Influence of Relative Density on Static Soil–Structure Frictional Resistance of Dry and Saturated...

ORIGINAL PAPER

Influence of Relative Density on Static Soil–StructureFrictional Resistance of Dry and Saturated Sand

Binod Tiwari • Ahmed Raad Al-Adhadh

Received: 26 July 2013 / Accepted: 18 December 2013

� Springer Science+Business Media Dordrecht 2013

Abstract Soil–structure frictional resistance is

required while designing foundation systems and

retaining walls. Although much more attention has

been paid in recent years regarding soil–structure

interaction for dynamic loading, highly conservative

values of the static frictional resistance between soil

and structure are used in design. Not much emphasis

has been given lately to evaluate static frictional

resistance between soil and structure. In this study, a

well graded sand, as per USCS classification system,

was prepared in the laboratory at different relative

densities and moisture contents i.e. dry and saturated,

and frictional resistances of those soils were measured.

Those soil samples were also sheared against wood,

concrete, and steel blocks and corresponding soil–

structure frictional resistances were measured. More-

over, similar experiments were performed for satu-

rated and loose poorly graded sand (SP), silty sand

(SM) and poorly graded sand with silt (SP–SM). The

study result shows that the difference between

frictional resistance of soil and skin friction depends

on the type of soil, relative density and the moisture

content. Interestingly, shear envelopes for soil–soil

and soil–structure shearing resistance exhibited cur-

vature. The traditionally adopted soil–structure

frictional resistance values adopted by various geo-

technical manuals were found to be highly

conservative.

Keywords Interface friction �Wood �Concrete � Steel � Sand � Relative density �Saturation

1 Introduction

Shear strength of the interface between soil and

structural material is important while designing var-

ious geotechnical structures including deep founda-

tions such as pile and drilled shaft, shallow

foundations such as spread footing and mat, retaining

wall, sheet pile etc. However, not many research

articles are available regarding the recommended soil–

structure shearing resistance. Majority of the designs

are based on empirical values i.e. ratio of skin friction

or adhesion to the internal friction or cohesion of

foundation soil. In current geotechnical engineering

practice, the soil–structure friction or the skin friction

values recommended by the NAVFAC EM 7.02 (US

Department of Navy 1986) has been widely used.

Early work of Potyondy (1961) has been cited by

many articles in the literature as well as design

manuals in order to estimate the design skin frictional

resistance. Potyondy (1961) conducted a research to

measure the ratio of skin friction and adhesion with

soil friction and cohesion, respectively. He conducted

B. Tiwari (&) � A. R. Al-Adhadh

Civil and Environmental Engineering Department,

California State University, Fullerton, 800 N State

College Blvd, E-419, Fullerton, CA 92831, USA

e-mail: [email protected]

123

Geotech Geol Eng

DOI 10.1007/s10706-013-9723-6

direct shear test on the interface of concrete, steel, and

wood with sand, sandy silt, cohesive soil, rock flour

(called it as silt), and clay. Potyondy (1961) conducted

tests for certain pre-set moisture contents as well as for

dry specimens and concluded that frictional resistance

of a soil depends on the proportion of sand in it. He

also proposed ratios for design frictional resistance of

construction materials with soil that ranged from 0.4

for saturated loose sand to 1.0 for saturated dense sand.

It is interesting to note that the values of skin frictional

resistance recommended by NAVFAC EM 7.02 are

much lower than the values reported by Potyondy

(1961). Moreover, NAVFAC recommendations are

too general in terms of type of soil to be considered.

Coyle and Sulaiman (1967) investigated the frictional

resistance between sand and steel pile, whereas

Kulhaway and Peterson (1979) measured the frictional

resistance between sand and concrete. Several other

researchers such as Evgin and Fakharian (1996),

Hryciw and Irsyam (1993), Uesigi et al. (1988) and Hu

and Pu (2004) conducted direct shear tests on the

interface between steel or concrete and sand to

measure the interface frictional resistance. Other than

the direct shear device, Paikowsky et al. (1995)

developed a dual interface apparatus whereas Yoshimi

and Kishida (1981) developed a ring shear device to

measure interface frictional resistance for a larger

deformation.

Although there are numerous literature that

reported the interface frictional resistance of soil and

construction material, Potyondy (1961) was the only

literature that shows a significant amount of experi-

mental study on soil–structure interface. As explained

earlier, Potyondy (1961) did comprehensive study to

measure the frictional resistance (or skin friction)

between soil–steel, soil–wood, and soil–concrete for

dry and saturated sand. He measured the secant

frictional resistances (i.e. ratio between shear and

effective normal stress) for two different effective

normal stresses and observed that the secant frictional

resistance between soil and structure decreases with an

increase in effective normal stress. However, the

results presented by Potyondy (1961) seem to have

encountered several issues that mainly control the

shearing behavior between the soil–structure inter-

face. These issues include possibility of having degree

of saturation of soil less than 100 %, possibility of

error due to small size shear box as he used square

shear box with 50 mm internal dimension, possibility

of linear interpolation errors as the tests were done for

two effective normal stresses only, and the possibility

of having partially drained situation as the structural

materials did not have drainage holes. Later, Al-

Mhaidib (2006) evaluated the displacement rate effect

on skin friction of steel–sand interface. He observed

that skin friction increases with an increase in

displacement rate. Likewise, Tiwari et al (2010)

measured the skin frictions for the interface of steel,

wood, and concrete with SW, SM, SP–SM, MH, ML,

and CL materials prepared at the void ratio of 0.7 and

observed that concrete shows higher skin friction

compared to wood, whereas the skin friction between

wood–soil interface was higher than that between the

steel–soil interface. Gireesha and Muthukkumaran

(2011) measured soil–structure skin friction between

soil and different structures for SW and SP materials

that were prepared at three different relative densities

in a 50 mm 9 50 mm size shear box and proposed the

relationship between relative density and skin friction.

However, they did not mention actual values of

relative densities except the relative density of 50 %.

Laskar (2011) did studies on the skin friction between

structures with different roughness coefficients and

sand at the relative density of 85 % and proposed

relationships between surface roughness and skin

friction of sand. Although studies have been done

frequently to evaluate the skin friction for major

construction materials (Bosscher and Ortiz 1987;

Boulon 1989; Hong and Hua 1995; Hsieh and Hsieh

2003; Lui et al. 2005; Liu et al. 2009; O’Rourke et al.

1990; Subba Rao et al. 1988; Uesugi and Kishida

1986; Wang and Richwien 2002), there is a lack in

systematic study to evaluate the effect of void ratio/

relative density, saturation, and effective stress on the

skin friction between soil and construction materials.

This study shows an innovative approach to eval-

uate the skin friction between various construction

materials and different types of sands for different

compaction conditions (relative density) and moisture

contents, in addition to different effective normal

stresses. It is to be noted that there are six different

classifications for sand as per the Unified Soil

Classification System (USCS) i.e. SW, SP, SC, SM,

SP–SC, and SP–SM. To evaluate the effect in almost

all classes of sand, skin frictional resistances were

measured for SP, SM, and SP–SM materials after a

comprehensive study was conducted on the SW

material. Evaluations pertinent to the effects of

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saturation and relative density on skin frictional

resistance of SP, SM, and SP–SM materials were not

performed due to time shortage. A significant

improvement was made in the experimental set-up

and preparation of soil and construction materials in

this study, compared to the methodologies previously

reported in the literature.

2 Materials and Soil Testing Method

2.1 Soil Material

To evaluate the effects of moisture and relative density

on skin frictional resistance of soil and structural

materials, an angular well-graded sand (SW) was used

for this study. SW material was preferred in this study

due to its preferred acceptability as foundation mate-

rial. The sand was obtained from a stack of fine

aggregate materials used for concrete. The grain size

distribution of the material used is presented in Fig. 1.

Specific gravity, effective size, mean size, uniformity

coefficient, coefficient of curvature, maximum void

ratio, and minimum void ratio of the SW material were

2.65, 0.16, 0.85, 7.5, 1.05, 0.85, and 0.48 mm,

respectively. This sand was compacted at different

relative densities to prepare samples at different

compaction states. To evaluate the skin frictional

resistance between soil and structural materials in SP,

SM, and SP–SM materials, loose and saturated

samples were prepared for these sands. The SP

material was obtained from a stack of Ottawa Sand

(standard sand). Specific gravity, maximum void ratio,

and minimum void ratio of the sand were 2.66, 0.92,

and 0.51, respectively. Likewise, SM and SP–SM

materials were prepared by mixing appropriate pro-

portion of kaolinite in SW material and SP materials,

respectively. The liquid limit and plasticity indices of

the kaolinite used in this study were 72 and 41 %,

respectively. Please note that moisture contents less

than the one corresponding to the degree of saturation

of 100 % (except dry samples) were not considered in

this study because shearing at partially saturated

conditions involve suction, which makes the analysis

relatively complex. Total number and types of tests

conducted for this study are presented in Table 1.

2.2 Structural Materials

For the evaluation of interface frictional resistance

between soil and structures, three types of building

materials were prepared—(a) plain concrete, (b) steel,

and (c) wood. Steel used for this study was prepared in

the lab from a metal sheet. Five holes of 5 mm

diameter were made in the steel block, as presented in

Fig. 2a to facilitate drainage during consolidation and

shearing phases. Please note that these drainage holes

had had negligible effect on the shearing resistance of

the soil–structure interface. The concrete used in this

study was prepared in the lab using aggregates and

cements identical to that used in the concrete piles

(Fig. 2b). Five lubricated nails of appropriate size

were used during pouring of concrete to make smooth

holes of 5 mm diameter for drainage purpose, as

explained earlier. The wood used in this study was cut

from a wooden plank available in the Home Depot

(Fig. 2c). The drainage holes of 5 mm diameter were

made smoothly in the wooden block, in a similar

manner as in the steel. Shearing in wood was applied

parallel to the grain. The size of all structural materials

were 100 mm 9 100 mm 9 6.25 mm, which is

exactly same as the size of the opening of lower box

of the direct shear device used for this study. It is

desirable to prepare these materials at different

roughness. However, comparison of skin frictional

resistance for different roughness coefficients of the

structural materials is not the scope of this study.

2.3 Soil Testing Method

A fully automated direct shear device was used for this

study. Size of both the upper and lower shear boxes

Fig. 1 Grain size distribution curves of the SW, SP, SM, and

SM–SM materials used in this study

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Table 1 Total number and types of tests conducted for this study

Soil type Interface Relative

density (%)

Normal stresses (kPa) Dry Saturated

50 100 200 300

SW Soil 95 X X X X X X

Concrete 95 X X X X X X

Steel 95 X X X X X X

Wood 95 X X X X X X

Soil 68 X X X X X X



Wood 68 X X X X X X

Soil 40 X X X X X X



Wood 40 X X X X X X

Soil 14 X X X X X X



Wood 14 X X X X X X

SP Soil 10 X X X * X

Concrete 10 X X X * X

Steel 10 X X X * X

Wood 10 X X X * X

SM Soil 10 X X X * X


Steel 10 X X X * X

Wood 10 X X X * X

SP–SM Soil 10 X X X * X


Steel 10 X X X * X

Wood 10 X X X * X

* 150 kPa was used instead of this stress

Fig. 2 Materials used for this study as structural materials: a Steel, b Concrete and c Wood blocks

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was 100 mm 9 100 mm 9 6.25 mm each (Fig. 3a).

Please note that this shearing area is four times larger

than the area used by Potyondy (1961) and Gireesha

and Muthukkumaran (2011). Vertical displacement,

horizontal displacement, and shear force were

recorded automatically in separate data acquisition

channels through vertical linear variable differential

transformer (LVDT), horizontal LVDT and load cells,

respectively. The loading arm in the device is set in

such a way that a 10:1 mechanical advantage can be

achieved in the normal stress. First, the lower box of

the direct shear device was completely blocked with

the building materials (Fig. 3b), i.e. concrete, steel and

wood. In order to prepare soil samples with 14 %

relative density, SW material of calculated dry weight

corresponding to 14 % relative density (that was

calculated based on specific gravity, target void ratio,

minimum void ratio, and maximum void ratio of the

soil) was obtained in a bowl. Then, the entire mass was

divided into three equal proportions. The 6.25 mm

total height of the upper shear box was divided equally

into three equal heights and marked inside the box by

ink. One-third portion of the soil was poured into the

shear box and compacted with a wooden tamper

uniformly until the compacted soil layer was leveled

with the first one-third height mark. Then, the second

and the third layers were also sequentially compacted

in a similar manner. In this way, the uniformity of soil

sample for required relative density was ascertained.

The soil samples corresponding to the relative densi-

ties of 40, 68, and 95 % were also prepared in a similar

manner by utilizing the corresponding dry weights of

the soil sample. These relative densities, correspond-

ing to the void ratios of 0.8, 0.7, 0.6, and 0.5, are the

characteristics of very loose to loose, medium dense,

medium dense to dense, and very dense sands,

respectively. The compaction process and the shear

boxes are presented in Fig. 3. To compare the skin

frictional resistance with the shear strength of soil,

shear strength of soil specimens were also measured

by removing the construction material block from the

lower box, filling the SW, SP, SM, and SP–SM

materials (as appropriate) in both upper and lower

shear boxes, and compacting to the required relative

densities in three equal layers, as explained earlier. All

tests for the SW materials were conducted for two

extreme moisture conditions: (a) dry, and (b) fully

saturated. To maintain the fully saturated condition,

the sample was submerged in distilled water for more

than 6 h and was sheared under fully submerged

condition. Then, the soil samples were consolidated

until the primary consolidation was completed. The

shearing rate was, first, calculated based on required

time for the attainment of the primary consolidation,

as explained in the ASTM D 3080-04. However, the

samples were sheared at the shearing rate five times

slower than the calculated shearing rate to be in a

conservative side in order to accommodate the possi-

bility of slower drainage at the lower half of the box.

The method specified by ASTM for the drained direct

shear test (ASTM D-3080-04) was followed during

shear testing. The computer software used for the test

can capture the data and plot the real time consolida-

tion curves as well as the stress-displacement curves.

For each specimen, tests were done at least for four

different normal stresses (50, 100, 200, and 300 kPa)

for most of the samples. Two identical samples,

prepared as explained earlier, were tested for each

testing condition. For samples having inconsistent

results in those identical specimens, additional con-

firmative tests were performed. Average values of two

closest results obtained from two (or three) identical

samples and tests are reported in this paper. The same

procedure was repeated several times to measure the

frictional resistance of soil at the interface of concrete,

steel, and wood by blocking the lower shear box with

the respective materials. The experimental set up is

presented in Fig. 3d.

After completion of direct shear tests on SW

materials with the test set-up explained earlier, SP,

SM, and SP–SM materials were tested. These mate-

rials were exactly same materials tested by Tiwari

et al. (2010). However, samples were prepared at an

initial relative density of 10 % (i.e. loose state) and

fully saturated condition. The soil testing procedure

was exactly same as the procedure explained above for

the SW materials.

3 Test Results and Analysis

3.1 Soil Test on SW Material

3.1.1 Stress-Displacement Results

Shown in Fig. 4a–d are the shear stress-horizontal

displacement as well as vertical deformation–hori-

zontal deformation curves for the dry and saturated

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soil samples, respectively, initially compacted at the

relative density of 14 %. As expected, the shear stress-

horizontal displacement and volume change behavior

exhibited the behavior of loose sand or contractive

material. Failure condition was assumed after the

sample exhibited distinct peak or more or less constant

shear stress for more than 0.25 mm of displacement.

However, due to the capacity of the shear testing

device, tests had to be stopped at the horizontal

displacement of 7.1 mm. All samples except one

sample showed failure stress prior to 7.1 mm of

displacement. For that specimen, shear stress at

7.1 mm of horizontal displacement was assumed to

be the peak shear stress. Peak shear stresses were

observed at the shear displacement of 4–7 mm for

loose sand and 2–5 mm for dense sand. Dry and

saturated soil exhibited similar pattern in shear stress-

horizontal displacement relationship. However, dry

soil generally exhibited higher shear strength com-

pared to the saturated soil, except for low relative

density and low effective stress. Shown in Fig. 5 are

the shear stress-horizontal displacement curves for the

loose sand (with relative density of 14 %) sheared at

the effective normal stress of 300 kPa for dry and

saturated conditions. As expected, dry sample exhib-

ited higher shear stress compared to the saturated

sample. Figure 6 depicts the shear envelopes for dry

and saturated SW materials tested at the relative

density of 40 %. As expected, the dry sand had higher

shear strength compared to the saturated sand for all

effective normal stresses. However, the difference was

higher for higher values of normal stress. Please note

that, the shear envelopes did not exhibit straight line

type regression. Almost all sand samples exhibited

curvature in the failure envelopes. The details about

those curvatures will be discussed later.

Fig. 3 Soil testing method used in this study; a Lower and upper box of the direct shear device used for this study; b Photograph of

lower shear box, filled with the structural material; c Compaction process; d Experimental set-up of the direct shear device

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Fig. 4 Shear stress-horizontal displacement curve for SW material initially compacted at the relative density of 14 %; a Dry sample;

and b Saturated sample

Fig. 5 Comparison for the shear stress-horizontal displacement

curves for dry and saturated SW materials compacted at the

relative density of 14 % and sheared at the effective normal

stress of 300 kPa

Fig. 6 Effective shear envelopes for dry and saturated SW

materials compacted at the relative density of 40 %

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3.1.2 Effect of Relative Density on Shear Strength

of Sand

Presented in Fig. 7a, b are the shear stress—horizontal

displacement curves for the sand tested at different

initial relative densities (ranging from 14 through

95 %) at the effective normal stress of 300 kPa.

Similar trend was observed while the soils were tested

at other normal stresses as well. As could be observed

in Fig. 7, dense sand exhibited dilation and peak shear

stress was obtained earlier than the loose sand. For

loose sand, peak shear stresses were observed at the

shear displacement of 4–7 mm, whereas the dense

sand exhibited the peak shear stress at the shear

displacement of 2–5 mm. These behaviors were

similar irrespective of whether the sand was dry or

saturated. Although it would be beneficial to know the

value of the critical state void ratio of the soil, it was

not measured.

3.1.3 Effect of the Type of Interface Material on Shear

Strength of Soil

The main objective of this research was to evaluate the

soil–structure interface shearing resistance for SW

material at different relative densities and dry as well

as saturated conditions, as well as loose and saturated

SP, SM, and SP–SM materials. Shear envelopes for

the interface between soil and concrete, wood, and

steel for the loose SW material i.e. relative density of

14 % are presented in Fig. 8. Figure 8a shows the

shear envelopes for dry soil–structure interfaces and

Fig. 8b shows the shear envelopes for saturated soil–

structure interfaces. As can be observed in Fig. 8a, a

significant reduction was observed in the interface

shearing resistance compared to the shearing resis-

tance of soil. The highest reduction was observed for

soil–steel compared to soil–concrete and soil–wood

interfaces. Soil–concrete interface exhibited lowest

reduction. This finding concurs with the findings

reported in the literature (Potyondy 1961; Gireesha

and Muthukkumaran 2011). This observation is true

both for dry and saturated sand. The detailed discus-

sion on the reduction in shear strength will be

discussed later.

3.1.4 Relationship Between Linear Regression

Friction Angle and Void Ratio

First, change in linear regression friction angle with

the change in relative density was observed. The

change in linear regression friction angle with the

relative density for dry and saturated soil samples are

presented in Fig. 9a, b, respectively. As can be

observed in Fig. 9, the values of linear regression

friction angle increased with an increase in relative

density in all cases. However, the effect was signif-

icant on the soil–soil friction and soil–concrete

friction. The effect was negligible for soil–wood and

soil–steel interface, although soil–wood interface

showed slightly higher friction angle compared to

soil–steel interface. The relationship explained above

is true for both dry and saturated sand.

Fig. 7 Shear stress-horizontal displacement curves for the SW materials compacted at different relative densities and sheared at the

effective normal stress of 300 kPa; a Dry soil; and b Saturated soil

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3.1.5 Effect of Effective Normal Stress on the Shear

Stress of Soil

The curvature of the shear envelope can be clearly

observed in Fig. 6. First, secant frictional coefficients

(shear stress/effective normal stress) were measured at

all effective normal stresses to evaluate the changes of

friction angles with normal stresses. Shown in Fig. 10

are the changes in effective friction ratios with

effective normal stress for both dry and saturated

sands prepared at the relative density of 40 %. Similar

charts were prepared for other samples as well.

However, they could not be presented here due to

space limitation. As can be observed from Fig. 10,

there were consistent drops in secant friction

Fig. 8 Shear envelopes for the soil–soil and soil–structure interfaces for the SW materials compacted at the relative density of 14 %;

a Dry soil; and b Saturated soil

Fig. 9 Variation in the linear regression friction angles with the relative densities for the SW materials; a Dry soil; and b Saturated soil

Fig. 10 Variation in secant frictional coefficients for the SW

materials compacted at the relative density of 40 %

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coefficients with normal stress. This shows that a

curvilinear failure envelope could be fitted to evaluate

the shear strength. A second order parabola (Eq. 1)

with zero cohesion was fitted into all 32 shear

envelopes, prepared for the SW material.

sr0¼ a� r0 þ b ð1Þ

where, ‘‘s’’ represents shear stress in kPa, ‘‘r0’’represents effective normal stress in kPa, ‘‘a’’ repre-

sents coefficient that quantifies curvature (negative

values shows concave downwards), and ‘‘b’’ repre-

sents average slope (when there is no curvature) or

slope at the effective vertical stress close to zero (when

curvature is present). The values of ‘‘a’’, ‘‘b’’ and

regression coefficient (R2) for all 32 cases of shear test

are presented in Table 2. The values of a, b, drop in

shear stresses for different materials and relative

densities as well as different moisture conditions will

be discussed below. The value of regression coeffi-

cient (R2) for dry and saturated soils ranged from

0.935 to 1 with an average of 0.994, and 0.994 to 1

with an average of 0.998, respectively. This shows that

the regression type has been appropriately chosen.

3.1.6 Relationship Between Secant Friction Angle

and Relative Density

In order to incorporate the effect of curvature in the

shearing resistance or friction angle of soil for

cohesionless soil and normally consolidated soil,

friction angles are generally expressed in terms of

secant friction angle, i.e. tan-1(peak shear stress/

effective normal stress), for specified normal stresses.

In this study, curves described by Eq. (1) were fitted

into all 32 shear envelopes and the corresponding

values of ‘‘a’’ and ‘‘b’’ were calculated and presented in

Table 2. Corresponding values of shear stress at a

particular normal stress can be calculated using Eq. (1)

for the data presented in Table 2. The ranges of values

of secant friction angles for the effective normal stress

of 100 kPa, secant friction angles corresponding to

‘‘b’’ values, and the ratio of soil–structure interface

friction and soil–soil friction angles for both dry and

saturated SW materials are presented in Table 3.

Table 3 also incorporates the range of the ratios of

secant friction angles for dry and saturated samples.

Using the ‘‘a’’ and ‘‘b’’ parameters presented in

Table 2, secant friction angles were calculated for

Table 2 Values of curvature parameters ‘‘a’’ and ‘‘b’’ and corresponding regression coefficients ‘‘R2’’ for tested soil samples

Interface Relative

density (%)

Dry Saturated

a b R2 a b R2

Soil 95 -0.0011 1.4042 0.999 -0.0018 1.5697 1.000

Concrete 95 -0.0010 0.8651 0.999 -0.0007 0.7956 0.997

Steel 95 -0.0012 0.7465 0.970 -0.0006 0.7255 1.000

Wood 95 -0.0004 0.6553 0.997 -0.0011 0.7981 0.995

Soil 68 -0.0001 1.2750 0.999 -0.0011 1.3859 1.000

Concrete 68 -0.0007 0.7570 0.994 -0.0008 0.7681 1.000

Steel 68 -0.0001 0.7056 1.000 -0.0003 0.7120 0.994

Wood 68 -0.0007 0.6828 0.980 -0.0002 0.6834 0.997

Soil 40 -0.0004 1.0969 1.000 -0.0017 1.3007 1.000

Concrete 40 -0.0006 0.6159 0.935 -0.0000 0.6504 0.989

Steel 40 -0.0001 0.5662 1.000 -0.0010 0.7490 1.000

Wood 40 -0.00000 0.5897 0.996 -0.0000 0.6452 0.999

Soil 14 -0.0004 0.9603 1.000 -0.0009 0.9716 0.990

Concrete 14 -0.0000 0.6977 0.999 -0.0000 0.5692 0.997

Steel 14 -0.0004 0.6305 0.997 -0.0000 0.5688 1.000

Wood 14 -0.0003 0.6881 0.999 -0.0003 0.6598 1.000

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0.7

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.75

92

2.2

15

1.0

36

1.0

43

Geotech Geol Eng

123

the effective normal stress of 100 kPa, while present-

ing the values in Table 3. Secant friction angles were

calculated for all other effective normal stresses using

the parameters ‘‘a’’ and ‘‘b’’. However, they are not

presented here due to space limitation. Secant friction

angles were also calculated when a = 0 and are

presented in Table 3. Generally, secant friction angles

are calculated for the effective normal stress of

100 kPa because normalization of shear stress with

atmospheric pressure is quite common in geotechnical

engineering practice. Atmospheric pressure is close to

100 kPa. Figure 11a, b shows the values of secant

friction angle for the effective normal stress of 100 kPa

for soil–soil and soil–structure interfaces for dry and

saturated sand, respectively, tested at different relative

densities. As observed in Fig. 11, there was a signif-

icant increase in secant friction angle with an increase

in relative density for both dry and saturated sands.

However, the effect was small in the soil–structure

interface. Dry samples did not exhibit a significant

effect of relative density in the soil–structure interface

friction for relative densities higher than 40 %.

Using the data presented in Table 2, % reduction in

secant friction angle at different effective normal stresses

were calculated and compared with the corresponding

values of relative densities. The reduction in secant

friction angle is calculated by using Eq. (2).

% reduction ¼ /soil�soil � /soil�structure

/soil�soil

� 100 ð2Þ

where, % reduction is % reduction in secant friction

angle at the effective normal stress of 100 kPa,

/soil–soil is the secant friction angle at the effective

normal stress of 100 kPa for soil–soil shearing,

/soil–structure is the secant friction angle at the effective

normal stress of 100 kPa for soil–structure interface.

Variation in the reduction in secant friction angle

(at the effective normal stress of 100 kPa) for soil–soil

and soil–structure interface for dry and saturated sand

(compared to soil–soil secant friction angle) with the

relative density of soil are presented in Fig. 12a, b,

respectively. Although the % drop in secant friction

angle increased with an increase in relative density for

all types of interfaces evaluated in this study with dry

sands, there was no general trend of increase in secant

friction angle with the increase in relative density. The

rate of reduction in secant friction angle with an

increase in relative density was not significant for

relative densities higher than 40 %. Steel generally

showed higher % of reduction compared to wood and

concrete for lower values of relative densities, whereas

the % reduction in the shearing resistance was similar

in wood and steel interfaces at higher relative densi-

ties. However, there were consistent relationships

between relative density and % reduction in secant

friction angle in case of saturated sand. These

relationships for soil–concrete, soil–steel and soil–

wood interfaces are presented in Eqs. (3), (4) and (5),

respectively. Unlike the dry samples, the saturated

samples exhibited lower % of reduction in soil–wood

interface although the % reduction increased at higher

relative densities. Eqs. (3), (4), and (5) can be utilized

to estimate the % drop in secant friction angle from the

sand–sand friction in case of sand–concrete, sand–

Fig. 11 Variation in the secant friction angle at the effective normal stress of 100 kPa with the relative density for the SW materials

compacted at different relative densities and interfaced with different structural materials; a Dry soil; and b Saturated soil

Geotech Geol Eng

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steel, and sand–wood interfaces, respectively for

different relative densities of the SW materials. Please

note that these correlations were developed with very

limited number of samples. Nevertheless, they are

very useful as no correlation is available so far.

% drop ¼ 2:8454 lnðDrÞ þ 21:238 ð3Þ% drop ¼ 4:9717 lnðDrÞ þ 14:122 ð4Þ% drop ¼ 7:5074 lnðDrÞ þ 3:3169 ð5Þ

where, Dr is relative density in %.

The results presented in Table 2 show that the

values of ‘‘a’’ (i.e. curvatures) in all 16 shear envelopes

for dry sand and the structural interfaces with dry sand

ranged from -0.0001 to -0.0012. Specifically, the

ranges of the values of ‘‘a’’ for soil–soil, soil–concrete,

soil–steel, and soil–wood, interfaces were -0.0001 to

-0.0011 (with an average of -0.0004), -0.0006 to

-0.001 (with an average of -0.0009), -0.0001 to

-0.0012 (with an average of -0.0004), and -0.0003

to -0.0007 (with an average of -0.0004), respec-

tively. Likewise, the results presented in Table 3 show

that the values ‘‘a’’ in all 16 shear envelopes for

saturated sand and the structural interfaces with dry

sand ranged from -0.0001 to -0.0018. Specifically,

the ranges of the values of ‘‘a’’ for soil–soil, soil–

concrete, soil–steel, and soil–wood, interfaces were

-0.0009 to -0.0018 (with an average of -0.001),



and -0.0002 to -0.0011 (with an average of

-0.0005), respectively. These values are consistent

both in saturated and dry sands and the corresponding

interfaces. This proves that the shear envelopes are

curved in all 32 cases of this study. Moreover, the data

presented in Table 3 shows that the secant friction

angle (for effective normal stress of 100 kPa) in dry

sand, sand–concrete interface, sand–steel interface,

and sand–wood interface ranged from 42.6�–52.3�,

29.1�–37.4�, 29.1�–32.1�, to 30.4�–33.3�, respec-

tively. Likewise, the data presented in Table 3 shows

that the secant friction angle (for effective normal

stress of 100 kPa) in saturated sand, sand–concrete

interface, sand–steel interface, and sand–wood inter-

face ranged from 41.4�–54.3�, 29.6�–36.0�, 30.0�–

33.62�, to 32.2�–34.5�, respectively. This shows that

although the effect of relative density on soil–soil

friction is very high, it is not significantly high in soil–

structure interface. While evaluating the drop in secant

friction angle for dry and saturated sand, Table 3 was

utilized. As presented in Table 3, the ratio of secant

friction angles for soil–structure interface and corre-

sponding dry sand ranged from 0.62–0.82, 0.61–0.72

to 0.60–0.78, respectively in soil–concrete, soil–steel,

and soil–wood interfaces, respectively. Likewise, the

ratio of secant friction angles for soil–structure

interface and corresponding saturated sand ranged

from 0.66–0.72, 0.62–0.73 to 0.64–0.78, in soil–

concrete, soil–steel, and soil–wood interfaces, respec-

tively. As observed in the relationship presented in

Table 3, secant friction angle drops significantly for

soil–structure interface, especially for high relative

Fig. 12 Variation of the reduction in the secant friction angle at the effective normal stress of 100 kPa with the relative density for the

SW materials compacted at different relative densities and interfaced with different structural materials; a Dry soil; and b Saturated soil

Geotech Geol Eng

123

density. However, the rate of reduction in shearing

resistance for relative densities higher than 40 % was

much less than the values with the relative densities

lower than 40 %. It is to be noted here that bearing

capacity of soil is high and settlement is low for the

soil with higher relative density. This can be attributed

to the fact that the relative density of 40 % separates

sand from loose to dense state (generally 35 % relative

density is considered to be the limit of loose sand).

This shows that the drop in secant friction angle in

soil–structure interface is constant irrespective of the

relative density for the dense sand although it varies

with the relative density in the loose sand. Please note

that the reduction in soil–structure friction angle is

also high for the soil with high relative density.

Therefore, caution should be applied while using soil–

structure friction angle for foundation design. Another

parameter that can be observed in Table 3 is the ratios

between secant friction angles for dry soil and

saturated soil. The ratios were higher for soil with

low relative density. For example the ratio of secant

friction angle for dry and saturated soil, soil–concrete,

soil–steel, and soil–wood interfaces ranged from

0.96–1.03 (dense–loose), 0.88–1.18, 0.88–1.02 to

0.93–1.04, respectively. This shows that dense dry

sand has lower friction angle than the saturated sand,

whereas loose dry sand has higher secant friction angle

than the saturated sand. This is true for all interfaces

with structures. Although we didn’t consider this

factor in this study, we observed that the loose sand,

which was first prepared at the dry density corre-

sponding to the relative density of 14 % without water

exhibited settlement of particles (i.e. possible increase

in relative density) right after immersing it into water

and the application of sustained load. This might have

caused an increase in friction angle of saturated sand at

lower relative densities.

3.1.7 Interface Friction Angles of SP, SM, and SP–SM

Materials

Presented in Figs. 13, 14, and 15 are the shear

envelopes for soil–soil as well as soil–structure

interfaces for saturated SP, SM, and SP–SM materials

tested at the relative density of 10 %. These loose sand

samples were prepared in a similar manner, explained

earlier for the SW material. Although the values are

different, the trend in the reduction in shearing

resistance for soil–structure interface is similar to

SW material. In these soils also, the shear envelopes

exhibited curvatures. The values of ‘‘a’’, ‘‘b’’, secant

friction angle at the effective normal stress of 100 kPa,

and reduction in secant friction angle at the soil–

structure interface (compared to the soil–soil inter-

face) for SP, SM and SP–SM materials are presented

Fig. 13 Soil–soil and soil–structure shear envelopes for satu-

rated SP material, compacted at the relative density of 10 %


rated SM material, compacted at the relative density of 10 %


rated SP–SM material, compacted at the relative density of

10 %

Geotech Geol Eng

123

in Table 4. As can be observed in Table 4, the trend in

the reduction in secant friction angle for soil–structure

interface exhibited similar trend as in the loose and

saturated SW material. The SP–SM material exhibited

the lowest reduction i.e. 2.5, 11.5, and 16 % reduction

for soil–concrete, soil–wood, and soil–steel interfaces,

respectively. Likewise, in general, SP materials

exhibited highest reduction in interface friction

(except soil–concrete interface), which is 6, 13.6,

and 21.7 % in soil–concrete, soil–wood and soil–steel

interfaces, respectively. The reduction in the interface

frictional resistance in SP material was almost a

quarter in soil–concrete, one half in soil–steel, and

slightly less in soil–wood interfaces in the SP material

compared to that in the SW material presented above.

This shows that SW material is more susceptible to

reduction soil–structure frictional resistance. Further

research is recommended to evaluate this effect.

4 Discussion

As explained earlier, almost all shear envelopes

exhibited curvature, irrespective of the type of soil,

moisture condition, or the type of soil–structure

interface. Therefore, it is recommended to character-

ize the soil–structure frictional resistance with the

parameters of parabola—‘‘a’’ and ‘‘b’’, where the

value of parameters ‘‘a’’ and ‘‘b’’ show the extent of

curvature and the extent of friction angle, respectively.

Potyondy (1961) realized this fact; however he did not

study the effect of effective normal stress in detail. As

the shape of the shear envelopes are curved, it is

essential to express the ratio of soil–structure friction

angle and soil–soil friction angle for different effective

normal stresses. Expressing those ratios for the

atmospheric pressure or 100 kPa would be beneficial

for general comparison. Friction ratio (d//, where, d is

soil–structure friction angle and / is soil–soil friction

angle), as explained in different literature and NAV-

FAC manual is misleading as it shows the average

friction angle for different effective normal stresses.

The ranges of d// values at the effective normal stress

of 100 kPa for reported relative densities are presented

in Table 5. Table 5 also includes the d// values

proposed by Potyondy (1961), NAVFAC and Giree-

sha and Muthukkumaran (2011) for similar (close

value) relative densities and geo-materials. As can be

observed in Table 5, the experimental values from this

study are much higher than the values presented in

NAVFAC and Potyondy (1961). Please note that the

values presented in the NAVFAC are presented in a

general manner and are conservatively low. This study

clearly shows that while estimating soil–structure

frictional resistances caution should be applied to get

the tabulated values for the appropriate ranges of

normal stresses. For example, lower normal stress

range is applied for the design of shallow foundation

Table 4 Parabolic curve properties ‘‘a’’ and ‘‘b’’, regression coefficient (R2), secant friction angles at effective normal stress of

100 kPa and at ‘‘b’’ parameter, ratios of structure–soil friction, and reduction in structure–soil friction for SP, SM, and SP–SM

materials

Interface Type of

Material

a b R2 Secant friction angle (deg.) at Ratios of

structure–soil

friction

Reduction in

structure–soil

friction (%)r0 = 100 kPa ‘‘b’’

Soil SP -0.0001 0.6093 1.000 30.9 31.4

Concrete SP -0.0003 0.6163 1.000 29.1 31.6 0.94 6.0

Wood SP -0.0001 0.5136 0.994 26.7 27.2 0.86 13.6

Steel SP -0.0002 0.4899 0.992 24.2 26.1 0.78 21.7

Soil SM -0.0001 0.6587 0.995 32.9 33.4

Concrete SM -0.0001 0.5887 0.998 30.0 30.5 0.91 8.9

Wood SM -0.0002 0.5824 0.998 28.5 30.2 0.87 13.4

Steel SM -0.0000 0.5194 0.997 27.4 27.4 0.83 16.7

Soil SP–SM -0.0001 0.5798 0.995 29.2 30.1

Concrete SP–SM -0.0001 0.5602 0.997 28.4 29.3 0.97 2.9

Wood SP–SM -0.0006 0.6049 0.998 25.9 31.2 0.88 11.5

Steel SP–SM -0.0004 0.5373 0.996 24.6 28.2 0.84 16.0

Geotech Geol Eng

123

and retaining wall, where as higher normal stress range

is to be considered for the design of deep foundation

and sheet piles.

5 Conclusions

Direct shear tests were conducted on the interfaces

between dry and saturated SW materials and wood, steel

and concrete structures, at the relative densities of 14,

40, 68 and 95 %. Moreover, direct shear tests were

conducted at the interfaces of loose (relative density of

10 %) and saturated SP, SM, and SP–SM materials with

concrete, steel and wood. Based on the results obtained

from this study and their pertinent analyses, the authors

came up with the following conclusions.

• Shear envelopes for sand–sand and sand–structure

interface were curved, showing dependency

between secant friction angle and effective normal

stress. Therefore, such relationships should be

derived/ estimated for an appropriate effective

normal stress corresponding to the field condition.

• Friction angle of SW material increased by 23 %

when the state of compaction changed from loosest

to the densest condition. The soil–concrete inter-

face friction also increased by 7 % when the

compaction state changed from the loosest to the

densest condition. However, the effects of such

change in density were inconsistent for the skin

friction angle between soil and wood or steel.

• Variations in the ratios of soil–structure and soil–

soil friction with relative density were inconsistent

for dry SW material. The ratios ranged from

0.624–0.818, 0.613–0.711 to 0.604–0.782 in soil–

concrete, soil–steel and soil–wood interfaces.

• The ratios of soil–structure and soil–soil friction in

saturated SW material decreased with an increase

in relative density. Those ratios for soil–concrete,

soil–steel, and soil–wood interfaces ranged

from 0.663–0.716, 0.620–0.725 to 0.636–0.778,

respectively.

• The ratios of soil–structure and soil–soil friction in

saturated SP, SM, and SP–SM materials ranged

from 0.78–0.94, 0.83–0.91 to 0.84–0.97, respec-

tively. The lowest value was observed for soil–

steel interface, whereas the highest value was

observed for soil–concrete interface.

• The ratios of sand–structure and sand–sand friction

recommended by NAVFAC are highly conserva-

tive and too generally presented.

Acknowledgments The authors appreciate the support of the

IRA funding at California State University, Fullerton to

purchase the research materials.

Table 5 Comparison of the ratios of soil–structure and soil–soil friction angles obtained from this study and the data available in

literature

Type of soil Dr (%) Pertinent literature* Interface d//

Concrete Steel Wood

SW–dry 68 This study 0.74 0.6 0.65

Potyondy (1961) 0.86 0.5 0.86

SW–saturated 68 This Study 0.72 0.64 0.7

Potyondy (1961) 0.86 0.57 0.84

Gireesha and Muthukkumaran (2011) 0.79 0.77 0.75

NAVFAC (1986) 0.45–0.55 0.3 N/A

SW–saturated 95 This study 0.69 0.62 0.6


SW–saturated 14 This Study 0.88 0.79 0.81


SP 10 This Study 0.94 0.86 0.78


NAVFAC (1986) 0.35–0.45 0.25 N/A

* The relative densities presented in the literature were not exactly same as the one used in this study, but were close enough to have

comparison

Geotech Geol Eng

123

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