REASERCH REPORT NO - UTCB - Școala doctoralăsd.utcb.ro/_upload/content/docs/1566_carastoian_andreea_-_raport... · REASERCH REPORT NO.3 ... unsaturated parameters or laws, application

THE TECHNICAL UNIVERSITY OF CIVIL ENGINEERING, BUCHAREST

THE FACULTY OF HYDROTECHNICS

REASERCH REPORT NO.3

MODELLING THE EFFECT OF UNSATURATED

PROPERTIES IN SLOPE STABILITY

ANALYSIS

By Ph.D.Student

Eng. Andreea CARASTOIAN

Research Supervisor

Prof.Ph.D.eng. Loretta BATALI

2014 - 2015


Modelling the effect of unsaturated properties in slope stability analysis

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Contents

1. INTRODUCTION............................................................................................................ 3

2. UNSATURATED SLOPE STABILITY ANALYSIS .......................................................... 3

2.1. Unsaturated phi-b method ....................................................................................... 4

2.2. Unsaturated Fredlund method ................................................................................. 5

2.3. Unsaturated Vanapalli method ................................................................................ 6

2.4. Unsaturated Vilar method ........................................................................................ 6

2.5. Unsaturated Khalili method ..................................................................................... 6

3. CASE STUDY ................................................................................................................ 7

3.1. General description ................................................................................................. 7

3.2. Geotechnical characteristics .................................................................................... 8

3.3. Site activity .............................................................................................................. 8

3.4. Laboratory activity ..................................................................................................12

3.5. Slope stability analysis ...........................................................................................17

3.6. Synthesis of analyses results .................................................................................31

3.7. Steps ......................................................................................................................31

4. CONCLUSIONS ............................................................................................................31



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1. INTRODUCTION

The third report presents the problem of considering the unsaturation of soils above water

table in the slope stability analysis, condition for obtaining realistic results in both cases of

rainfall infiltrating into the soil mass and drainage for improving soil stability.

It presents in its first part a brief review methods related to unsaturated stress analysis

applied for slope stability analysis, such as Unsaturated phi-b, Unsaturated Fredlund,

Unsaturated Vanapalli, Unsaturated Khalili and Unsaturated Vilar model. These methods

are estimating in different manners the shear strength depending on soil unsaturated

conditions.

These methods are applied in the second part of the report in a case study, presenting a

site affected by landslides located in Cluj-Napoca, Romania. For the slope stabilization a

siphon drain system has been proposed and installed. An experimental program started

and is ongoing on site, compromising site monitoring of suction using jet fill tensiometers

and laboratory testing. Site measurement of suction in presence of drainage system was

used for perform slope stability analyses using SVSlope software and the embedded

methods for estimating the increase in soil shear strength when passing from saturated to

unsaturated state.

2. UNSATURATED SLOPE STABILITY ANALYSIS

Slope stability analysis is a common element in the designing process of civil engineering

projects. There are several possibilities for performing a slope analysis, for example:

- limit equilibrium methods (LEM) based on slice discretization of the soil mass, assuming

various geometrical forms for the slip surface. As these are largely implemented into the



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engineering practice, they have been subject of evolution in the last years as introduction of

unsaturated parameters or laws, application of modern optimization techniques based on

genetic management of computations, multiple wedge analysis etc. (Tran, C., Srokosz, P.,

2012);

- numerical methods using displacement-based finite element method (FEM), using various

constitutive models, enabling to calculate the progressive failure and safety using "phi-c

reduction" or "shear stress reduction" techniques;

- Limit analysis approaches based on lower and upper bound theorems of classical

plasticity (Tran, C., Srokosz, P., 2012);

- Variation methods;

- Probabilistic methods; etc.

For taking into account the soil shear strength modification due to suction evolution, several

methods are available and implemented in commercial software. We will refer to and later

apply some of the methods included in SVSlope software, which are estimating in different

manners the shear strength depending on unsaturated soil conditions. These are:

Unsaturated Phi-b, Unsaturated Fredlund, Unsaturated Vanapalli, Unsaturated Khalili and

Unsaturated Vilar model. (SVOffice 2009 )

2.1. UNSATURATED PHI-B METHOD

The Unsaturated phi-b method defines the parameter ϕ� as the angle defining the increase

in shear strenght for an increase in matric suction(u� − u�). The unsaturated shear

strenght angle varies between 0 and ϕ′. Fredlund and al. (Fredlund, D.G., Morgenstern,

N.R. and Widger, R.A., 1978) proposed the following equation, as the failure criterion for an

unsaturated soil, expressed in terms of two stress state variables, the net normal stress

(σ − u�) and the matric suction (u� − u�)(Figure1.).

τ = c′ + (σ� − u�)tanϕ′ + (u� − u�)tanϕ

� (1)

where: τ - shear strenght; c′ - effective cohesion; σ - total normal stress; u� - pore air

pressure; u� - pore water pressure; ϕ� - unsaturated shear strength angle.



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2.2. UNSATURATED FREDLUND METHOD

The Unsaturated Fredlund method requires the entry of the soil-water characteristic curve

(SWCC - Figure 2.), depending on the volume of water present in the soil at a particular

suction level.

(a) Unsaturated Soil Mechanics - planar envelope; (b) Saturated Soil Mechanics

Figure 1: Modified Mohr-Coulomb Shear Strength Envelopes (Fredlund, D.G., 2005)

Figure 2: Typical soil-water characteristic curve (Fredlund, D.G., Xing, A., 1994)



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2.3. UNSATURATED VANAPALLI METHOD

The Unsaturated Vanapalli method depends also on the soil-water characteristic curve.

Based on Fredlund and Xing equation (2), Vanapalli and Fredlund proposed a more general

non-linear function, for modeling the strength contribution of unsaturated soil using SWCC.

� = �� ′ + (�� − ��)��′] + [(�� − ��) (Θ!)(�� ′)"# (2)

where: k - the fitting parameter used for obtaining a best-fit between the measured and

predicted values; $ - the normalized water content. Later, Vanapali et al (Vanapalli,S.K.,

Fredlund,D.G., Pufahl, D.E. and Clifton, A.W., 1996) have proposed a modified equation (3)

without using the fitting parameter, k.

� = %� ′ + (�� − ��)��′] + [(�� − ��) &('()'*'+)'*

)(�� ′),- (3)

where: .� - the volumetric water content; ./ - the saturated volumetric water content; .0 -

the residual volumetric content.

2.4. UNSATURATED VILAR METHOD

The Unsaturated Vilar method is not dependent on the soil-water characteristic curve as

Fredlund's and Vanapalli's methods. This method allows defining a maximum cohesive

strength. Rohn and Vilar (Rohn,S.A., Vilar, O.M., 1995) proposed the following equation:

c(ψ) = c′ + ψ

�1�ψ (4)

where: �(2) - the maximum cohesive strength; c' - the effective cohesion; a and b - fitting

parameters solved by SoilVisionSlope.

2.5. UNSATURATED KHALILI METHOD

The Unsaturated Khalili method allows the modeling of the strength contribution of

unsaturated soils. Khalili and Khabbaz (Khallili, N., Khabbaz, M.H., 1998) have extended

Bishop's equation as follows:

� = �� ′ + (�� − ��)��′] + [(�� − ��) (3)(��′)"# (5)

where: 4 - parameter depending on saturation grade, values between 0 and 1. An empirical

formula has been suggested for the parameter 3:



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4 = &(56)5()7(56)5()8

,)9,;;

(6)

where, (�� − ��)< is the matric suction at failure conditions.

All these methods will be applied for the following case study.

3. CASE STUDY

3.1. GENERAL DESCRIPTION

This case study presents a site affected by landslides located in Cluj-Napoca city, in center

of Romania (figure 3). The project to be developed on the site is an industrial park.

Figure 3: Satellite view on Cluj-Napoca site

The site has approx. 80 ha and it is located on Hoia hill, on its Northern side, hill which is

affected by numerous instability phenomena on approx. 15 % on the surface, while other 25

% have high instability potential. The slope of the hill in the site area is 12°. Geotechnical

investigations performed in the area concluded that the main cause of instability

phenomena is the excess pore-water pressure due to both rainfall infiltration and

groundwater.



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Existing landslides were classified as shallow ones, their maximum depth reaching 4 – 5 m.

The preliminary analysis performed for design purposes showed possible instability for

seismic conditions (the site is characterized by a design seismic ground acceleration ag =

0.1g) without drainage measures.

Therefore, a drainage system based on siphon drain network was designed and lately

implemented.

3.2. GEOTECHNICAL CHARACTERISTICS

Table 1 presents the main geotechnical parameters of the strata. borehole data. Ground

water was found at -5.20 m.

Table 1: Geotechnical data

Characteristics

Man-

made fill

(1.00m)

Silty Clay

(3.10 m)

Sandy

Clay

(1.60 m)

Green-Brown

Loam (1.70

m)

Grey

Sandston

e

(1.10 m)

Marl

(1.90 m)

Water content, w(%) 17.42 18.78 16.22 16.85 16.54 20.92

Plasticity index Ip(%) 17.14 19.73 20.04 19.48 28.18

Unit weight γ (kN/m3) 17.25 18.00 20.00 19.00 22.00 19.83

Consistency index, Ic 0.9 1.05 1.05 1.06

Saturation degree, Sr 0.54 0.65 0.54 0.65 0.64 0.87

Oedometric modulus

M2-3 (daN/cm3) 46.83 70.14 107.18 114.34 88.79 109.58

ϕ (°) 7 10 11 15 34 12

c (kPa) 10 14 15 40 55 73

3.3. SITE ACTIVITY

An experimental research program has been implemented for this site consisting of:

- 3 boreholes (figure 4) of 1.70 m depth for monitoring the vadose zone;



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Figure 4: Tensiometers position on site - detail

Figure 5: Site photo. - Borehole no.1




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- 3 jet fill tensiometers were installed in the boreholes at depth varying from 1.3 to 1.70,

in order to monitor suction values before and after siphon drains installation (see fig.

4 and table 2);

In the following table are presented the values recorded by the tensiometers.

Table 2: Geotechnical data

Date Suction [centi bar] Meteo Observations

28.02.2015 0 S - instalation

03.03.2015 7.5 kPa S + Pp

12.03.2015 6 kPa Pp

18.03.2015 7 kPa S

23.03.2015 7.5 kPa S

30.03.2015 0 Pp

13.04.2015 5 kPa S

07.05.2015 8 kPa S - drainage system on

03.06.2015 9kPa Pp

30.06.2015 8.5 kPa S

22.07.2015 12 kPa S

12.08.2015 20 kPa S - drought

03.09.2015 18.5 kPa Pp - last value

Note: S - sunny; Pp - rain

It is concluded that the maximum value for suction in "perfect" condition as, dryness

and drainage system on it was 20 kPa.



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Figure 8: Values registered with tensiometers



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In the following figure is presented the measured suction values, as recorded by

tensiometers.

Figure 9: Measured grand water table and suction values

It can be seen that the maximum suction recorded with drainage system in function was of -

20 kPa, compared to -7.5 kPa before its installation. This conclusion is not a final one, as

monitoring should be continued and further conclusion will be drawn.

3.4. LABORATORY ACTIVITY

Next pictures present laboratory activity using Sandbox. This can be used to apply a range

of pressure from pF 0 (saturation) to pF 2.0 (-100hPa).

The results of measurements taken with this sandbox correspond with points on the drying

curve of the relevant samples (decreasing pressure).



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Figure 10: SandBox - Colentina laboratory, UTCB

Figure 11: Sample on 1.70 m depth



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Figure 12: Sample soil

Figure 13: Nylon cloth fixed to the bottom side of the sample with an O-ring



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Figure 14: Water-saturated sand

Figure 15: Soil sample placed in the sandbox

The soil used for this laboratory program is clay and therefore the samples needed to stay

in the sandbox to be saturated for 2 weeks.

After saturation, it was applied a pressure of -2.5 cm head and leave it to reach the

equilibrium for one week.



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3.5. SLOPE STABILITY ANALYSIS

For the conceptual understanding of the phenomena, five scenarios were analyzed:

1. initial state, with ground water table at 5.20 m bgl, static conditions.

2. initial state, as above, seismic conditions.

3. saturated slope, presumably after rainfall with ground water table at 1.00 m,

static conditions.

4. saturated slope as scenario 3, seismic conditions.

5. siphon drains in function, including maximum measured suction, seismic

conditions and ground water table at -8.50 m bgl.

For all scenarios were performed slope stability analyses using SVSlope software - various

methods (as describe above) for estimating unsaturated soils shear strength and also 6

analysis methods (Fellenius, Bishop, JanbuS, Spencer, Fredlund’s GLE and Sarma). The

slope model is shown below (fig.16):

Figure 16: Slope model



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Next are presented the results of slope stability analysis using the GLE - Fredlund for Step

1 - the slope in the initial state, with the ground water table at 5.20 m depth - using Mohr-

Coulomb method

Figure 17. Step1 - static - GWT=-5.20m - Fos = 1.106 - MohrCoulomb method



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The result of slope stability using the GLE - Fredlund for Step 2 - using Mohr-Coulomb

method:

Figure 18. Step2 - dynamic - GWT=-5.20m - Fos = 0.885 - MohrCoulomb method

It can be observed the influence of dynamic forces.



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method:

Figure 19. Step3 - static - GWT=-1.00m - Fos = 1.009 - MohrCoulomb method



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method:

Figure 20. Step4 - dynamic - GWT=-1.00m - Fos = 0.808 - MohrCoulomb method



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method:

Figure 21. Step5 - dynamic - drainage system on - Fos = 1.181 - MohrCoulomb method



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After analyzing the slope stability for this case it can be observed that the stability factor is

below the limit, as it is an active landslide. Therefore, beside drainage system solution,

were implemented also other type of measures to assure the stability, as retaining walls

and piles.

The aim of this program it is to observe the effectiveness of drainage system in combination

with unsaturated properties.

Below are presented the results using suction values equal to 20 kPa, value registered on

the site. Phi-b Method, Fredlund Method, Vanapalli, Vilar and Khalili Methods are used .

a) Phi-b Method

This method requires introducing the internal friction angle value for unsaturated soils, Øb.

Input condition is that the value Øb is less than the internal friction angle. J Krahn proposed

a simplified formula of this parameter, being half the effective of internal friction angle. In

the analyses presented suction value was taken constant at 20 kPa.

Figure 22: Phi-b parameter value



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Figure 23. Step5 - dynamic - drainage system on - Fos = 1.22 - Unsaturated phi-b method



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b) Fredlund Method

The method depends on the characteristic soil-water curve, using the Fredlund and Xing

(1994) soil-water curve values.

Figure 24: Experimental values

Figure 25: Characteristic soil-water curve, according to Fredlund and Xing



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Figure 26. Step5 - dynamic - drainage system on - Fos = 1.216 - Unsaturated Fredlund method



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c) Vanapalli Method

The method depends on the characteristic soil-water curve, using the Fredlund and Xing,

1994.

Figure 27: Experimental values

Figure 28: Characteristic soil-water curve, Fredllund and Xing



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Figure 29. Step5 - dynamic - drainage system on - Fos = 1.257 - Unsaturated Vanapalli method

d) Vilar Method

The method doesn't depend on soil water-characteristic curve, but rather allows defining a

maximum cohesion, higher than the effective cohesion.



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Figure 30. Vilar parameters

Figure 31. Step5 - dynamic - drainage system on - Fos = 1.25 - Unsaturated Vilar method



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e) Khalili Method

Figure 32. Khalili parameters

Figure 33. Step5 - dynamic - drainage system on - Fos = 1.25 - Unsaturated Khalili method

3.6. SYNTHESIS OF ANALYSES RESULTS

For a clear conclusion about the methods, the results were summarized in the next table.

3.7. STEPS Static

Dinamic

Method Fellenius Bishop Janbu

S

Spencer GLE Sarma

Step 1 Static Mohr-Coulomb 1,086 1,104 1,081 1,111 1,106 1,104

Step 2 Dynamic Mohr-Coulomb 0,868 0,886 0,865 0,889 0,885 0,883

Step 3 Static Mohr-Coulomb 0,988 1,009 0,987 1,015 1,009 1,009



Step 5 Dynamic Phi-b 1,207 1,217 1,192 1,226 1,220 1,218

Step 5 Dynamic Fredlund 1,203 1,213 1,188 1,222 1,216 1,215

Step 5 Dynamic Vanapalli 1,245 1,254 1,229 1,263 1,257 1,256

Step 5 Dynamic Vilar 1,238 1,247 1,221 1,256 1,250 1,248

Step 5 Dynamic Khalili 1,247 1,255 1,230 1,264 1,258 1,257

4. CONCLUSIONS

The results reflect the importance of using the parameters of unsaturated soils in slope

stability analysis. The existing cracks in the ground and seasonal variations of humidity lead

to rapid infiltration of water, modifying the mechanical properties of the soils. Using the

unsaturated methods, applying a constant suction value we can see an improvement for the

factor of safety.

The most favorable method is the method Khalili.

Considering the unsaturated properties of soils above water table in slope stability analyses

allow to obtain more realistic results and to assess the efficiency of methods such as

drainage. However, the availability of all unsaturated parameters is scarce and in the large

majority of cases designers prefers to perform analyses only in saturated conditions for

obtaining the minimum possible value of the global safety factor. Or, if unsaturation cannot

be avoided, as in presence of drainage, designers need a simple method for estimating the



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shear strength parameters in unsaturated conditions. Databases, included or not in

commercial software can, of course, be useful. Some methods are now available for

estimating the increase in shear strength due to increasing in suction.

The report has reviewed briefly the available methods and then applied them for a case

study. In the case study an unstable slope has been consolidated using mainly drainage

measures (siphon drains), whose efficiency was assess using suction measurement on site

and by re-evaluating the slope stability based on measured suction value and on

introducing estimated shear strength parameters for unsaturated soils.

Stability analyses performed using 6 different and current methods of analysis and also 5

specific unsaturated methods, using SVSlope software, showed for the studied case that

improvements of the slope stability was obtained. Drainage has proven to be effective and

leading the slope into a marginal safety domain, which can demand further consolidation

measures. Anyhow, consideration of only drawdown of water table couldn’t correctly model

the real situation.



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