defined numerically

Gens and Nova [10] defined a model for soft rocks based on modified Cam Clay Model, in

which bonding is quantified by bonding parameter b. The values of b are limited by b=b0 (the

bonds are intact) and b=0 (fully debonded case). At a fully debonded case volume changes are

free to occur and stiffness for stress changes reaches the minimum value. By adopting

intermediate values of b it is possible to simulate progressive loss of structure, or debonding.

The definition of this parameter is


(3)

with

(4)

where b0, h0, h1 and h2 are constants, and d pand e

are total and volumetric plastic

deformations, respectively.

Based on Modified Cam Clay model, Gens and Nova defined a model in which the size of the

yielding space, controlled by the isotropic yield stress p'c, increases as function of a bonding

parameter b, as shown in figure 1. In this figure the critical state line has slope Mc constant

independently from bonding.

Figure 1. Yielding space proposed by Gens and Nova [10].

The isotropic yield stress of the bonded material p'cb is therefore function of the bonding

parameter b and the isotropic yield stress at the reference state, p'c:

p'cb= (1+b) p'c (5)

The presence of the physical connections made by the bonds justifies the introduction of

tensile strength given by p't,

p't= b p'c (6)

which is function of the isotropic yield stress at the reference state, p'c and a constant . It is

usual to consider ranging between 0.10 and 0.15 [13, 14].

This elastoplastic hardening constitutive model is formulated in the destructured space [10]

and then the yielding stress value is updated in the structured space considering the definition

of the bonding parameter. The model simplifies when defined for isotropic compression

loading, dp'. In this case, the volumetric elastic deformations e, the volumetric total

deformations and plastic volumetric deformations p can be computed as

(7)

q

p'pc' (1+b)pc'bpc' 0

Mc

Mc

reference case

structured case


(8)

(9)

where v is specific volume, is the elastic compression index and is the elastoplastic

compression index.

Finally, the specific volume after loading is computed in the structured space using the

equation of the normal compression line (N is a constant),

(10)

or of the unloading-reloading curve. In both cases, the changes in the elastic and total final

specific volumes, respectively dve and dv, are given by

if p' p'cb

if p'> p'cb (11)

in which the isotropic yielding stress for current bonding p'cb must be defined. The bonding

parameter b defined by Gens and Nova [10] can be simplified to consider only isotropic

compression:

(12)

where d|vp| is the accumulation of plastic volumetric strains and b0 (initial bonding

parameter) and hb are constants calibrated numerically.

The plastic volumetric strains are computed using equation 11, after updating the yielding

stress p'cb using equations 5 and 12. The constants necessary to define the bonding parameter

for this model are two, b0 and hb. Soon the concept of degree of bonding was adapted to

artificially cemented materials [14-16] and will be used in this paper to simulate the

oedometer behaviour of biocemented sands. The constants necessary to define the model for

isotropic compression are in Table 1.

Constant Definition p'c Isotropic yielding stress for the reference case (kPa)

elastic compression index

elastoplastic compression index.

bo Initial bonding parameter hb Constant

Table 1. Constants for the model considering the bonding parameter.

2.3. Bonding parameter considering the geometry of the bonds

The model defined by Gajo et al. [11] is also based on Cam Clay Model and the yielding

space is presented in figure 2. As for the model by Gens and Nova [10], in the model by Gajo

et al [10] there is a reference space representing th behaviour of the destructured material. It


can be seen that tension yielding stress is p'tens and compression yielding stress is p'c + p'comp

are also necessary to define the model. The original version of the model was defined

considering bond loss due to mechanical loading and dissolution, but only the part related

with isotropic mechanical loading is considered, for simplification.

Figure 2. Yielding space proposed by Gajo et al. [10].

Parameters p'comp and p'tens are due to the presence of the bonds and can be computed as a

percentage of the compression and tensile strength of the cement material bonding de grains

(respectively c,cement and t,cement) as follows:

p'comp= ab c,cement (13)

p'tens = ab t,cement (14)

This percentage is given by parameter ab defined for materials with high void ratio as

(15)

where Nba is the number of active bonds per unit volume (a percentage of the total number of

connections Nb) and Rb is the radius of the bond (see figure 3). Nba and Nb are different to

consider that only some bonds are actively contributing to stiffness and strength. In addition,

the model considers spherical particles.

Figure 3 presents the other physical parameters necessary for the complete definition of the

model defined for mechanical loading: Rg is the particle radius (assumed spherical) and Lb and

h are related with the geometry of the bond.

q

p'pc' pc'+p'compp'tens 0

Mc

Mc

reference case

structured case


Figure 3. Bond geometry considered in the model proposed by Gajo et al. [11].

This is a micromechanical approach because the bonds are considered explicitly in the model.

For this model the active bonds affect parameter Nba, which must be updated to consider

increasing amount of bonds mobilized during loading. For isotropic compression, the rate of

this parameter is given by Nba

(16)

where Nba,0 is the initial value, k is a constant and d|vp| is the accumulation of plastic

volumetric strains. This parameter is quite similar to the definition of bonding parameter b

(eq. 12).

This model is closer to the physical loading process but requires the definition of more

constants based on the geometry of the bonds if the complete version of the model is used. So

far, the definition of these parameters is also numerical, although the tendency is to calibrate

them based on digital analysis of tomography images, as it was done by Terzis [17]. This

author was able to reproduce the behaviour of biocemented sands with good results.

Finally, in this paper the parameters necessary for this model are in Table 2.

Constant Definition p'c Isotropic yielding stress for the reference case (kPa)

elastic compression index

elastoplastic compression index.

c,cement Compression strength of the cement material (kPa)

Rb Bond radius (m) Nba,0 Initial number of active bonds per volume (m

-3)

k Constant

Table 2. Constants for the model considering the physical pesence of the bonds.

3. EXPERIMENTAL DATA

3.1 Materials and experimental setup

Oedometer tests were performed on 7 cm diameter and 2 cm height samples prepared with an

uniform graded size river silica sand (D50= 1.20 mm and D10= 0.60 mm and density of the


solid particles Gs= 2.65). Two different kind of samples were prepared: (i) with water and

without treatment, to provide data on the destructured material, and (ii) with bacteria, to

which feeding solution was added to promote the precipitation of biocement. Both kind had

the same void ratio of 0.9 at preparation. The volume of bacteria solution used in sample

preparation is the volume of voids computed with this void ratio, assuming that the material

would be saturated in the oedometer ring.

The bacterial species used is Sporoscarcina Pasteurii, which is non-pathogenic and can be

found in soils. It was supplied by American Type Culture Collection (strain #11859).

Optimum conditions for growing are pH between 8 and 9 and temperature closer to 36ºC. S.

Pasteurii was cultured in a liquid medium composed by 20 g/l yeast extract, 10 g/l of

ammonium sulphate and 0.13 M Tris buffer pH 9.0, at 37°C under aerobic condition, up to a

cell density of 108 cells/mL (optical density at 600nm of 1). The feeding solution was

prepared with 1:10 diluted culture medium supplement (20 g/l yeast extract, 10 g/l of

ammonium sulphate and 0.13 M Tris buffer pH 9.0) with 0.5 M of urea and 0.5 M of calcium

chloride (calcium source).

As presented in figure 3, the treatment with bacteria was done by submersion of the

specimens in the feeding solution. Treatment fluid could circulate from the top to the bottom

because the rings with the material were above a plastic grid [12]. Curing was done for 21

days in a oven at 30°C. This period allowed the occurrence of the chemical reactions for

calcite precipitation.

The two kind of samples were tested in oedometer cells, where stress increment in each step

doubled that of the previous one until reaching 1000 kPa. Data from these tests is used to test

the constitutive models chosen to reproduce the behaviour of artificially bonded soils.

a) b) c)

Figure 3. Experimental setup adopted to treat the samples with bacteria [12]: a ) confinement rings; b) grid

allowing fluid circulation through the samples; c) samples submerged in the feeding solution.

3.2 Experimental curves and data for model calibration

Figure 4 presents the compressibility curves measured in the tests of the samples without

treatment (untreated sand) and after being treated with biocementation (biocemented sand).

The case without treatment corresponds to the destructured material and is the reference case.

The case with the treatment is the structured case, in which bonds are formed by calcium

carbonate. In the computation of isotropic stress it is assumed that radial stress is half the

vertical stress applied in the odometer.


Figure 4. Experimental data.

Experimental data of the untreated material allowed to find the model parameters

presented in Table 3. The parameters found for the untreated material are the model

parameters for the reference case, when b=0 or ab=0.

Parameter Untreated material

(reference case) Biocemented sand

p'c 50 kPa 118 kPa

0.007 0.006

0.019 0.043

N 1.974 2.061

Table 3. Experimental data and model parameters.

4. RESULTS AND DISCUSSION

4.1. Bonding parameter defined numerically

The model proposed by Gens and Nova was used to simulate the oedometer tests of the

biocemented sand. The comparison between the isotropic yielding stress for the untreated

and the cemented material presented in Table 3 allows defining the initial bonding

parameter b0 assuming that there is no bond loss in elastic loading-unloading. In this case,

using equation 5, b0=1.36. These are the constants used to define bonding parameter using

equation 12, assuming hb=0.1. The constants for the reference case were defined before

and are in Table 3. Latter the model was improved using b0=1.0 and hb=0.1. The results

of the simulation are in figure 5, where it can be seen a good adjustment.

1.76

1.78

1.80

1.82

1.84

1.86

1.88

1.90

1.92

1 10 100 1000

spec

ific

vo

lum

e v

isotropic stress p' [kPa]

untreated sand

biocemented sand


a)

b)

Figure 5. Simulation using the model from Gens and Nova [10] using:

a) data from experimental tests; b) data adjusted to improve the simulation .

4.2. Bonding parameter defined considering the geometry of the bonds

Considering now the model proposed by Gajo et al [11], the initial value of ab can be

computed using equation 13, with p'comp being the difference between the biocemented

and reference yielding stresses presented in Table 3 (p'comp= 68kPa). Considering that the

compression strength of biocement is c,biocement=60 MPa [17], equal to the compression

strength of calcite it can be found ab = 0.0011. For particles with 1.2 mm diameter,

assuming Rb=20 m [17], with this ab and using equation 15 it can be found

Nab= 8.56x108 m

-3. This constant was used in equation 16, adopting k=0.1. The results of

the simulation are in figure 6. Because the adjustment was not good, the simulation was

repeated considering ab = 0.0054 and keeping the other parameters constant. The results

of the new simulation are also in figure 6, where it can be seen a better adjustment.

The value of Nab could have been changed considering data on samples preparation, as

total volume, voids ratio and average particles diameter is known. Indeed, the number of

spherical particles in the oedometer samples is 5.82x108. The number of bonds could be

1.76

1.78

1.80

1.82

1.84

1.86

1.88

1.90

1.92

1 10 100 1000

spec

ific

vo

lum

e v


numerical curve

biocemented sand

1.76

1.78

1.80

1.82

1.84

1.86

1.88

1.90

1.92

1 10 100 1000

spec

ific

vo

lum

e v


numerical curve

biocemented sand

b0=1.36 hb=0.1

b0=1.0 hb=0.1


found assuming a coordination number for the particles (varying between 1 and 11 [17]),

and then converted in number of bonds per volume. The number of active bonds per

volume, Nba, would be a percentage of this number of bonds. For the Nab, adopted,

considering that all bonds are active, a coordination number of 1.45 was found. This is a

small value, but still within the values suggested in the literature.

a)

b)

Figure 6. Simulation using the model from Gajo et al. [11] using:

a) data from experimental tests; b) data adjusted to improve the simulation .

4.3. Discussion

Comparing first the number of parameters of the two models, more constants are

necessary for the model defined by Gajo et al [11] than for the model defined by Gens e

Nova [10]. This is because the first requires information on the bonds and particles

geometry, and on the physical arrangement of the particles. These constants can be

difficult to be determined and some are also adjusted numerically. For example, the

coordination number of the grains and the percentage of active bonds considering the total

amount of bonds can be adjusted to define a better Nab. A simple approach was adopted in

1.76

1.78

1.80

1.82

1.84

1.86

1.88

1.90

1.92

1 10 100 1000

spec

ific

vo

lum

e v


numerical curve

biocemented sand

1.76

1.78

1.80

1.82

1.84

1.86

1.88

1.90

1.92

1 10 100 1000

spec

ific

vo

lum

e v


numerical curve

biocemented sand

ab=0.0011 Nab=8.56x10

8 m

-3

k=0.1

Rb= 20 m

c,biocement=60 MPa p'comp= 68 kPa

ab=0.0054 Nab=8.56x10

8 m

-3

k=0.1

Rb= 20 m

c,biocement=60 MPa p'comp= 324 kPa


this paper using available experimental data.

The comparison of the two models (Figs.5b) and 6b)) allows concluding that both are able

to reproduce the behaviour of the biocemented material. However the model from Gens e

Nova [10] appears to be better than the one of Gajo et al [11] in adjusting the transition

between the elastic and elastoplastic behavior. This may be because a simplified version

of the model from Gajo et al [11] was adopted, valid only for materials with high voids

ratio.

6. CONCLUSIONS

The models from Gens and Nova [10] and Gajo et al [11] were adopted to simulate the

mechanical behaviour of biocemented sand under oedometric compression. The first

model only requires the definition of the bonding parameter and destructuring law and is

calibrated numerically. The second model adopts a micromechanical approach and

therefore requires the definition of more constants related with the geometry of the bonds.

The difficulty on calibration will certainly be solved in the future by using optimization

techniques, for example using genetic algorithms. In addition, recent visualization

techniques such as tomography can be used to define intervals for the calibration

parameters. Some contribution can also came from simulations of identical materials

using discrete elements models in which bonds are incorporated.

The two models appear to adjust well the experimental curves, although a simplified

version of the model from Gajo et al [11] was adopted. This confirms that the mechanical

behaviour of biocemented materials can be adjusted using models for artificially

structured materials, where bonds presence and their progressive loss during mechanical

loading are taken into consideration.

ACKNOWLEDGEMENTS

The authors acknowledge Professor Gabriel Monteiro from IBB for helping in bacteria

preparation, and funding from FCT project BIOSOIL, ref. PTDC/ECI-EGC/32590/2017.

REFERENCES

[1] DeJong, JT, Soga, K., Kavazanjian, E., Burns, S., Van Paassen, L. A. , Al Qabany,

A., Aydilek, A., Bang, S. S., Burbank, M., Caslake, L. F.. Chen, C. Y., Cheng, X.,

Chu, J., Ciurli, S., Esnault-Filet, A., Fauriel, S., Hamdan, N., Hata, T., Inagaki, Y.,

Jefferis, S., Kuo, M., Laloui, L., Larrahondo, J., Manning, D.A.C., Martinez, B.,

Montoya, B.M., Nelson, D.C., Palomino, A., Renforth, P., Santamarina, J.C.,

Seagren, E.A., Tanyu, B., Tsesarsky, M. and Weaver, T. (2013). Biogeochemical

processes and geotechnical applications: progress, opportunities and challenges.

Geotechnique, 63: 287–301.

[2] Terzis, D., Bernier-Latmani, R. and Laloui, L (2016). Fabric characteristics and

mechanical response of bio-improved sand to various treatment conditions.

Geotechnique letters, 6(1)

[3] Chu, J., Ivanov, V., Stabnikov, V (2013). Microbial method for construction of

aquaculture pond in sand. Géotechnique, 63: 871–875.


[4] Salifu, E., MacLachlan, E., Iyer, K.R., Knapp, C.W. and Tarantino, A. (2016).

Application of microbially induced calcite precipitation in erosion mitigat ion and

stabilisation of sandy soil foreshore slopes: A preliminary investigation.

Engineering Geology, 201: 96–105

[5] DeJong, J.T., Fritzges, M.B, Nusslein, K. (2006). Microbially induced cementation

to control sand response to undrained shear. J. Geotechnical and Geoenvironmental

Engineering,132: 1381-1392.

[6] Montoya, B. M., DeJong, J., Boulanger, R. (2013). Dynamic response of

liquefiable sand improved by microbial-induced calcite precipitation,

Geotechnique, 63 (4): 302–312.

[7] Latil, M.-N., Van der Zon, W., Lehnen, C., Ineke, E., Marcelis, F., Van Eijden, J.,

Baaijens, T., Baaijens, T. Bol, G. (2008). Environmental friendly technology for

biological sand-consolidation of oil and gas wellbore, Proc. 1st Bio-Geo Engng

Conf., Deltares:. 82–89.

[8] Van Paassen, L., Ghose, R., van der Linden, T., van der Star, W. & Van

Loosdrecht, M. (2010). Quantifying Biomediated Ground Improvement by

Ureolysis: Large-scale Biogrout Experiment. J. Geotechnical and

Geoenvironmental Engineering, 136: 1721-1728.

[9] Gomez, M., Martinez, M., DeJong, J.T., Hunt, C. de Vlaming, L. Major, D.

Dworatzek, S. (2015). Field-scale bio-cementation tests to improve sands. Ground

Improvement, Proceedings of the Institution of Civil Engineers, ICE , 168 (3): 206-

216.

[10] Gens A. and Nova R. (1993). Conceptual bases for a constitutive model for bonded

soils e weak rocks. Geotechnical Engineering of Hard Soils – Soft Rocks, Balkema,

Rotterdam, pp. 485-494.

[11] Gajo, A., Cecinato, F. and Hueckel, T. (2015). A micro-scale inspired chemo-

mechanical model of bonded geomaterials. International Journal of Rock

Mechanics e Mining Sciences, 80, pp. 425-438.

[12] Pires, I. (2016). Effect on soil biocementation of the presence of fines. MSc Thesis.

Instituto Superior Técnico, Universidade de Lisboa, Portugal (in Portuguese)

[13] Consoli, N., Cruz, R., Floss, M. e Festugato, L. (2010). Parameters controlling

tensile e compressive strength of artificially cemented sand. Journal of

Geotechnical e Geoenvironmental Engineering, v. 136, pp. 759-763

[14] Cardoso, R., Ribeiro, D e Néri, R. (2017). Bonding effect on compressive e tensile

strength of sand-cement mixtures. Soils e Foundations, 57, pp. 655–668.

[15] Rios, S., Ciantia, M., Gonzalez, N., Arroyo, M, e Viana da Fonseca, A. (2016).

Simplifying calibration of bonded elasto-plastic models. Computers e Geotechnics,

73, pp. 100-108.

[16] Ribeiro, D. (2017). Prediction of the hydro-mechanical behaviour of jet grouting

columns. PhD Thesis. Instituto Superior Técnico, Universidade de Lisboa,

Portugal.

[17] Terzis, D (2017). Kinetics, Mechanics e Microstructure of Bio-cemented soils. PhD

Thesis, Ecóle Polytechnique Federale de Lausanne, Suiça.

modelling oedometer tests on biocemented soils …

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