estimation of shear strength increase beneath embankments

1 BACKGROUND

The Swedish railway system is currently being

upgraded for faster and heavier trains. In this context,

it will be of great benefit if the shear strength beneath

old embankments on soft soil, many of which were

constructed up to 100 years ago, can be utilised.

However, this requires verification of the shear strength

increase in relation to the soil outside the embankment,

which involves certain problems. The size of the

settlements that have occurred and the exact load that

has been applied are rarely known. Traditional

geotechnical investigations require access to the

embankment and drilling through it. On the other hand,

the railway authorities have set demands on

uninterrupted traffic and prohibit equipment or

personnel on the embankment for safety reasons. There

is thus a considerable need for a method to estimate

the shear strength increase that does not require access

to the embankment itself.

2 HYPOTHESIS

Measurement of the shear wave velocity in the field is

often used to estimate the in situ initial shear modulus

G0. It has been shown that the shear modulus in soft

cohesive soils can be expressed as a function of the

undrained shear strength (e.g. Larsson and Mulabdic,

1991). In principle, it should therefore be possible to

estimate also the undrained shear strength from the

measured shear wave velocity. However, both the shear

modulus and the undrained shear strength are functions

of the square of the shear wave velocity and very

accurate measurements of the shear wave velocity are

therefore required. Furthermore, the relation between

the undrained shear strength and the shear wave

velocity is also a function of the overconsolidation ratio

(Andersen et al., 1988; Atkinson, 2000). However, a

prerequisite for considerable consolidation settlements

and shear strength increases beneath embankments is

construction on normally consolidated or only slightly

overconsolidated soft ground. The soil beneath the

embankment will then remain in a normally

consolidated or only slightly overconsolidated state

also after the load application and throughout the

consolidation process, unless a significant unloading

is carried out. It should thus be possible to estimate

the undrained shear strength beneath such

embankments from the shear wave velocity.

3 SCOPE OF THE INVESTIGATION

The method of seismic cross-hole tomography has been

used in an effort to estimate its usefulness to assess

Estimation of shear strength increase beneath embankments

by seismic cross-hole tomography

R. LarssonSwedish Geotechnical Institute, Linköping, Sweden

H. MattssonGeoVista AB, Luleå, Sweden

Keywords: seismic test, cross-hole tomography, clay, undrained shear strength, strength increase, embankment

ABSTRACT: There is a great demand to utilise the shear strength increase resulting from consolidation beneath

old embankments on soft soils when these structures are to be widened, raised or subjected to heavier or faster

traffic loads. There are often no records of the loads and settlements, and access to the embankment for traditional

geotechnical investigations is often restricted, particularly in the case of railway embankments. The method of

seismic cross-hole tomography in order to estimate the increase in shear strength has therefore been tested

beneath a number of well documented test embankments. The results have been shown to provide a good general

picture of the shear strength beneath the embankments, in addition to fairly good estimates of the actual magnitudes

of the shear strengths.

971

Proceedings ISC-2 on Geotechnical and Geophysical Site Characterization, Viana da Fonseca & Mayne (eds.)© 2004 Millpress, Rotterdam, ISBN 90 5966 009 9

the increase in shear strength due to consolidation

beneath three test embankments. These embankments

are about 50 years old and loads, settlements, pore

pressures and shear strength increases are well known.

The study has been designed as a pilot project in order

to determine whether the method can be used in

practical applications and the accuracy with which the

shear strength increase can be estimated.

4 THE TEST EMBANKMENTS

The measurements have been made in the test fields

at Skå-Edeby and Lilla Mellösa, which are supervised

by the Swedish Geotechnical Institute. A total of eight

instrumented test embankments were constructed in

these fields during the period 1945–1961 and have

since been monitored continuously. Three of the

embankments were built on natural ground and these

have been used in this project.

The soft soils in the test fields consist of only

slightly overconsolidated high-plastic clay on top of

firm layers of sand or till. The average over-

consolidation ratio beneath the thin crusts is about 1.15.

The thickness of the clay layers vary between 12 and

15 metres and the top layers consist of organic clays.

The liquid limits of the clays range from 130 to 55%

and the plasticity indices from 85 to 30%.

The oldest embankment (test fill) was built in 1945

at Lilla Mellösa on top of 14 metres of clay. It had a

height of 2.5 metres and a square outline with a base

length of 30 metres. The settlements today amount to

about 2.0 metres and are continuing at a current rate

of approximately 10 mm/year. The compression of the

soil layers is fairly evenly distributed over the depth

of the soft soil profile. The undrained shear strength

beneath the embankment has increased throughout the

profile, but most significantly in the upper part, Fig. 1.

The test fill at Skå Edeby was constructed in 1957

on top of 12 metres of clay. It was 1.5 metres high and

had a circular outline with a base diameter of 35 metres.

In 2002, the total settlements amounted to 1.1 metres

and the rate of ongoing settlements was 5–6 mm/year.

Here, too, the settlements have with time become fairly

evenly distributed with depth. The shear strength

beneath the fill has been measured by field vane tests

on two occasions after construction and the results in

the latest investigation have also been checked by

direct simple shear tests in the laboratory. Beneath the

central parts of the fill, the shear strength has increased

fairly evenly throughout the clay profile, Fig. 2.

A narrow embankment with a length of about

40 metres was also constructed at Skå-Edeby in 1961.

It was similarly given a height of 1.5 metres but the

Fig. 1. Measured undrained shear strength beneath the test fill at

Lilla Mellösa.

0

2

4

6

8

10

12

14

16

0 10 20 30 40

Undrained shear strength measured by

field vane tests, kPa

Ori

gin

al d

ep

th, m

1945

1967

1979

2002

Fig. 2. Measured undrained shear strength beneath the test fill at

Skå-Edeby.

0

2

4

6

8

10

12

14

0 5 10 15 20 25

Undrained shear strength, kPa

Ori

gin

al d

ep

th, m

Natural ground

Below centre 1971

Below crest of slope 2002

About midway between crest and

centre 2002Direct simple shear tests 2002

972 © 2004 Millpress, Rotterdam, ISBN 90 5966 009 9

crest was only 4 metres wide and the base 8.5 metres

wide. The depth of the clay layers at this location was

about 15 metres. The total settlements in 2002

amounted to about 1.1 metres, of which about 0.2 metre

is related to horizontal movements in the subsoil. Due

to the narrow embankment and the load distribution,

the compression of the soil layers is mainly confined

to the upper half of the soil profile. According to the

estimated changes in water content, the compression

of the soil is fairly evenly distributed down to an

original depth of 8–9 metres, whereas results from

oedometer tests and shear strength tests indicate that

this limit is located at 7–8 metres depth, Fig. 3.

the shear wave velocity, Vs, and the density, ρ, it is

possible to calculate the shear modulus, G,

ρ2

sVG =

The shear modulus that is measured in most seismic

tests is the initial shear modulus at very small strains,

G0. The relation between the initial shear modulus and

the undrained shear strength, cu, in Swedish normally

consolidated or only slightly overconsolidated clays

has been found to be (Larsson and Mulabdic, 1991)

L

u

w

cG

5040 ≈

where wL is the liquid limit.

The undrained shear strength in the correlation

refers to values obtained in corrected field vane tests

and direct simple shear tests.

5.2 Seismic tomography

Tomography is a well-known technique for creating

images of projections (tomograms) of hidden objects

by using X-rays, ultrasound or electromagnetic waves.

The technique used in this project is termed seismic

crosswell direct wave traveltime tomography, but is

commonly called cross-hole tomography. Its basic

principle is to estimate a velocity model of the ground

by measuring the time it takes for elastic waves to

propagate from a source to a receiver. To perform

cross-hole tomography it is necessary to have at least

two boreholes. An array of geophones is inserted in

one hole and in the other an elastic wave is generated.

A seismograph measures the time it takes for the wave

to travel from the source point to the geophones. The

source is then moved to another position in the hole

and the procedure is repeated. The measurements will

produce a number of arrival times of waves that have

crossed the investigated area. The geophone distance

and the wave frequency mainly govern the data

resolution; the shorter the distance and the higher the

frequency, the better the resolution. The spatial relation

between the depth of, and distance to, the boreholes is

also an important parameter since shallow boreholes

and a large distance will lead to poor ray coverage,

Fig. 4.

The measured first arrival times and the co-

ordinates of the geophones and the source points are

stored in a data file. The area between the boreholes is

divided into a grid of velocity cells. Each cell is

assigned an initial start value. A model program then

calculates the time it takes for different rays to travel

Fig. 3. Measured undrained shear strength beneath the test

embankment at Skå-Edeby.

0

2

4

6

8

10

12

14

16

0 5 10 15 20 25


Ori

gin

al d

ep

th, m

Natural ground

Toe of slope

Centre of fill

Direct simple shear test

Further details of the soil conditions and the

embankments at the test fields at Skå-Edeby and Lilla

Mellösa can be found in Hansbo (1960), Chang (1981),

Larsson (1986) and Larsson and Mattsson (2003),

among other publications.

5 TEST METHOD

5.1 Seismic waves

Seismic investigations are based on the propagation

of elastic waves in the ground. These waves are usually

separated into compression waves, shear waves and

surface waves. Shear waves have a particle motion that

is perpendicular to the direction of propagation. The

propagation velocities of shear waves are governed

by the shear modulus and density of the ground. From

973Proceedings ISCʼ2 on Geotechnical and Geophysical Site Characterization, Viana da Fonseca & Mayne (eds.)

through the area between the boreholes. The calculated

times are compared to the measured travel times, and

the errors in the calculations are the differences

between these two parameters. Different rays intersect

each cell and the best-fit velocity is estimated by the

least squares method. The procedure is repeated for a

predetermined number of iterations or until a chosen

acceptable difference between the measured travel time

and the corresponding value calculated by the model

is reached, the so-called RMS residual, which indicates

the fit of the model. The size of an acceptable RMS

value depends mainly on the measuring accuracy of

the travel times for the shear waves. In this particular

case, an RMS value of up to 25–30 ms is considered

to indicate a good model fit. The velocity model does

not provide a unique solution to the inversion problem,

but with information about the geological conditions

at the site it is possible to determine whether the

established model is physically reasonable.

The software used in this project is called 3DTOM

(Jackson and Tweeton, 1996). For inversion of travel

time data, 3DTOM uses the SIRT method

(Simultaneous Iterative Reconstruction Technique;

Peterson et al., 1985). It is possible to model straight

rays, crooked rays or combinations of these (hybrid

modelling). The start model can be varied between a

homogenous, a horizontally layered or a chequerboard

model.

6 FIELD EQUIPMENT AND PROCEDURE

The equipment for collecting the data consisted of a

TERRALOC MARK 3 (ABEM) seismograph and

Fig. 4. Schematic picture of the coverage of the wave paths.

three 5-component 28 Hz sensor geophones (BG-K5)

with pneumatic clamping devices. The vibration source

was a screw plate attached to a hollow drilling pipe. A

free-running inner rod system was inserted into the

pipe. The rods were lifted and allowed to fall onto the

top of the screw plate to generate vertically polarised

shear waves. The triggering of the seismograph was

carried out by a standard geophone (PE-3) attached to

the drill pipe at its upper end. The geophones were set

up to detect vertically polarised shear waves and were

mounted at a distance of 1.0 metre from each other.

The geophones were lowered inside a vertical

borehole with a casing and attached by inflating the

pneumatic clamping devices. The casing consisted of

a plastic bellows hose that is vertically elastic, which

ensures good transmission of the signal from the clay

to the geophones. In the first measurement position,

the uppermost geophone was placed as close as

possible to the ground surface, after which the second

and third geophones were positioned at about 1 and

2 metres depth respectively. The screw plate was

screwed 0.1–0.2 metre into the ground. The trigger

geophone was attached to the pipe and a measurement

was performed. The set of geophones was then lowered

3 metres and a new measurement performed. When

the geophone array reached the bottom of the borehole,

the screw plate was advanced downwards to 1 metre

depth and the procedure was repeated with the

geophones instead being lifted in 3-metre stages. This

was repeated with the screw plate being advanced in

1-metre steps until it reached firm ground. Since the

trigger geophone was mounted at the top of the drill

pipe, a time delay was introduced as the wave had to

travel upwards along the pipe before it reached the

trigger geophone. Each data set was corrected for this

delay.

The measurements beneath the square and circular

fills were performed with one borehole positioned in

the central part, but well outside the permanent

instrumentation, and the other at the perimeter of the

fill. The conditions in the other directions were

assumed to be identical. The measurement beneath the

embankment was preformed across it with one

borehole at each side and the measurements in natural

ground outside the fills were performed with

geometries similar to those beneath the fills. The

distance between the boreholes varied between 9 and

15 metres and the depth to solid ground varied in

approximately the same way, which resulted in fairly

square geometries and a ray coverage of about

0°–45°.


7 TEST RESULTS

Fig. 5 shows the tomograms from beneath the circular

fill at Skå-Edeby and of the natural soil outside. There

is a large velocity contrast between the gravel fill and

the clay soil. Down to about 5 metres depth, there are

still considerably higher velocities under the test fill

than in the undisturbed soil. At 6–7 metres depth, there

is a horizontal high-velocity sub-layer that cuts across

the entire soil section. Beneath this layer, from 7 to

9 metres depth, the shear wave velocity is still higher

under the test fill than in the natural soil outside. When

the bottom of the clay layer is reached, the velocity

rapidly increases, which indicates that a stiffer material

underlies the clay. The dome shape of this layer is most

probably an artefact created during the model

inversion, which is caused by a combination of a fast

velocity increase and a lack of data related to the bad

ray coverage close to the boundary. A similar effect

can be seen beneath the fill material and at the lower

boundary of the section in natural soil. The circular

anomalies appearing along a vertical line at the 13 m

distance are also caused by the lack of coverage and

true data due to the borehole being situated in this

position. The RMS value of the test fill model is 21 ms

and for the undisturbed soil 25 ms.

The tomograms from the road-like test

embankment at Skå-Edeby are shown in Fig. 6. Here,

the increase in shear wave velocity under the

embankment is considerably less and can only be

readily observed to a depth of about 5 metres. The RMS

value of 39 ms is fairly high and indicates problems in

fitting the model data to the measured travel times.

The results of the measurements at Lilla Mellösa

greatly resemble those from the circular fill at Skå-

Edeby, Fig. 7. The RMS values are low,: the level for

the embankment model being 16 ms and for the natural

soil 10 ms, which indicates that the models fit

statistically well to the measured data. The boundary

between the soft soil and the bottom is not as well-

defined at the Lilla Mellösa site as at the Skå-Edeby

site. At Lilla Mellösa, the clay layers are underlain by

sand, whereas those at Skå Edeby lie on rock or till.

8 CORRELATION BETWEEN ESTIMATED

AND MEASURED SHEAR STRENGTH

From a first glance at the tomograms in Figs 5–7, it is

obvious that a considerable increase in shear wave

velocity and undrained strength has occurred beneath

the circular and square test fills in Skå-Edeby and Lilla

Mellösa. It also indicates that any such increase

beneath the road-like test embankment at Skå-Edeby

is considerably smaller and is limited to the upper

layers beneath the embankment. When making a more

detailed evaluation, certain aspects have to be taken

into account. These are:

• values close to the boreholes are more or less

erroneous because of poor wave path coverage and

are thereby misleading.

• values at the upper and lower boundaries of the

section in a portion midway between the boreholes

are more or less erroneous if the soft soil is overlain

and underlain by considerably stiffer material. Even

when this is not the case, the values are uncertain

because of poor coverage in these parts.

• The relation between undrained shear strength and

shear wave velocity is sensitive to the liquid limit

(or plasticity index) of the soil.

Before evaluation, the data in the vertical strips

with poor coverage close to the boreholes should be

excluded. The width of these strips can be estimated

from a sketch of the wave paths for the actual distances

between the boreholes and depths between the

measuring points, see Fig. 4. A similar estimate of

uncertain zones at the upper and lower boundaries

should also be made.

Since information on the distribution of the liquid

limit beneath the loaded area under the present

conditions is normally absent, this has to be estimated

from the data in the natural soil outside or from

investigations performed before the load application

together with an estimate of the distribution of

settlements with depth. The estimation of the total

settlements beneath the fill material is fairly

straightforward since the border between this material

and the underlying clay is rather distinct. The

estimation of the distribution with depth is more

approximate and has to be made with consideration to

the way in which the levels of different layers and

stiffness borders beneath and outside the embankments

are located in relation to each other. From the visual

inspection of the tomograms beneath the large fills at

Skå-Edeby and Lilla Mellösa, it is quite obvious that

downward movements have occurred throughout the

clay profiles beneath the fills. A more detailed

distribution is difficult to interpret, but an assumption

of an even distribution of compression with depth

appears to be reasonable and will have to suffice. The

estimation of the settlement distribution with depth

beneath the road-like embankment is more difficult.

However, the tomogram clearly indicates that the

embankment has settled about 1 metre and that there

are no significant settlements below 6–7 metres depth.

A rough estimate is that the settlements are evenly

distributed down to this depth.


Fig. 5. Contour plot of the tomograms from the circular test fill and natural soil at the Skå-Edeby site.

Fig. 6. Contour plot of the tomograms from the road-like test embankment and natural soil at the Skå-Edeby site.

Fig. 7. Contour plot of the tomograms from the square test fill and natural soil at Lilla Mellösa.


The next step is to draw detailed tomograms with

closely spaced contour lines for the shear wave

velocities. For the tomograms of the natural soil,

horizontal lines are drawn at selected evenly spaced

depths. The zones with estimated erroneous data are

excluded and the average velocity at each depth within

the remaining zone is estimated. The same procedure

is used for the tomograms beneath the loaded areas,

but here the horizontal lines are adjusted while taking

into consideration the estimated settlements at each

level in such a way that lines corresponding to the

original depths are produced. A relevant comparison

can then be made between the estimated average

velocities at the 'original' depths beneath the loaded

areas and in natural ground.

There are then two ways of estimating the

undrained shear strength beneath the loaded areas. The

first is to use the empirical relation between shear wave

velocity, density and liquid limit and the undrained

shear strength. The estimated shear wave velocity

beneath the fill is then used together with density and

liquid limit at the original depth. In large settlements,

there is also a certain increase in density, but this is of

limited importance. However, there is always a certain

spread in such relations. A more direct way is to use

the undrained shear strength measured in the natural

ground outside the loaded area. The shear wave

velocities at each depth are then compared to velocities

corresponding to the same original depths beneath the

loaded area. The undrained shear strength beneath the

loaded area is then calculated as the undrained shear

strength in the natural soil multiplied by the square of

the quotient between the shear wave velocities (see

relations given in section 5.1)

2

1

212 =

s

suu

V

Vcc

where

cu2

= undrained shear strength beneath loaded area

cu1

= undrained shear strength in natural ground

Vs2

= shear wave velocity beneath loaded area

Vs1

= shear wave velocity in natural ground

The evaluated shear wave velocities in natural

ground and beneath the loaded areas suggest that an

increase in shear wave velocity has occurred

throughout the profiles beneath the large fills. This

increase is large at the top but decreases with depth.

Beneath the narrow embankment at Skå-Edeby, there

is a significant increase in velocity down to 4 metres

depth. The effect probably extends down to 6–7 metres

depth, but an anomaly found in the shear strength

determinations by the field vane tests at 4 metres depth

also appears in the shear wave velocities. Below 6–7

metres depth, there is no indication of any increase in

shear wave velocity.

The undrained shear strength calculated from the

measured shear strengths in the field and the

amplification (Vs2

/Vs1

)2 estimated from the measured

shear wave velocities are shown in Fig. 8. This method

provides the best estimate of the shear strength

compared to using the empirical relation.

0

2

4

6

8

10

12

14

0 10 20 30 40 50


Co

rre

cte

d d

ep

th, m

Field vane test in

natural ground

Calculated from

seismic amplification

Field vane test below

centre of fill

Fig. 8. Evaluated undrained shear strength using the undrained

shear strength in natural ground and the amplification estimated

from the measured shear wave velocities.

a) At the circular fill at Skå-Edeby

a)


0

2

4

6

8

10

12

14

16

0 5 10 15 20 25


Co

rre

cte

d d

ep

th,

m

Field vane test in natural

ground

Calculated from seismic

amplification

Field vane test below centre

of embankment

9 CONCLUSION

The possibility of estimating the increase in shear

strength due to consolidation beneath embankments

by seismic cross-hole tomography has been illustrated.

The measurements were performed with readily

available equipment and evaluation programs. The

results have a certain degree of scatter, but the general

pattern of the shear strength variation is obtained and

an estimate of the operative strength on the basis of

the tomograms would prove to be fairly close to the

actual measured values.

ACKNOWLEDGEMENT

The project described in this paper was sponsored

by the Swedish National Rail Administration,

GeoVista AB and the Swedish Geotechnical Institute.

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Andersen, K.H., Kleven, A. and Heien, D. (1988). Cyclic Soil

Data for Design of Gravity Structures. Norwegian

Geotechnical Institute, Publication No. 175, Oslo.

Atkinson, J.H. (2000). Non-linear soil stiffness in routine design.

Geotechnique, Vol. 50, No. 5, pp. 487-508.

Chang, Y.C.E. (1981). Long-term consolidation beneath the test

fills at Väsby, Sweden. Swedish Geotechnical Institute, Report

No. 13, Linköping.

Hansbo, S. (1960). Consolidation of Clay with Special Reference

to Influence of Vertical Sand Drains. Swedish Geotechnical

Institute, Proceedings No. 18, Stockholm.

Jacksson, M.J. and Tweeton, D.R. (1996). 3DTOM: Three-

dimensional geophysical tomography. Instruction manual. U.S.

Geological Survey, Report of investigation 9617.

Larsson, R. (1986). Consolidation of soft soils. Swedish

Geotechnical Institute, Report No. 29, Linköping.

Larsson, R. and Mattsson, H. (2003). Settlements and shear

strength increase below embankments. Swedish Geotechnical

Institute, Report No. 63, Linköping.

Larsson, R. and Mulabdic, M. (1991). Shear moduli in

Scandinavian clays - Measurements of initial shear modulus

with seismic cones - Empirical correlation for the initial shear

modulus in clay. Swedish Geotechnical Institute, Report No.

40, Linköping.

Peterson, J.E., Paulson, B.N.P. and McEvilly, T.V. (1985).

Applications of algebraic reconstruction techniques to cross-

hole seismic data. Geophysics 50, pp. 1566-1580.

0

2

4

6

8

10

12

14

0 10 20 30 40

Undrained Shear strength, kPa

Co

rre

cte

d d

ep

th,

m

Field vane test in natural

ground

Calculated from seismic

amplification

Field vane test below centre

of fill

Fig. 8. Evaluated undrained shear strength using the undrained

shear strength in natural ground and the amplification estimated

from the measured shear wave velocities.

b) At the square fill at Lilla Mellösa

c) At the test embankment at Skå-Edeby

b)

c)


estimation of shear strength increase beneath embankments

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