### Leal-Vaca J.C.

*Facultad de Ingeniería*

*Universidad Autónoma de Querétaro, México*
*E-mail: jcesarlealv@hotmail.com*

### Gallegos-Fonseca G.

*Facultad de Ingeniería*

*Universidad Autónoma de Querétaro, México *
*E-mail: gfonseca@uaslp.mx,*

### Rojas-González E.

*Facultad de Ingeniería*

*Universidad Autónoma de Querétaro, México *
*E. mail: erg@uaq.mx*

## The Decrease of the Strength of Unsaturated Silty Sand

*Disminución de la resistencia de una arena limosa no saturada*

Information on the article: received: January 2009, reevaluated: September 2009, accepted: March 2012
**Abstract**

It is generally considered that the shear strength of fine soils continuously increases with suction; however, this is not the case for all types of soils. There are some soils whose strength reaches a maximum at certain suction and then reduces with further of suction. Nevertheless, such cases have not been completely documented and analyzed. This paper presents the results of a series of suction controlled triaxial tests made on silty sand. The tests were made for both the wetting and the drying path. Suction was controlled by circulating air at a constant relative humidity. The retention curve was also obtained for the wetting and the drying path. The variation of cohesive stress was determined using some of the existing equations and the solid-porous model proposed by Rojas (2008a y 2008b). These equations include Bishop’s χ parameter, evaluated theoretically and experimentally. The triax-ial tests results show that the strength of the soil increases to a maximum at certain suction and then decreases when suction is further increased.

**Resumen**

*Generalmente se considera que la resistencia cortante de los suelos finos se incrementa *

*con la succión; sin embargo, esto no ocurre para todos los tipos de suelos. Existen *
*al-gunos suelos cuya resistencia alcanza un máximo para cierta succión y luego se *
*redu-ce para valores mayores de succión. No obstante, tales casos aún no se han *
*documen-tado y analizado completamente. Este artículo presenta una serie de pruebas triaxiales *
*con succión controlada realizadas en una arena limosa. La succión se controló *
*median-te circulación de aire con humedad relativa constanmedian-te. Las pruebas triaxiales se *
*hicie-ron en trayectorias de humedecimiento y secado. La curva de retención también se *
*ob tuvo para ambas trayectorias. Se determinó la variación del esfuerzo cohesivo *
*utili-zando algunas de las ecuaciones existentes y el modelo sólido-poroso propuesto por *

**Ro-Keywords**

• unsaturated soils

• silty sand

• effective stress

• strength

• triaxial test

• retention curve.

**Descriptores**

• *suelos no saturados*

• *arena limosa*

• *esfuerzo efectivo*

• *resistencia*

• *prueba triaxial*

**Introduction**

The interest on the mechanics of unsaturated soils has recently increased because many engineering projects deal with these types of soils. It is known that the volu-metric and strength behavior of saturated soils is con-trolled by the effective stresses ( ').σ However, in the case of unsaturated soils, there is still controversy re-garding the existence of an effective stress equation that may explain the volumetric and strength behavior of these materials.

Bishop (1959) proposed an effective stress equation for unsaturated soils which generated a lengthy contro-versy which to this day is still ongoing. This equation follows

### (

### )

*a* *a* *w*

*u* *u u*

σ′= −σ +χ − (1)

where σ’ is the effective stress, (σ−*ua*)is the net stress,
(*u ua*− *w*)is the suction andχ is Bishop’s parameter. The
product χ

### (

*u ua*−

*w*

### )

represents the cohesive stress. Onedrawback of Bishop’s equation is that a method or equation for the precise determination of the value of parameterχhas not been established. Bishop’s equation was questioned because it could no predict the phenom-enon of collapse upon wetting once the soil was dried and loaded above the preconsolidation pressure (Jennings and Burland, 1962). Many other equations have been pro-posed (Garven and Vanapilli, 2006). Some of these equa-tions are as follows: the two first equaequa-tions were proposed by Vanapalli et al. (1996), the third equation was proposed by Oberg and Sallfours (1995), and the fourth equation belongs to Khalili and Khabbaz (1998).

( )*Sw* κ

χ= (2)

(*S _{w}*

*S*) / (1

_{r}*S*)

_{r}χ= − − (3)

*w*
*S*

χ= (4)

### (

### )

### (

### )

0.55

*a* *w*

*a* *w b*
*u u*
*u u*
χ
−
_{−}
=
−

(5)

where *Sw*is the degree of saturation; *Sr*is the residual

degree of saturation;

### (

*u ua*−

*w b*

### )

is the air entry value; and κ is a fitting parameter that varies with the plasticity in-dex (Vanapalli et al., 2000). However none of them is ad-equate for all types of soil and for all range of suction.The shear strength is dependent of the effective
stress, and one of the most well known equations to
de-termine the shear strength was proposed by Fredlund
*et al. (1978), who believes that the cohesion varies with *
the suction along the constant inclination angle_{ϕ}*b*_{. This }

equation is written as

## (

## )

' ( ) tan ' tan *b*

*ff* *c* *ua f* *u ua* *w f*

### τ

= +### σ

−### ϕ

+ −### ϕ

(6)where

### τ

*is the shear strength;*

_{ff}*c*'is the effective cohe-sion; (

### σ

−*u*) is the net normal stress state on the fail -ure plane at fail-ure; ϕ'is the angle of internal friction associated with the net normal stress state variable,

_{a f}(

### σ

−*u*) ;

_{a f}## (

*u u*−

_{a}

_{w f}## )

is the matric suction on the failure plane at failure; and_{ϕ}

*b*

_{ is the angle indicating the rate }

of increase in shear strength relative to the matric suc-tion,

## (

*u u*−

_{a}

_{w f}## )

.Murray (2002) presented an equation of state for un-saturated soils. He developed an analysis considering the enthalpy within a soil system under equilibrium conditions. His equation is the following:

' _{1}

*c*
*t*

*p*
*q M _{s}*

**

_{s}= _{} − _{}+ Λ

(7)

where

*q* is the deviator stress,

*s* is the suction,
'

*c*

*p* is the average volumetric coupling stress,

*t*

*M* is the total stress ratio, and

Λ is the intercept on the *q s*axis at *p sc*' =1.

However, the above equation is indeterminate when the
soil is completely saturated, with*s*=0.

The investigations of the unsaturated soil strength
are few; there are some low suctions from 0 to 50 kPa
(Kumara and Uchimura, 2006). The results indicate
these investigations as in the saturated soils where the
angle _{ϕ}'_{remains constant.}

Experimental results seem to indicate that the
strength of some soils reaches a maximum and then
de-creases with further inde-creases in suction. These early
results have been reported only for specimens
previ-ously saturated, and increasing the suction by draining,
without considering the differences between drying
and wetting paths (Pereira et al., 2006). However, these
results do not show a clear tendency and raise some
other questions, for example, does the cohesive stress
reduces to zero for a completely dry soil, and the
*maxi-jas (2008a y 2008b). Estas ecuaciones incluyen al parámetro χ de Bishop, evaluado teórica *

mum strength can be observed only at drying, or does it also appear at wetting. In the case of clays with large specific surface, the physico-chemical forces and the adsorbed water play an important role in the soils be-havior. For these types of soils the strength reduction at high suctions has not been experimentally observed (Rojas, 2006). In that sense, it is necessary to carry out more experimental work on this issue in order to better understand the behavior of unsaturated soils and fi-nally to improve the expressions related to the strength of these materials for all the range of suctions.

Rojas (2008a) developed a solid-porous model based on the analysis of stress on the skeleton of an unsatu-rated soil showing a bimodal structure, and proposed that Bishop’s equation can be written as

* *s* *u*(1 *s*)

*i* *nti* *s f* *Sw* *f*

σ =σ + _{} + − _{} (8)

where

*_{i}

σ _{ represents the equivalent stress in the direction }_{i}

and is related to the stress that supports the phase solid of soil in that direction,

*nti*

σ represents the net stress in the direction *i*,

*s* is the suction,

*s*

*f* represents the saturated fraction of the soil,

*u*
*w*

*S* is the degree of saturation of the unsaturated
frac-tion.

Equation (7) can be rewritten as

*_{i}_{nti}*s*

σ =σ + χ _{ } _{(9)}

with

(1 )

*s* *u* *s*
*w*

*f* *S* *f*

χ= + − (10)

and

(1 )

*u* *s*

*f* = − *f* , the unsaturated fraction of the soil. (11)

Rojas’s model answers some of the above questions,
which is the reason to use it for theoretical analysis of
shear strength behavior in terms of cohesive stress.
Soils with bimodal structure means that its distribution
of pores has two different types of elements: the
macro-pores, which are very large pores and the sites which
include the mesopores and micropores. The model is
built in a regular network where the nodes represent
the pores and their connections represent the bonds.
The model is based on realistic assumptions that allow
simulating the soil-water retention curve (SWRC) in
wetting and drying. This model is capable of describing
the distribution of the water inside the pores of a soil,
and hence, it can be used to obtain the parameters _{f}s

and *u*
*w*

*S* that cannot be determined in the laboratory
(Rojas, 2008b).

It is necessary to have an experimental base to de-velop a model capable of describing the behavior of soils comprising the whole range of suctions. Develop-ing a model only for low suctions would be incomplete for understanding their total behavior from the theo-retical point of view.

The objective of this paper is to experimentally ob-serve and measure the decrease of strength on unsatu-rated silty sand and do a comparison of the strength with some existing equations. For this purpose series of triaxial tests using controlled suction were performed on samples of silty sand.

**Materials and methods**

The soil used for the experimental program came from Valle de Santiago, Mexico. This soil was classified as silty sand. The grain-size distribution curve for the soil is shown in Figure 1, and its index properties are sum-marized in Table 1. It is noteworthy that this soil does not show any clay content.

Table 1. Index properties and grain sizes of soil

% Gravel % Sand % Silt % PI Gs USCS 0.00 79.00 21.00 No plastic 2.43 SM where Gs is the specific gravity of solids

The soil was initially dried at room temperature (20°C +/- 1°C) and all particles larger than 2 mm (sieve No. 10) were removed. The remaining soil was divided in two equal parts. One half was washed using a No. 200 sieve; Figure 1. Grain-size distribution of soil tested. This soil

then both, the washed half and the unwashed half were mixed together again. Enough water was added to ob-tain 19.53% moisture content. The mixture was used to make soil specimens by static compaction. All specimens were fabricated in five layers. The soil for each layer was weighed (0.70 N) and placed in a cylindrical mould. Then the layer was statically compacted at a maximum stress of 3140 KPa. With these samples an experimental program was utilized to define the retention curve of wetting and drying paths, as well as the strength of the soil at different suctions following both the wetting and drying path. In order to determine the retention curves, the following procedure was applied: two sets of com-pacted specimens of silty sand were prepared; all sam-ples in the first set were dried at different water contents so as to obtain the drying path. For the wetting path, all the samples of the second set were completely dried in an oven and then they were re-hydrated at different wa-ter contents by spraying varying amounts of wawa-ter on them. The amount of water was controlled by using a scale. All these specimens were placed in hermetic con-tainers and their suction was measured with the filter paper method in controlled temperature ambient (20°C + 1°C) according to the test method D 5298-9403 of the American Society for Testing and Materials (Annual book of ASTM STANDARDS, 2004). The filter paper used in these tests was the Schleicher and Schuell No. 589. This paper was previously calibrated also according to the same standardized ASTM procedure. The results of the calibration procedure are shown in Figure 2, and include a correlation equation.

Other soil specimens were tested in a suction con-trolled triaxial apparatus to examine the effects of the drying and wetting on the strength of the material.

**Testing procedure**

All triaxial tests were performed on samples showing the following characteristics: 50 mm in diameter and

100 mm in height, a dry density of 14.89 KN/m3_{ and a }

gravimetric water content of 19.53%. Specimens used for the wetting and drying path were prepared in the same way as those used for the retention curves. Dur-ing the tests, suction was kept constant by circulatDur-ing an atmosphere of a saline solution of NaCl placed in a container outside the triaxial cell. The circulation of the air was maintained by using a peristaltic pump specifi-cally designed for fluid transfer.

The pumping rate was fixed at 15 rpm, correspond-ing to a flow rate of 8.81 ml/min through a polyvinyl chloride pipe with an internal diameter 3.16 mm. The pump circulated the relative humidity of the container from the bottom to the top of the specimen throughout the shearing process. Figure 3 shows a schematic view of the triaxial apparatus with the suction system.

**Results and discussion**

Shear behavior

The results of the triaxial tests done at a confining stresses of 150 KPa are presented in Figure 4. This fig-ure shows the deviator stress at failfig-ure versus the de-gree of saturation. The arrows in Figure 4 indicate the trajectories of the drying and wetting processes. It was observed that the strength of the material is less during wetting than during drying. In both curves the strength increases with suction up to a maximum and then de-creases.

The figure shows the behavior of the resistance indi-cated for the deviator stress versus the degree of satura-tion. The arrows in the figure indicate the humidifying Figure 2. Calibration of filter paper Schleicher and Schuell No. 589

and drying process trajectories. Figure 5 shows the de-viator stress as a function of the suction of the soil. Some values of suction were checked with the filter pa-per method. These graphs indicate that the deviator stress is greater during drying than wetting for suctions over 980 KPa. For suctions lower than 980 KPa this be-havior is not maintained. Therefore, the way in which water distributes into the pores of the soil influences its strength.

The figure shows the behavior of the resistance
indi-cated for the deviator stress versus the suction. The
ar-rows in the figure indicate the humidifying and drying
process trajectories It was determined the angle of
in-ternal friction of soil in consolidated drained triaxial
tests used for this purpose were saturated and five
specimens were tested, the angle was 39.25 °, obtained
graphically from the Mohr circles, shown in Figure 6.
Figure 7 shows the results of those tests saturated
tri-axial through *p q*'− diagrams. In these diagrams *p*' is
calculated with equation (12).

1 2 3 ' ( ' ' ' ) / 3

*p* = σ σ σ+ + (12)

Considering the angle of internal friction and the
re-sults of the unsaturated specimens shown in Figure 5,
was determined the variation of cohesion with suction.
For this a tangent line was searched with inclination of
39.25° in the Mohr circle for each of the specimens
test-ed, under confinement of 150 kPa, and was projected
onto the plane τ−*s*, thus the ordinate in this plane
rep-resents cohesion. This is shown in Figure 8 for the
tra-jectory of wetting and in Figure 9 for the tratra-jectory
drying. The variation of cohesion with respect to the
suction is shown in Figure 10.

We can observe in Figure 10 that in the drying path, the cohesion has a maximum value greater that wetting path. In both trajectories it was obtained that cohesion was not changed by a constant angle with the variation of suction, and shows greater variation in the trajectory of drying. Wetting trajectory maintains a slope reaching its maximum cohesion of 28.84 kPa with 1169.87 kPa of suction, but then changes this trend for higher values of suction. These results of soil testing shows that equa-tion (6), proposed by Fredlund et al. (1978), is not valid for this soil (SM) tested.

Figure 4. Behavior of the triaxial tests consolidated drained (CD) for silty sand

Figure 5. Behavior of the triaxial tests consolidated drained (CD) for silty sand

Figure 6. Results of triaxial (CD) of saturated specimens and determination of the angle of internal friction

The variation of cohesion and deviator stress for the soil tested can be explained as follows:

a) the strength increases to a certain value when the soil is wetted due to the formation of meniscus that contribute to the shear strength, then this strength is lost because saturation increases and decreases the number of meniscus,

b) in the path of drying, the number of meniscus increas-es when the soil driincreas-es which contribute to the increase of strength to a maximum value, then this maximum value begins to decrease the number of meniscus which is reflected in the consequent loss of strength. The way in which water is retained in the pores of a soil and with respect to the suction can be represented by the SWRC. Figure 11 shows the SWRC at wetting and drying. This curve shows the relationship between the water content and the matric suction of the soil. The

SWRC shows different curvatures indicating that soil has a complex pore sizes distribution. Because the SWRC depends on the pore size distribution of the soil, it is sensitive to changes of confining stress. This effect could not be measured, because the triaxial cell was not equipped with suction measuring devices or mini-probes.

As shown in Figure 11 for any degree of saturation the curve of water retention in the drying process has higher values of suction wetting curve. In the drying curve, it can be observed that large water losses occur for smaller values at 2100 kPa suction coming to have a de-gree of saturation of approximately 17.5%. To drain the water after the suction value, greater amounts of energy are required to reach a saturation level close to zero, it takes about 1,000,000 kPa suction. In the curve of wetting the ground path were initially tested in a state of high suction, close to 670 000 kPa, and when it starts wetting the degree of saturation is increased slowly to values of suction on the order of 850 kPa for a degree of saturation of approximately 14.0%, for lower values of this suction the degree of saturation increases more rapidly.

Figure 8. Representation of the results of triaxial tests in unsaturated conditions (CD) in the wetting trajectory, and determination of cohesion

Figure 9. Representation of the results of triaxial tests in unsaturated conditions (CD) in trajectory drying and determination of cohesion

Figure 10. Variation of cohesion with suction for drying and wetting trajectories obtained from triaxial tests with controlled suction

**Theoretical results**

Trying to describe exactly a three-phase porous media is quite complicated, for this composition would require at least including a wide range of sizes of solids, mil-lions of pores, their interaction with water, and the con-tacts between solid particles. Rojas’s model is a computational tool that relates the three phases of soil and considers their behavior hydromechanical. This model is formed by four elements: sites or cavities, mac-ropores, bonds and solids. The sites represent the pores of medium to small size. The macropores are the largest pores in the soil and differ from the sites in that the for-mer shrink with increasing suction. The bonds are ele-ments that link together two sites. The solid-porous model that simulates the processes of wetting and dry-ing, is able to reproduce the hydraulic hysteresis oh the SWRC and shrinkage of the macropores. The network model can be elementarily represented in the Figure 12.

In the model, it is necessary to determine the number of
nodes in the network, then the number of macropores,
sites, bonds, and solids for each size. In this case
poro-simetry was proposed to reproduce the SWRC and the
experimental particle size distribution. All nodes in the
network are assigned to a pore size. In general the
number of macropores is usually smaller than the
num-ber of sites. Nevertheless, volumes are similar. In the
case of solids, the process is similar from granulometric
analysis. Once the number of elements in each size has
been defined, the sites and bonds are placed on the
net-work at random. Later proceed to place the macropores
and to place the solids so that in areas where there are
small pores, they will be surrounded by small particles
and vice versa. The pores filled with water and dried
are governed by Laplace equation (13), which involves
the surface tension of the contractile skin( )*T _{s}* .

2 cos /

*a* *w* *s* *c*

*u u*− = *T* α *R* (13)

where*Rc*, the critical radius of the meniscus of the

con-tractile skin; corresponds to the maximum pore size
that remains saturated for some suction(*u ua*− *w*), and

αis the solid meniscus contact angle.

The drainage of pores will occur when the pore size
is greater than *Rc* and one of its bonds that connect to

it is drained or dry. The drying process is to consider the network completely saturated and the suction is zero. After suction is modified in a small increase and this leads drainage of macropore or sites located in the periphery of the network, and the process continues only when the tubules connectors to those pores are dry. This process yields the drying SWRC curve gov-erned by the tubules connectors.

The saturation of pores will occur if the pore size is
less than or equal to *Rc* and one of the connectors is

saturated. During the process of wetting it is consid-ered that initially the nodes or pores are dry and the suction is high, then the suction is reduced and smaller tubules at the periphery of the network are filled with water. Later, to continue the process for sites that are connected to those saturated tubules, they should be filled with water. This process yields the wetting SWRC curve that is controlled by the distribution of sites and macropores.

The distributions used for sites, macropores, and solid bonds are normal distributions. These distribu-tions are defined by two parameters: arithmetic mean and standard deviation. This will require as input into the model the mean radius and standard deviation of sites, macropores, solid, and bonds.

Figure 13 shows the pore distribution (PSD) used; for its proposal, the experimental observations made by Simms and Yanful (2001) were considered. They ob-served that pore volume related to the pore size showed Figure 12. Representation of the porous-solid network

two peaks. According to the above, the two peaks or crests can be seen in Figure 13. The first of these crests, the one located at approximately 0.38 μm, corresponds to smaller pores. The other crest (located at approxi-mately 950 μm) corresponds to the macropores. The solids distribution (SD) is shown in the same figure; it presents its crest at approximately 100 μm. The param-eters used for their distributions were the following:

Table 2. Parameters used in the model: mean radius and standard deviation

Crest Mean radius (μm) Standard deviation

First crest (PSD) 0.0075 4

Second crest (PSD) 1.2 6

Crest (SD) 1 4.5

With the previous PSD model, the SWRC was deter-mined. This curve is shown in Figure 14, the points are experimental measurements and the full line curves are

fitted by the model. The size of solids experimental and theoretical distribution is shown in Figure 15. Slight differences can be observed between these two curves, especially for the larger sizes.

With the value of all parameters defined, it is
possi-ble to simulate a wetting and drying process and define
the values of the parameters (1_{−}* _{f}u*)

_{ and }

*u*

*w*

*S* for different
de-grees of saturation. These parameters are shown in
Figures 16 and 17. The volume of the saturated fraction
(1_{−}* _{f}u*)

_{ is obtained by adding the volume of solids }completely surrounded by water to the volume of voids surrounding these solids.

With the experimental information obtained concern-ing the shear strength and the porosimetry proposed, which reproduces the SWRC, it is possible to evaluate the Bishop’s parameter χ using equation (10) proposed by Rojas (2008a). The theoretical and experimental re-sults are shown in Figure 18.

Figure 14. Theoretical soil-water retention curve (SWRC) and experimental points for silty sand obtained in the drying and humidifying processes

Figure 15. Experimental solid size and model fit

Figure 16. Representation of the unsaturated soil fraction versus the degree of saturation, obtained from the model

The best results are presented in low degrees of
satura-tion. This is because at low degrees of saturation volume
changes are minor and the degree of saturation is
influ-enced by changes in volume. Some differences in the final
results of _{f}s_{ can be expected, and therefore also of the }

resistance since the processes of wetting and drying of the solid-porous model are developed by invasion. That is, to move water or gas continuity in the phases is required. This means that a site or a bond cannot be invaded if at least one adjacent element has not been invaded.

Finally the soil resistance can be calculated. With
the values of parameter (1_{−}* _{f}u*)

_{ and }

*u*

*w*

*S* already defined, it is
possible to obtain the cohesive stress of the soil. The
cohesive stress is the product *s*χin equation (9).
Theo-retical and experimental values of *s*χ for drying and
wetting paths are shown in Figure 19. In this figure, the
product *s*χ, considering *s*from SWRC and the
param-eter χ, was calculated using equations (2), (3), (4) and
(5). The same figure shows the theoretical result set
ob-tained with the model equation (10).

In developing Figure 19 the value of κ=1.6 in equa-tion (2) was used. The residual degrees of saturaequa-tion were obtained from the SWCR in Figure 11, with 0.04 for the path of wetting and 0.0325 for the path of drying.

Theoretical and experimental values of cohesive stress are greater in the drying process that in the pro-cess of wetting.

The equations to better approximate the
experimen-tal values are equations (2) and (3) of Vanapalli *et al.*
(1996) in the wetting trajectory; in this case the values of
the model are lower than the experimental values. In
the trajectory of drying, the equation with values closer
to the experimental values is equation (2) of Vanapalli
*et al. (1996) and the theoretical results of the model are *
closer to the experimental values from 5% degree of
saturation on.

Engineering practice is still using relationships that provide values of shear strength of unsaturated soils that differ from the actual values. This is because the evaluation of effective stress involved in them has not been done properly. Uncertainties are mistakenly ab-sorbed into problems of stability or load capacity in safety factors, but this leads to not really know the mar-gin of safety with respect to the ultimate strengths.

Understanding the shear strength of this type of soil will affect the safety of engineering structures; to support this assertion simply check that each year during the rainy season landslides occur on slopes that affect struc-tures. These facts account for lost lives and major eco-nomic damage left, this occurs because geotechnical designs do not consider the behavior of unsaturated soils.

**Conclusions**

It has been experimentally verified that the strength of
silty sand reaches a maximum and then reduces with
suction for both the wetting and drying path.
There-fore, the angle *ϕb*_{ is not constant for the tested soil and }
depends on the path of wetting or drying.

Theoretical and experimental values of cohesive stress are greater in the drying process than in the pro-cess of wetting.

The extension of the conclusions from this soil to other soil types should take into consideration the influ-ence of soil composition and stress history soil behavior. There are no equations that can predict the behavior of Figure 18. Theoretical and experimental values of χ for

trajectories of wetting and drying of silty sand (SM)

the shear strength of all soils. Therefore, not only are more experiments necessary, but also the extension of the theoretical developments of unsaturated soils.

**Acknowledgements**

The authors are grateful to the Universidad Autonoma de Queretaro, Mex., for the facilities rendered to use the laboratories.

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**About the authors**

*Julio César Leal-Vaca. Civil Engineer, obtained his M.Sc. degree in 1998 in engineering in the area of *
Mecha-nics of Soils. He is a professor in the Engineering Faculty of the Universidad de Guanajuato, Mexico,
since 1999. At present He is a Ph. D. student at the Universidad Autónoma de Querétaro.

*Gustavo Gallegos-Fonseca. Civil Engineer, obtained his M.Sc. degree in 2002 in engineering in the area of *
Me-chanics of Soils. He is a professor in the Engineering Faculty of the Universidad Autónoma de San Luis
Potosi, Mexico, since 1993.

*Eduardo Rojas-González. Professor and researcher in the Engineering Faculty of the Universidad Autónoma *
de Querétaro, Mexico.

**Citation for this article:**

**Chicago citation style**

Leal-Vaca, Julio C., Gustavo Gallegos-Fonseca, Eduardo
Ro-jas-González. The Decrease of the Strength of Unsaturated
Silty Sand. *Ingeniería Investigación y Tecnología XIII, 04 (2012): *
393-402.

**ISO 690 citation style**