Soil Mechanics for Unsaturated Soils phần 8 docx

Changes in void ratio and water content due to an increase in total stress or matric suction can now be predicted using the computed volume change indices.. - u,E = matric suction corres

Matric suction, (u, - ) u , (kPa) Figure 13.18 Soil-water characteristic curve obtained from a pressure plate test on a silt com- pacted dry of optimum water content

Initial conditions

0.4 -

a 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

wGs (a) Till (dry of optimum)

w = 15.2% e, = 0.642 Silt (dry of bptimbm) I

de/4wGs) or (ae/a(u, - u , ) ) / ( W G ) / W , - u,))l is

equivalent to the ratio of volume change indices (Le., The combined plot of Figs 13.17, 13.18, and curve 2 [i.e., constructed from Figs 13.18 and 13.19(a)] is de- picted in Fig 13.20, which illustrates the volume change characteristics of an unsaturated, compacted silt The vol- ume change indices (Le., C,, Cm, D,, and 0,) can be com- puted from Fig 13.20 Changes in void ratio and water content due to an increase in total stress or matric suction can now be predicted using the computed volume change indices

The same test procedures were applied to other com- pacted silt and the glacial till specimens Figure 13.19(b) summarizes the results of shrinkage tests on various com- pacted specimens Typical volume change relationships far

the compacted silt and glacial till are presented in Figs 13.21, 13.22, and 13.23 The relationships are similar to that shown in Fig 13.20 The computed volume change indices for the compacted silt and glacial till are tabulated

in Table 13.2 These indices can be converted to other vol- ume change coefficients such as “m, and m2” or “a and b,” as explained in Chapter 12

In summary, oedometer tests, pressure plate tests, and shrinkage tests are the experiments required to obtain the volume change indices corresponding to the loading of an unsaturated soil These tests can be performed using con- ventional soil mechanics testing procedures The test re- sults give rise to the volume change relationships for an unsaturated soil

Cm /Dm Gs ) *

a 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

wGs (b)

Figure 13.19 Results from shrinkage tests on compacted silts

and glacial tills (a) Shrinkage test data for the compacted silt;

(b) shrinkage test data for compacted silts and glacial tills

Determination of Volume Change Indices Associated with the Transition Plane

The entire void ratio constitutive surface in a semi-loga- rithmic form can be approximated by three planes, as il- lustrated in Fig 13.24 and described in Chapter 12 The

volume change indices, C, and Cm, are associated with or-

13.2 TEST PROCEDURES AND EQUIPMENTS 383

1.1

1 o

0.9-

Average initial condition: G = 2.72, e, -0.699, w, = 16.5% w,G, = 0.420

consolidation test results

Stress state variables, (a - u.) or (u - u,) (kPa)

Figure 13.20 Volume change relationships for the silt compacted dry of optimum water content

Average initial condition: G, = 2.72, e = 0.606, w = 19.0%, w,G, = 0.61 6

1 0' 102 10s l(r 1V 1 0 7

Stress state variables, (a - UJ or (u - ) u , (kPa)

Figure 13.21 Volume change relationships for the silt compacted at optimum water content

Stress state variables, (a - us) or (Un - u, ) (kPa)

Figure 13.22 Volume charge relationships for the till compacted dry of optimum water content

384 13 MEASUREMENTS OF VOLUME CHANGE INDICES

Average initial condition: G, = 2.76, e, = 0.567, w, = 18.7% w.G, = 0.516

from combined pressure

Stress state variables, (u - u,) or (u, - u,)(kPa)

Figure 13.23 Volume change relationships for the till compacted at optimum water content

thogonal planes I and 111, respectively, and can be deter-

mined from the test results presented in the previous sec-

tions The volume change indices, C; and Cg, are

associated with transition plane 11, and can be determined

graphically as outlined in this section The procedure is

applicable to stable-structured soils

Figure 13.25 illustrates the graphical determination of

the volume change indices, C; and Ch, based on the “con-

stant volume” oedometer test results and the measured val-

ues of the C, and Cm indices The first step is to determine

the corrected swelling pressure, PJ, as detailed in the next

section Having determined the corrected swelling pres-

sure, point A in Fig 13.25 can be plotted with a coordinate

equal to (log P i ) and eo where eo is the initial void ratio

A line can be drawn through point A with a slope of C, to intersect the convergence void ratio, e * (i.e., the point where the lines converge)

The second step is to determine the initial matric suction,

(u, - uw)& A line can be drawn through the convergence void ratio, e*, at a slope of Cm, as shown in Fig 13.25

The line intersects the initial void ratio line (Le., eo)

at the logarithm of the initial matric suction (i.e., log The magnitudes of Pi and (u, - uw)g are used to deter- mine the location of points B, and B2 along the constant void ratio plane (Fig 13.26) The straight line of constant void ratio on the arithmetic plot [Fig 13.26(a)] must be conveIted to a semi-logarithmic plot, as shown in Fig

(u, - uw);)

Table 13.2 A Summary of the Experimentally Measured Volumetric Deformation Indices”

“All indices have a negative sign, as described by the sign convention in Chapter 12

b“DS” stands for silt at dry of optimum initial water content “OS” stands for silt at optimum initial water content

“DT” stands for glacial till at dry of optimum initial water content “OT” stands for glacial till at optimum initial water content

‘Average slope of the unloading curve

%ope of the linear portion of the unloading curve

13.2 TEST PROCEDURES AND EQUIPMENTS 385

& Convergence void ratio, e*

1,111 =Orthogonal planes I1 =Transition plane

Figure 13.24 Approximate form for the void ratio constitutive surface on a logarithmic plot

13.26(b) Log Pj and log (u, - u,,,): are joined by line

“A,” which constitutes the chord of the asymptotic curve

in Fig 13.26(b) Line “B,” tangent to the asymptotic

curve, is drawn parallel to line “A.” Line “B” intersects

the log (a - u,) and log(u, - u,) axes at points BI and

B2, respectively As a result, the abscissas of points BI and

B2 along the initial void ratio line are known

The third step is to draw lines extending from the con-

vergence void ratio, e*, to points BI and B2 on the initial

void ratio [Fig 13.251 The slopes of these lines are equal

to the C; and CA indices associated with transition plane I1 (see Fig 13.24)

The above procedure is used for obtaining the volume change indices associated with transition plane I1 on the

semi-logarithmic form of the void ratio constitutive sur-

face In the arithmetic form of the constitutive surface, the volume change coefficients obtained from the extreme planes (Le., (u - u,) = 0 plane and (u, - u,) = 0 plane)

,V -.,-nce void ratio, e*

Arrows indicate the directions

of the graphical construction

Log (u - u.) or LOe (u - uw) Figure 13.25 Graphical determination of the volume change indices

386 13 MEASUREMENTS OF VOLUME CHANGE INDICES

- (D

C

c

s

Matric suction, (u - u,) Typical Results from Pressure Phte Tests

P; =corrected swelling pressure

(u - u,E = matric suction corresponding

to zero net normal stress

at a constant void ratio

c

Legend -Actual stress path

Approximated s%ss path

(b)

Figure 13.26 Construction of lines A and B from “constant vol-

ume” oedometer test results (a) “Constant volume” stress plane

on an arithmetic scale; (b) “constant volume” stress plane on a

logarithmic scale

are assumed to be applicable to every state point along a

constant void ratio plane or a constant water content plane

The significance of this assumption has been explained in

Chapter 12

Soil-water characteristic curves obtained from pressure plate tests are an important part of the water phase consti- tutive surface for an unsaturated soil An unsaturated soil

in the field is often subjected to more significant and fre- quent changes in matric suction, than in total stress The soil undergoes processes of drying and wetting as a result

of climatic changes On the other hand, the applied total stress on the soil is seldom altered Therefore, it is impor- tant to know the nature of the soil-water characteristic curve

of an unsaturated soil in order to predict the water content changes when the soil is subjected to drying or wetting

Croney and Coleman (1954) have summarized soil-water

characteristic curves which illustrate the different behavior observed for incompressible and compressible soils Figure

13.27 compares the soil-water characteristic curves of soft

and hard chalks, which are considered relatively incom- pressible The drying curves of these incompressible soils exhibit essentially constant water contents at low matric suctions and rapidly decreasing water contents at higher suctions The point where the water content starts to de- crease significantly indicates the air entry value of the soil The data show that the hard chalk has a higher air entry value than the soft chalk The high preconsolidation pres-

sure during the formation of the hard chalk bed results in

a smaller average pore size than for the soft chalk Another noticeable characteristic is that the drying curves for both hard and soft chalks become identical at high ma- tric suctions (Fig 13.27) This indicates that at high suc- tions, both soils have similar pore size distributions There

is a marked hysteresis between the drying and wetting curves for both soils

The effect of initial water content on the drying curves

Matric suction, (u - u , (kPa)

Figure 13.27 Soil-water characteristic curves for soft and hard chalks with incompressible soil structures (from Croney and Coleman, 1954)

13.2 TEST PROCEDURES AND EQUIPMENTS 387

3

Metric suction, (u - u,) (kPa)

Figure 13.28 Effects of initial water content on the drying curves of incompressible mixtures

(from Croney and Coleman, 1954)

of incompressible mixtures is demonstrated in Fig 13.28

An increase in the initial water content of the soil results

in a decrease in the air entry value This can be attributed

to the larger pore sizes in the high initial water content

mixtures These soils drain quickly at relatively low matric

suctions As a result, the water content in the soil with the

large pores is less than the water content in the soil with

small pores at matric suctions beyond the air entry value

In other words, soils with a low initial water content (or

small pore sizes) require a larger matric suction value in

order to commence desatumtion There is then a slower

rate of water drainage from the pores

The initial dry density of incompressible soils has a sim-

ilar effect on the soil-water characteristic curve, as was

illustrated by the initial water contents As the initial dry

density of an incompressible soil increases, the pore sizes

are small and the air entry value of the soil is higher, as

illustrated in Fig 13.29 The highdensity specimens de-

saturate at a slower rate than the low-density specimens

As a result, the high-density specimens have higher water

contents than the low-density specimens at matric suctions

beyond their air entry values In addition, the hysteresis

associated with the high-density specimens is less than the

hysteresis exhibited by the lowdensity specimens

Croney and Coleman (1954) used the soil-water char-

acteristic curve for London clay (Fig 13.30) to illustrate

the behavior of a compressible soil upon wetting and

drying The gradual decrease in water content upon drying

results in the air entry value of the soil being indistinct In

this case, the shrinkage curve of the soil (Fig 13.31) must

be used together with the soil-water characteristic cume in

order to determine the air entry value of the soil The

shrinkage curve clearly indicates the compressible nature

of the soil The total and water volume changes caused by

an increase in matric suction are essentially equal until the

water content reaches 22% As a result, the shrinkage curve above a water content of 22% is parallel and close to the saturation line, indicating essentially a saturation condi- tion The soil starts to desaturate when the water content

goes below 22%, causing the shrinkage cume to deviate

from the saturation line The void ratio of the soil reaches

Metric suction (u - u,.,) (kPa)

Figure 13.29 Effect of initial dry density on the soil-water char- acteristic curves of a compacted silty sand (from Cronev and Coleman, 1954)

388 13 MEASUREMENTS OF VOLUME CHANGE INDICES

10-1 IOD 10’ 102 103 1 0 4 106 108

Figure 13.30 Soil-water characteristic curves for London clay

(from Croney and Coleman, 1954)

Matric suction, (u - u,) (kPa)

a limiting value (Le., e = 0.48), corresponding to a water

content of 0% A water content of 22 % corresponds to a

matric suction in the natural soil of approximately lo00

kPa, as indicated by the soil-water characteristic curve

(Fig 13.30)

Some irreversible structural changes causing an irrever-

sible volume change occur primarily during the first drying

process, as indicated by curve A in Fig 13.30 Subsequent

wetting and drying cycles follow curves B and C (Fig

13.30), respectively Curves B and C have lower water

contents than curve A, with the difference indicating irre-

versible volume change

Curve D in Fig 13.30 was obtained from initially slur-

0 9 r 1 I I I I I I i

Water content, w (%I

Figure 13.31 Shrinkage curve for London clay (from Croney

and Coleman, 1954)

ried specimens where the soil structure was partially dis- turbed Curve A for the natural soil joined curve D at a matric suction of 6300 m a , indicating the maximum suc- tion to which the clay has been subjected during its geo- logical history The maximum suction has a similar mean- ing to the preconsolidation pressure of a saturated soil, and this is explained in further detail in Chapter 14 The devia- tions of the natural soil curves A, B, and C from the ini-

tially slurried soil curve D represent the natural state of disturbance due to past drying and wetting cycles

Another curve plotted in Fig 13.30 is curve G that re- lates the water content to the matric suction for disturbed soil specimens Curve G is not a soil-water characteristic curve since the points on the curve were obtained from soil specimens with different soil structures A soil-water char- acteristic curve must be obtained from a single specimen

or several specimens with “identical” initial soil struc- tures Curve G appears to be unique for London clay, re-

gardless of the matric suction of the soil State points along the drying curve D or curve A will move to corresponding points on curve G when disturbed at a constant water con- tent Similarly, state points along any wetting curve will move to curve G when disturbed at a constant water con- tent Disturbance can take the form of remolding or thor- oughly mixing the specimens Similar relationships to curve

G have also been found for other soils (see Fig 13.7) It can therefore be concluded that there is a unique relation- ship between water content and matric suction for a dis- turbed soil, regardless of its soil structure, initial matric suction, or its initial state path (Croney and Coleman, 1954)

A similar relationship is commonly observed in soils compacted at various water contents and dry densities (see Chapter 4) In other words, compacted soils have a unique relationship between water content and matric suction, re- gardless of the compacted dry density of the specimens

Determination of In Situ Stress State Using Oedometer Test Results

One-dimensional oedometer tests are most often used for the assessment of the in situ stress state and the swelling properties of expansive, unsaturated soils The oedometer can only be used to perform testing in the net normal stress plane Therefore, the assumption is made that it is possible

to eliminate the matric suction from the soil and obtain the necessary soil properties and stress state values from the net normal stress plane The “free-swell” and “constant volume” tests (Fig 13.2) are two commonly used proce- dures which first eliminate the soil matric suction

‘ ‘Constant Volume ’ ’ Test

Let us first consider the “constant volume” oedometer test

In this procedure, the specimen is subjected to a token load and submerged in water The release of the negative pore- water pressure to atmospheric conditions results in a ten-

13.2 TEST PROCEDURES AND EQUIPMENTS 389

dency for the specimen to swell As the specimen tends to

swell, the applied load is increased to maintain the speci-

men at a constant volume This procedure is continued un-

til the specimen exhibits no further tendency to swell The

applied load at this point is r e f e d to as the “uncorrected

swelling pressure,” P, The specimen is then further loaded

and unloaded in a conventional manner

The test results are generally plotted as shown in Fig

13.2(b) The actual stress paths followed during the test

can be more fully understood by use of a three-dimensional

plot, with each of the stress state variables forming an ab-

scissa (Fig 13.32) It is important to understand the stress

paths in order to propose a proper interpretation of the test

data The void ratio and water content stress paths are

shown for the situation where there is a minimum distur-

bance due to sampling Even so, the loading path will dis-

play some curvature as the net normal stress plane is ap-

proached In reality, the actual stress path will be even more

affected by sampling (Fig 13.33)

Geotechnical engineers have long recognized the effect

of sample disturbance when determining the preconsoli-

dation pressure for a saturated clay In the aedometer test,

it is impossible for the soil specimen to return to an in situ

stress state after sampling without displaying some curva-

ture in the void ratio versus effective stress plot (i.e., con-

solidation curve) However, only recently has the signifi-

cance of sampling disturbance been recognized in the

measurement of swelling pressure (Fredlund et af., 1980)

Sampling disturbance causes the conventionally deter-

mined swelling pressure, P, , to fall well below the “ideal”

or “correct” swelling pressure, P i The “corrected”

swelling pressure represents the in siru stress state trans-

lated to the net normal stress plane The “corrected” swelling pressure is equal to the overburden pressure plus the in situ matric suction translated onto the net normal stress plane The translated in situ matric suction is called the “matric suction equivalent,” (u, - u,,,)~ (Yoshida et af., 1982.) The magnitude of the matric suction equivalent will be equal to or lower than the in situ matric suction The difference between the in situ matric suction and the matric suction equivalent is primarily a function of the de- gree of saturation of the soil The engineer desires to obtain the ‘‘corrected” swelling pressure from an oedometer test

in order to reconstruct the in siru stress conditions The procedure to accounting for sampling disturbance is dis- cussed later

%ree-Swell’ ’ Test

In the “free-swell” type of oedometer test, the specimen

is initially allowed to swell fmly, with only a token load applied (Fig 13.2(a) and Fig 13.34) The load required

to bring the specimen back to its original void ratio is termed the swelling pressure The stress paths being fol- lowed can best be understood using a three-dimensional plot of the stress variables versus void ratio and water con- tent, as shown in Fig 13.34 This test has the limitation that it allows volume change and incorporates hysteresis into the estimation of the in situ stress state On the other hand, this testing procedure somewhat compensates for the effect of sampling disturbance

Correction for the Compressibility of the Apparatus

The following procedure is suggested for obtaining the

“corrected” swelling pressure from “constant volume”

D

Metric suction, (u - I&,)

Figure 13.32 “Ideal” stress path representation for a “constant volume” oedometer test

390 13 MEASUREMENTS OF VOLUME CHANGE INDICES

Ideal stress - deformation path -Actual stress - deformation path

*

P; (corrected swelling Matric suction, (u - u,)

oedometer test results Detailed testing procedures are pre-

sented in ASTM D4546 When interpreting the laboratory

data, an adjustment should be made to the data in order to

account for the compressibility of the oedometer apparatus

Desiccated, swelling soils have a low Compressibility, and

the compressibility of the apparatus can significantly affect

the evaluation of in situ stresses and the slope of the re-

bound curve (Fredlund, 1969)

Because of the low compressibility of the soil, the com-

pressibility of the apparatus should be measured using a

steel plug substituted for the soil specimen The measured

deflections should be subtracted from the deflections mea-

sured when testing the soil Figure 13.35 shows the manner

in which an adjustment should be applied to the laboratory

data The adjusted void ratio versus pressure curve can be

Void ratio pressure

‘\ Water content

Figure 13.34 Stress path representation for the “free-swell”

type of oedometer test

sketched by drawing a horizontal line from the initial void ratio, which curves downward and joins the recompression curve adjusted for the compressibility of the apparatus

Correction for h p l i n g Disturbance

Second, a comtion can now be applied for sampling dis- turbance Sampling disturbance increases the compressi- bility of the soil, and does not permit the laboratory spec-

imen to return to its in situ state of stress at its in situ void

ratio Casagrande (1936) proposed an empirical construc-

tion on the laboratory curve to account for the effect of

Uncorrected Sketched swelling -connecting pressure, P portion

of oedometer Log (0 - u.) -

Figure 13.35 Adjustment of laboratory test data for the com- pressibility of the oedometer apparatus

13.2 TEST PROCEDURES AND EQUIPMENTS 391

Regina clay Liquid limit = 75%

Depth range = 0.75m - 5.3m

No of oedometer test = 34

sampling disturbance when assessing the preconsolidation

pressure of a soil Other construction procedures have also

been proposed (Schmertmann, 1955) A modification of

Casagrande’s construction is suggested for determining the

“corrected” swelling pressure

The following procedure is suggested for the determi-

nation of the “corrected” swelling pressure Locate the

point of maximum curvature where the void ratio versus

pressure curve bends downward onto the recompression

branch (Fig 13.36) At the point of maximum curvature,

a horizontal line and a tangential line are drawn The “cor-

rected” swelling pressure is designated as the intersection

of the bisector of the angle formed by these lines and a line

parallel to the slope of the rebound curve which is placed

in a position tangent to the loading curve

The need for applying a correction to the swelling pres-

sure measured in the laboratory, is revealed in numerous

ways First, it would be anticipated that such a correction

is necessary as a result of early experience in determining

the preconsolidation pressure for normally consolidated

soils b o n d , attempts to use the “uncorrected” swelling

pressure in the prediction of total heave commonly result

in predictions which are too low Predictions using “cor-

rected” swelling pressures may often be twice the magni-

tude of those computed when no correction is applied

Third, the analysis of oedometer results from desiccated

deposits often produces results which are difficult to inter-

pret if no correction is applied for sampling disturbance

Figure 13.37 shows an average oedometer curve ob-

tained from 34 tests performed on Regina clay The deposit

is of preglacial lacustrine origin, and the natural water con-

tents are near the plastic limit (Fredlund et al., 1980) The

average liquid limit is 75 96 The climate of the region is

semi-arid, and there is no evidence of a regional gmund-

water table in the deposit The soil is very stiff, and would

be anticipated to have high swelling pressures The oed-

ometer results show, however, that if a correction for sam-

6 .- 5 0.90

Log (a, - uw) W a )

Figure 13.37 Average data from dometer tests on Regina clay illustrating the need for the swelling pressure correction

pling disturbance is not applied, the swelling pressure is only slightly in excess of the average overburden pressure This soil could easily be misinterpreted as a low swelling clay However, swelling problems are common, with a to-

tal heave in the order of 5-15 cm Samples ‘from depths

deeper than 5.5 m often show “uncorrected” swelling pressures less than the overburden pressure In other words, the correction for sampling disturbance is imperative to the interpretation of the in situ stress state of the soil

Figure 13.38 shows a comparison of “corrected” and

“uncorrected” swelling pressure data from two soil de- posits The results indicate that it is possible for the “cor-

Uncorrected swelling pressure, P (kPa)

Figure 13.38 Change in swelling pressure due to applying the correction for sampling disturbance

392 13 MEASUREMENTS OF VOLUME CHANGE INDICES

rected” swelling pressures to be more than 300% of the Unloading Tests ajler Compression

“uncorrected” swelling pressures

13.2.2 Unloading Constitutive Surfaces

The unloading constitutive surfaces are illustrated in Fig

13.39(a) and (c) for the void ratio and water content sur-

faces, respectively The intersection curves 1 and 2 from

the void ratio surface [Fig 13.39(a)] are combined in Fig

13.39(b) The slopes of curves 1 and 2 are called the C,,

and C,,,, volume change indices, respectively The inter-

section curves 3 and 4 from the water content surface [Fig

13.39(c)] are combined in Fig 13.39(d) using the variable,

w G, , as the ordinate Therefore, the slopes of curves 3 and

4 in Fig 13.39(d) are also the product of the specific grav-

ity and the volume change indices (Le., (Dl, G,) and (Dm8

G,), respectively)

The following discussions outline the test procedures that

can be used to obtain the four indices associated with the

unloading constitutive surfaces (Le., C,,, C,,,, , D,,, and

0,) Tests similar to those described in Section 13.2.1 are

also applicable to the unloading surface when the tests are

conducted in an unloading mode

Curve 2

E

‘0 .-

8

Curve 1 of the unloading surface can be obtained from the

“free-swell” and “constant volume” oedometer tests, as illustrated in Fig 13.40 Curve 1 connects the void ratio ordinates at the end of the “free-swell” tests Curve 1 is

essentially parallel to the rebound curve, corresponding to the unloading portion of the test at a lower void ratio (Fig 13.41) The rebound curves are approximately parallel to one another and can be linearized on a semi-logarithmic scale (Schmertmann, 1955; Holtz and Gibbs, 1956; Gil- Christ, 1963; Noble, 1966; Lambe and Whitman, 1979; Lidgren, 1970; Chen, 1975) The slope of the rebound

curve is referred to as the swell index, C, , which is signif- icantly smaller than the compression index, C,

The slope of curve 1 (Le., the C, index) can be consid- ered to be essentially equal to the C, index from the re- bound curves As a result, the CIS index from the unloading constitutive surface is obtained by performing an unloading test after completion of the compression portion, in accor- dance with the conventional test procedures for saturated specimens (ASTM D2435, 1985)

The swelling index, C, , will generally range between 10-

Figure 13.39 Void ratio and water content relationship during unloading of an unsatueted soil

(a) Void ratio relationship for unloading; (b) Intersection curves between void ratio surface and (a - u,) or (u, - u,) plane; (c) water content relationship for unloading; (d) Intersection curves between water content surface and (a - u,) or (u, - uw) plane

13.2 TEST PROCEDURES AND EQUIPMENTS 393

20% of the compressive index, C,, for a particular soil

Figure 13.42 shows approximate swelling index values

which have been correlated with the liquid limit and the

rebound void ratio of a soil (NAVFAC, 1971) The plot is

useful for obtaining an estimate of the swelling index

Curve 3 in Fig 13.39(d) coincides with curve 1 from

Fig 13.39(b) since wG, is equal to the void ratio, e, when

the soil is saturated Therefore, the unloading water con-

tent index, Dls, can be computed as (Cl,/Gs)

Pressure Plate Wetting Tests

Curve 4 in Fig 13.39 is called the wetting portion of the

soil-water characteristic curve The wetting curve can be

established by performing pressure plate tests on speci- mens after the drying portion has been completed, as ex- plained in Section 13.2.1 The test procedures and equip- ments are similar to those used in the drying tests (ASTM D2325) The specimen is equilibrated to a lower matric suction by decreasing the air pressure in the pressure plate

extractor As a result, water from the compartment below

the high air entry disk moves into the specimen, causing

an increase in water content The time required for water

to be drawn into the specimen can be substantial and care must be taken to ensure that complete equilibrium has been attained The equilibrium water contents are then plotted against the corresponding matric suctions to establish wet-

Figure 13.41 Two-dimensional projections of " free-swell" one-dimensional oedometer data for compacted Regina clay (from Gilchnst, 1963)

394 13 MEASUREMENTS OF VOLUME CHANGE INDICES

Figure 13.42 Approximate correlation of swelling index versus

rebound void ratio (from NAVFAC DM-7, 1971)

Make attachment for

3.18 mm male pipe thread1 A “pig tail“ coil

,-of 3.18 mm OD Steel strip

Figure 13.43 Schematic layout of the modified loading cap of

the Anteus oedometer

ting curve 4, as shown in Fig 13.39(d) The slope of the

wetting curve 4 is equal to (0, G,)

Curve 2 in Fig 13.39 can also be constructed from the pressure plate test results when void ratio measurements are made at each point of matric suction equilibrium The measurements can be made by reducing the air pressure in the extractor to zero, dismantling the extractor, and mea- suring the total volume of the specimen The measure- ments must be made as quickly as possible in order to pre- vent changes in the water content of the soil Having measured the total volume, the specimen is placed back into the extractor, and the test is continued at a lower ma- tric suction value The computed void ratios at each equi- librium point are plotted against the corresponding matric suctions to give curve 2 in Fig 13.39(b) The slope of curve 2 is equal to the volume change index, C,,,,

Free-Swell Tests

Curves 2 and 4 in Fig 13.39 can also be obtained by con-

ducting a “free-swell” oedometer test (see Fig 13.40) with void ratio and water content measurements In this case, more specialized equipment such as a modified Anteus oedometer for the &,-loading condition (Fig 13.43) is re-

quired The modified Aneus oedometer allows the control

of total, pore-air, and pore-water pressures and the mea- surement of total and water volume changes during the tests The soil specimen can also be wetted by injecting water through hypodermic needles installed in the loading cap This procedure was used by Ho (1988) in an attempt

to expedite the entrance of water into the specimen

Net normal stress, (a - u.) (kPa)

Figure 13.44 Results for one-dimensional “constant volume” loading and unloading oedometer tests on silt compacted at optimum water content

13.2 TEST PROCEDURES AND EQUIPMENTS 395

Net normal stress, (a - u,) (kPa)

Figure 13.45 Results for one-dimensional “constant volume” loading and unloading oedometer tests on till compacted dry of optimum water content

Net normal stress, (a - u.) (kPa)

Figure 13.46 Results for one-dimensional “constant volume” loading oedometer tests on till compacted at optimum water content

Determination of Volume Change Indices

The silt and glacial till described in Table 13.1 were also

tested by Ho and Fredlund (1989) to determine the volume

change indices associated with the unloading constitutive

surfaces The rebound curves from the unloading portion

of the test are presented in Figs 13.17 and 13.44 for the

silt specimens, and in Figs 13.45 and 13.46 for the glacial

till specimens The slopes of the rebound curves are equal

to the volume change index C,s or (QG,) The results of the “free-swell” tests with void ratio and water content measurements on the silt and glacial till specimens are pre-

sented in Figs 13.47 and 13.48, respectively The tests

396 I 3 MEASUREMENTS OF VOLUME CHANGE INDICES

Legend

H e versus Log (u _ - u,) -

0-0 wG versus Log (Ua - u,) under ((I - u.) = 3.45 kPa

I

I 0.9

Matric suction, (u - u,) (kPa)

Figure 13.47 Unloading portion results for one-dimensional

“fme-swell” oedometer tests on silt specimens

were conducted using the modified Anteus consolidometer

Void ratios and water contents are plotted against the log-

arithms of matric suction The slope of the void ratio ver-

sus log (u, - u,) curve is equal to the C,, index, while

the slope of the (wG,) versus log (u, - u,) curve is equal

Legend

w e versus Log (u - u,)

M wG, versus Log (u - u,)

under (u - u.) = 3.45 kPa 0.9

Matric suction, (u - u,) (kPa)

Figure 13.48 Unloading portion results for one-dimensional

“free-swell’’ oedometer tests on till specimens

to the (D,,G,) index As a result, all four indices associ-

ated with the unloading surface (Le., C,,, C,,, D,,, and

0,) are obtainable These indices can be converted to

other volume change coefficients, such as “mls and m2,”

or the “a, and b,” coefficients, as explained in Chapter 12

CHAPTER 14

Volume Change Predictions

An unsaturated soil will undergo volume change when the

net normal stress or the matric suction variable changes in

magnitude The volume change theory and the modulus

measurements presented in Chapters 12 and 13, respec-

tively, can be used to calculate volume changes in an un-

saturated soil Under a constant total stress, an unsaturated

soil will experience swelling and shrinking as a result of

matric suction variations associated with environmental

changes In collapsible soils, the collapse phenomenon oc-

curs when the matric suction of the soil decreases

In this chapter, the methodology for the prediction of

heave in a swelling soil is described in detail The stress

history of a soil is an important factor to consider in un-

derstanding the swelling behavior The formulations and

example problems for heave prediction are presented and

supplemented with two case histories A detailed discus-

sion on the factors influencing the amount of heave is also

included At the end, there is a brief note on collapsible

soils and methods to predict the amount of collapse

Expansive soils are found in many parts of the world, par-

ticularly in semi-arid areas An expansive soil is generally

unsaturated due to desiccation Expansive soils also con-

tain clay minerals that exhibit high volume change upon

wetting The large volume change upon wetting causes ex-

tensive damage to structures, in particular, light buildings

and pavements In the United States alone, the damage

caused by the shrinking and swelling soils amounts to about

$9 billion per year, which is greater than the combined

damages from natural disasters such as floods, hurricanes,

earthquakes, and tornadoes (Jones and Holtz, 1987)

Therefore, the problems associated with swelling soils are

of enormous financial proportions

Table 14.1 summarizes examples of causes for founda-

tion heave as a result of the changes in the water content

of the soil These changes can originate from the environ- ment or from man-made causes Nonuniform changes in water content will result in differential heaves which can cause severe damage to the structure In fact, the differ- ential heave experienced by a light structure is often of similar magnitude to the total heave

The heave potential of a soil depends on the properties

of the soil, such as clay content, plasticity index, and shrinkage limit In addition, the heave potential depends upon the initial dryness or matric suction of the soil Many empirical methods have been proposed to correlate the swelling potential of a soil to properties such as are shown

in Table 14.2 and Fig 14.1 These relationships are useful for identifying the swelling potential of a soil In other words, these correlations reflect one component of the po- tential magnitude of heave

The amount of total heave can also be written as a func-

tion of the difference between the present in situ stress state

and some future stress state and the volume change indices for the soil In general, the net normal stress state variable remains constant, while the matric suction stress state vari- able changes during the heave process Matric suction changes result in changes in water content (Table 14.1) Therefore, total heave can be predicted by measuring the

in situ matric suction and estimating or predicting the future matric suction in the field under specific environmental conditions The volume change indices with respect to ma- tric suction changes must be measured in accordance with the procedures outlined in Chapter 13

There are several heave formulations related to the vol- ume change indices which have been proposed by various researchers (Table 14.3) These formulations differ pri- marily in the manner in which strain and soil suction are defined

The prediction of heave on the basis of matric suction measurements has not been extensively used due to diffi- culties associated with accurate measurements of matric suction and appropriate soil properties More common are the methods for heave prediction based on one-dimensional

397

398 14 VOLUME CHANGE PREDICTIONS

Table 14.1 Examples of Causes for Foundation Heave Resulting from Soil Water Content Changes (from

Headquarters, U.S Department of the Army, 1983)

Changes in field environment from 1)

natural conditions

2)

Changes related to construction 1)

2) 3) 4)

5 )

Usage effects

3) 4)

Significant variations in climate, such as long droughts and heavy rains, cause cyclic water content changes resulting in edge movement of structures

Changes in depth to the water table lead to changes in soil water content

Covered areas reduce natural evaporation of moisture from the ground, thereby increasing the soil water content

Covered areas reduce transpiration of moisture from vegetation, thereby increasing the soil water content

Construction on a site where large trees were removed may lead to

an increase of moisture because of prior depletion of soil water by extensive mot systems

Inadequate drainage of surface water from the structure leads to ponding and localized increases in soil water content Defective rain gutters and downspouts contribute to localized increases in soil water content

Seepage into foundation subsoils at soil/foundation interfaces and through excavations made for basements or shaft foundations leads

to increased soil water content beneath the foundation

Drying of exposed foundation soils in excavations and reduction in soil surcharge weight increases the potential for heave

Aquifers tapped provide water to an expansive layer of soil

Watering of lawns leads to increased soil water content

Planting and growth of heavy vegetation, such as trees, at distances from the structure less than 1-1.5 times the height of mature trees, aggravates cyclic edge heave

Drying of soil beneath heated areas of the foundation, such as furnace rooms, leads to soil shrinkage

Leaking underground water and sewer lines can cause foundation heave and differential movement

Table 14.2 Probable Expansion as Estimated from Classification Test Data’ (from Holtz and Kovacs, 1981)

Probable Expansion

as a % of the Total

Volume Change

“After Holtz (1959) and U.S.B.R (1974)

Wnder a surcharge of 6.9 kPa (1 psi)

14.1 LITERATURE REVIEW 399 oedometer test results In the oedometer methods, matric

suction measurements are not required A list of the var-

ious methods utilizing the oedometer test results is pre- sented in Table 14.4 Three of these methods are briefly

The direct model method is based on a “free-swell”

oedometer test on undisturbed samples (Fig 14.2) The specimens are subjected to the overburden pressure (or the load that will exist at the end of construction) and allowed free access to water The predicted heave is genemlly sig- nificantly below the actual heave experienced in the field The stress path followed by the test procedure is shown in Fig 14.2(b) The conventional two-dimensional manner for plotting the test data is shown in Fig 14.2b) The under- estimation of the amount of heave appears to be primarily

Clay fraction of whole sample, (%<2p)

Figure 14.1 Cornlation between soil properties and swelling

potential (from van de Merwe t19641)

Table 14.3 Definitions of Volume Change Indices with Respect to Suction Changes (from Hamberg, 1985)

Cm = A e / A log (u, - u,)

Slope of void ratio versus log matric suction, approximated by

where a = compressibility factor (0 < a

water content relationship

Slope of vertical strain versus the log of matric suction:

Slope of vertical strain versus the log of solute (osmotic) suction:

Value of linear strain corresponding to a suction change from 33 kPa to oven dry:

where MILD = linear strain relative to dry

dimensions, yD = bulk density of oven dry sample, yw = bulk density of sample at 33 kPa suction

I;I = € , / A log h I;,,, = € , / A log (u, - u,)

0.02-0.18 0.02-0.20 0.05-0.22

Engleford Yazoo clay Mancos

Red-Brown Clay

Western and Midwestern

U.S soils

Canada

Mississippi

Mississippi Texas Colorado Sicily

Texas Mississippi New Mexico

Adelaide, S

Australia

400 14 VOLUME CHANGE PREDICTIONS

Table 14.4 Various Heave Predictions Methods Utilizing Oedometer Test Results

Reference

Double oedometer method

Salas and Serratosa method

Volumeter method Mississippi method

Sampson, Schuster, and Budge’s method Noble method Sullivan and McClelland method

Holtz method Navy method Direct model method (Texas Highway Department) Simple oedometer method U.S.B.R method

Fredlund, Hasan and Filson’s method

Teng, T.C., Mattox, R.M., and Clisby, M.B

Teng, T.C and Clisby, M.B

Sampson, E., Schuster, R.L., and Budge, W D

Jennings, J.E., Firth, R.A., Ralph, T.K., and Nager, N

U.S

Canada U.S

due to a lack of consideration of disturbance which has

been experienced by the soil during sampling

The Sullivan and McClelland method is based on a “con-

stant volume” oedometer test on an undisturbed sample

initially subjected to the overburden pressure Once the

swelling pressure has been reached, the sample is re-

bounded The stress path followed is shown in Fig 14.3

The availability of published case histories is limited, but

it is anticipated that this method would underestimate the

amount of heave since sampling disturbance has not been

taken into account

The double oedometer method is based on the results of

two oedometer tests, namely, a “free-swell” odometer

test and a “natural water content” odometer test The

specimens are initially subjected to a token load of 1 kPa

No water is added to the oedometer pot during the “natural

water content” test The ‘‘natural water content” oedom-

eter test data are adjusted vertically to match the “free-

swell” test results at high applied loads Various loading conditions and final pore-water pressures can be simulated

in the analysis The stress paths followed by the two tests

are shown in Fig 14.4 The predicted heave is generally

satisfactory since the method of analyzing the data appears

to compensate for the effects of sampling disturbance In other words, the natural water content curve defines the effect of sampling disturbance The stress paths of more recent, updated versions of the double oedometer method can also be visualized on similar three-dimensional plots

in terms of net normal stress and matric suction

Fredlund et al (1980) proposed the use-of “constant vol-

ume” oedometer test results in predicting total heave It was suggested that the measured swelling pressure be cor- rected for sampling disturbance A graphical technique for correcting the measured swelling pressure was proposed (see Chapter 13) The correction was similar in procedure

to Casagrande’s construction for determining the precon-

14.1 LITERATURE REVIEW 401

Free swell test Starting stress

in laboratory I

Token load

Sampled soil Applied load

’ \ ,Reload (lab) nsitu stress

( b) Feure 14.2 Stress path followed in the direct model method

(a) Two-dimensional plot showing the stress path followed in the

field and in the laboratory; (b) three-dimensional plot of the stress

Clelland method (a) Two-dimensional plot of the stress path; (b)

three-dimensional plot of the stress path,

Figure 14.4 Stress paths followed when using the double oedometer method (Jennings and Knight, 1957)

solidation pressure The details of the procedure are ex- plained later in this chapter

The remainder of the pmedures listed in Table 14.4 will not be explained However, each procedure could be plot- ted on a three-dimensional plot with the stress state vari- ables used for the horizontal axes Later, a method for the prediction of heave will be outlined which is consistent with the fundamentals of the unsaturated soil theory of volume

change (Fredlund et al., 1980)

14.1.1 Factors Affecting Total Heave

The preceding review of the literature on swelling soil be- havior indicates that there are three primary factors con- trolling total heave, namely, the volume change indices and the present and future stress state variables The properties

of the soil have been shown to influence the volume change indices For example, soils compacted at various densities and water contents produce different soil structures which have different volume change indices In addition, various densities and water contents also affect the magnitude of

the stress state of compacted soils Soils compacted at low densities and high water contents (Le., wet of optimum water content) have a low matric suction value as compared

to the soils compacted dry of optimum water content Therefore, it can be concluded that the density and water content conditions in a soil affect both the volume change indices and the stress state These, in turn, control the amount of total heave

Chen (1988) studied the effect of initial water content and dry density of compacted soils on the amount of total heave The study was conducted using “fm-swell” oedometer tests on expansive shalcs from Denver, CO The

shale had 63% silt and 37% clay, with a liquid limit and plasticity index of 44.4 and 24.4%, respectively The re-

sults indicate that total heave increases with a decrease in the initial water content of specimens Compacted at a con-

402 14 VOLUME CHANGE PREDICTIONS

Surcharge pressure (kPa)

Figure 14.7 Effect on total heave of the surcharge pressure for

a specimen at a specified density and water content (from Chen,

1988)

Figure

content

1988)

Initial water content, w, (%)

14.5 Effect on total heave of varying the initial water

for specimens of constant initial dry density (from Chen,

stant initial dry density (Fig 14.5) On the other hand,

total heave increases with increasing initial dry density for

specimens compacted at a constant initial water content

(Fig 14.6)

In addition to soil pmperties such as dry density and water

content, the amount of total heave is also a function of the

total stress applied to the soil specimen Figure 14.7 dem-

onstrates the influence of the surcharge pressure during an

oedometer test on the amount of swelling The results show

that total heave decreases with an increasing surcharge

pressure In other words, it is possible to reduce the amount

of swelling by applying a high total stress to the soil Sim-

ilar observations were reported by Dakshanamurthy (1979)

as illustrated in Fig 14.8 In this case, a commercial so-

dium montmorillonite was statically compacted and tested

in a triaxial apparatus The specimens were first subjected

Initial dry dentsity, Pdo (kg/m’)

to various major and minor principal stresses, and then al- lowed to swell by imbibing water The results in Fig 14.8

indicate that total heave decreases with increasing mean normal stress, while the ratio of the principal stresses has

an insignificant effect on the total heave

Holtz and Gibbs (1956) summarized the effect of initial water content and dry density on the total heave of a com- pacted expansive clay (Fig 14.9) The heave was obtained

when the soil in an oedometer ring was submerged in water The specimens were subjected to a surcharge load of 7 kPa The diagram indicates an increasing total heave with re-

spect to a decreasing initial water content or an increasing initial dry density As an example, a clay compacted to optimum water content under standard AASHTO compac- tion will expand about 3% of its volume when saturated under a surcharge load of 7 kPa On the other hand, ex- pansion is reduced to zero at 3% wet of optimum water content, and is increased to 6% at a water content 3% dry

of optimum A similar diagram was also presented for the effect of dry density and water content on vertical swelling pressure (Fig 14.10) The vertical swelling pressure was

0 50 100 150 200 250 300 Mean normal stress, urn (kPa)

20

0 50 100 150 200 250 300 Mean normal stress, urn (kPa)

Figure 14.6 Effect on total heave of the initial dry density for

specimens, of constant initial water content (from Chen, 1988) Figure 14.8 Effect of various principal stress ratios on total

heave (from Dakshanamurthy, 1979)

14.2 PAST, PRESENT, AND FUTURE STATES OF STRESS 403

Initial water content, w, (%)

Figure 14.9 Effect of initial water content and dry density on

the expansion properties of compacted Porterville clay when wet-

ted (from Holtz and Gibbs, 1956)

defined as the pressure developed in a specimen placed in

an oedometer ring and saturated without allowing any vol-

ume change The diagram shows that the vertical swelling

pressure is more sensitive to variations in the initial dry

density than it is to variations in initial water content

Chen (1988) also studied the effect of volume-mass

properties on vertical and lateral swelling pressures The

vertical swelling pressure was found to be essentially in-

dependent of the initial water content and the surcharge

load This finding is in agreement with the observations

made by Holtz and Gibbs (1956), as shown in Fig 14.10

The vertical swelling pressure, however, increases expo-

nentially with an increasing dry density, as illustrated in

Fig 14.11 On the other hand, the lateral swelling pressure

was found to be a function of the initial dry density, the

Initial dry density, pdo (kg/mS)

Figure 14.11 Effect of initial dry density on swelling pressure (from Chen, 1988)

degree of saturation, and the surcharge load The experi- mental results indicate that the lateral swelIing pressure in-

creased rapidly to a peak value during saturation, and then decreased to an equilibrium state, as demonstrated in Fig 14.12 This observation is in agreement with the results of extensive research into lateral swelling pressure behavior conducted by Katti et al (1969)

14.2 PAST, PRESENT, AND FUTURE STATES

OF STRESS

The prediction of volume change requires information on possible changes in the stress state and the soil pmperty, known as a volume change index Oedometer tests ex- plained in Chapter 13 are commonly performed to deter- mine the present in situ state of stress and the volume change indices In this test, the present in situ state of stress

is translated onto the net normal stress plane, and is re- ferred to as the “corrected” swelling pressure The mea-

A Initial placement condition

Initial water content, wo(%)

Figure 14.10 Swelling pressure caused by wetting compacted

Porterville clay at various placement conditions (from Holtz and

404 14 VOLUME CHANGE PREDICTIONS

sured and corrected swelling pressure represents the sum

of the overburden pressure and the matric suction equiva-

lent The matric suction equivalent is the matric suction of

the soil translated onto the net normal stress plane Thus,

the oedometer test measures the in situ state of stress (on

the total stress plane) without having to measure the indi-

vidual components of stress

14.2.1 Stress State History

The development of an expansive soil can be visualized in

terms of changes in the stress state in the deposit Changes

in stress state occur during geological deposition, erosion,

and during environmental changes resulting from precipi-

tation, evaporation, and evapotranspiration The following

example illustrates the stress history of a preglacial lake

sediment that has evolved to become an expansive soil over

a period of time

Consider a preglacial lake deposit that was initially con-

solidated under its own self weight The drainage of the

lake and the subsequent evaporation of water from the lake

sediments result in desiccation of the deposit The term

"desiccation" refers to the drying of soils by evaporation

and evapotranspiration The water table is simultaneously

drawn below the ground surface As a result, the pore-

water pressures above the water table decrease to negative

values, while the total stress in the deposit remains essen-

tially constant In other words, the effective stress in the

soil increases, and consolidation takes places The negative

pore-water pressures act in all directions (i.e., isotropi-

cally), resulting in a tendency for cracking and overall de-

saturation of the upper portion of the profile (Fig 14.13)

The soil is further desaturated as a result of the growth

of grass, trees, and other plants on the ground surface Most

plants are capable of applying as much as 10-20 atm of

tension to the water phase prior to reaching their wilting

point A high tension in the water phase (i.e., high matric

suction) causes the soil to have a high affinity for water

[Fig 14.13(a)]

The surface deposit can also be subjected to varying and

changing environmental conditions The changing water

flux (Le., wetting and drying) at the surface results in the

swelling and shrinking of the upper portion of the deposit

Volume changes might extend to depths in excess of 3 m,

causing the surface deposit to be highly desiccated

Figure 14.14 illustrates the changes in the stress state of

the surface deposit during wetting and drying due to infil-

tration and evaporation, respectively Changes occur pri-

marily on the matric suction plane at an almost constant net

normal stress The stress paths followed during the wetting

and drying processes can be illustrated as hysteresis loops

on the matric suction plane

In arid and semi-arid regions, the natural water content

in a deposit tends to decrease gradually with time Low

Evaporation and

Cracks and fissures (unsaturated) Saturated

/ 'e%,* i'

(b)

Figure 14.13 Stress state repwsentation after lake sediments are subjected to evaporation and evapotranspiration (a) Pore-water pressures during drying of a lacustrine deposit; (b) stress-state path during drying of a lacustrine deposit

water content conditions in an unsaturated clay deposit in- dicate that the soil has a high swelling potential Unsatu- rated soils with a high swelling index, C,, in a changing environment are referred to as highly swelling and shrink- ing soils (i.e., expansive soils)

14.2 PAST, PRESENT, AND FUTURE STATES OF STRESS 405 14.2.2 In Situ Stress State

The prediction of heave requires infonnation on the present

in situ stress state and the possible future stress state The

difference between the present and future stress states is

one of the main variables which indicates the amount of

volume change or heave that can potentially occur There-

fore, it is important that the present in situ stress state be

accurately assessed When using laboratory oedometer tests

for assessing the present in situ stress state, it is imperative

to correct the results for sampling distuhce In this book,

most attention is given to the use of laboratory oedometer

test results for the assessment of the in situ stress state

This procedure appears to be satisfactory as long as the

oedometer test can be performed on specimens which ad-

equately represent the in situ soil mass When the soil mass

is highly fissured and cracked, it is difficult to obtain rep-

resentative samples Under these conditions, it is prudent

to give more attention to heave analysis procedures which

measure the in situ suction and the three-dimensional vol-

ume change modulus for the soil

When a soil is sampled for laboratory testing, its in situ

state of stress is somewhere along either the wetting or the

drying portion of the void ratio versus the stress state vari-

able relationship (Fig 14.14) In the field, the soil has been

subjected to numerous cycles of wetting and drying At the

time of sampling, the soil has a specific net normal stress

and a specific matric suction

The laboratory infomation desired by the geotechnical

engineer for predicting the amount of heave is an assess-

ment of 1) the in situ state of stress, and 2) the swelling

properties with respect to changes in net normal stress [Le.,

(a - u,)] and matric suction [Le., (u, - u,,,)] An under-

standing of the compressibility properties under loading

conditions would, also be useful A demanding testing fa-

cility and program would be required to completely assess

all of the above variables For this reason, it is necessary

to develop a simpler, more rapid, and economical proce-

dure to obtain the information required to predict heave for

practical problems

Several laboratory testing procedures have been used in

practice to obtain the necessary information Among these

procedures, the one-dimensional oedometer test is the most

commonly used to determine the present in situ state of

stress The “free-swell” and the “constant volume”

&dometer test methods have been explained in detail in

Chapter 13, together with the necessary correction proce-

dures Other oedometer test procedures have also been

used, but in general these pwedures are variations of the

“constant volume” and “free-swell” procedures

The oedometer test translates the in situ stress state onto

the net normal stress plane The in situ stress state is re-

ferred to as the “corrected” swelling pressure, Pj , which

is equal to the sum of the overburden pressure and the ma-

tric suction equivalent (Chapter 13)

Pa = preconsolidation pressure 0.2 J 1 1 1 1 1 ‘ 1 ‘ ’ “ ” ” ’ ‘ * I ‘ ’ L L

Log (0 - u.) (kPa)

Figure 14.15 Position of corrected swelling pressure relative to the preconsolidation pressure of the soil

Figure 14.15 shows typical laboratory oedometer test data plotted to a scale which allows comparison to the vir- gin compression curve Often, the entire laboratory loading curve is on the recompression portion, with the loading not even reaching the virgin compression branch In other words, the preconsolidation pressure of many desiccated soils, P,, may exceed the highest load applied during the test

The preconsolidation pressure refers to the maximum stress producing a volume decrease that the soil has ever been subjected to in its history Figure 14.15 illustrates the relative position of the comted swelling pressure, Pj , to the preconsolidation pressure, P, The corrected swelling pressure, P; , is located approximately at the intersection between the constant void ratio line and the recompression branch On the other hand, the preconsolidation pressure,

P, , is located at the intersection between the recompression branch and the virgin compression curve

Methods for determining the preconsolidation pressure have been described in many soil mechanics textbooks, and will not be repeated herein, However, it is appropriate and useful to redefine the overconsolidation ratio, OCR, as the ratio of the preconsolidation pressure, P, , to the corrected swelling pressure, Pi, where Pi is a representation of the

in situ stress state of the soil:

(14.1) where

OCR = overconsolidation ratio

P i = corrected swelling pressure

P, = preconsolidation pressure

Equation (14.1) is a modified definition for the overcon- solidation ratio At present, OCR is usually defined as the

406 14 VOLUME CHANGE PREDICTIONS

ratio of the preconsolidation pressure, Pc., to the in situ

vertical effective overburden pressure, u:, (Le., (u,, - u,),

where u,, = total overburden pressure and u, = pore-water

pressure) The use of the corrected swelling pressure, P,; ,

in Eq (14.1) eliminates the need for measuring the in situ

negative pore-water pressure and assessing how it should

be combined with the total stress when defining OCR In

addition, it seems more appropriate to define the degree of

overconsolidation with respect to the in situ stress state on

the net normal stress plane (i.e., P i )

14.2.3 Future Stress State and Ground Movements

Having determined the present in situ state of stress and

the swelling indices from oedometer tests, the analysis can

proceed to the prediction of possible changes in the stress

state at some future time The future state of stress corre-

sponding to several years after construction must be esti-

mated, based upon local experience and climatic condi-

tions Several procedures for estimating the final pore-

water pressure profile are discussed in the next section

Changes in total stress can be anticipated as a result of

excavation, replacement with a relatively inert material

(e.g., gravel), and other loadings The effects of these

changes can be taken into account using appropriate vol-

ume change indices for loading and unloading However,

it may be possible to assume that there is insufficient time

for the soil to respond to each individual loading and un-

loading The long-term volume change calculations will

then be approximated as the net loading or unloading

For discussions concerning possible future swelling, let

us assume that the final pore-water pressufes of the soil

may go to zero under a constant net normal stress Figure

14.16 shows the actual stress path that would be followed

by a soil element at the depth from which the sample was

retrieved Swelling would follow a path from the initial

void ratio, e,, to the final void ratio, er, along the rebound

surface on the matric suction plane The entire rebound

surface can be assumed to be unique since the direction of

deformation is monotonic (Matyas and Radhakrishna,

1968; Fredlund and Morgenstern, 1976) Therefore, it is

also possible to follow a stress path from the in situ stress

state point over to the “corrected” swelling pressure, and

then to proceed along the rebound curve on the net normal

stress plane to the final stress condition The advantage of

the latter stress path is that the volume change indices de-

termined on the net normal stress plane can be used to pre-

dict total heave

14.3 THEORY OF HEAVE PREDICTIONS

Heave predictions should ideally be conducted using the

volume change theories presented in Chapter 12 for various

loading conditions The volume change coefficients or in-

Analysis stress

path

Swelling pressure, p;

Figure 14.16 “Actual” and “analysis” stress paths followed during the wetting of a soil

dices and matric suction changes should be measured using the techniques presented in Chapters 13 and 4, respec- tively These changes should then be used to compute the total heave in a manner consistent with Eq (12.47) (Le.,

= mikd(uy - u,) + m;d(rc, - u,) where dey = incre- mental strain in the y-direction, (ay - u,) = net normal stress in the y-direction, (u, - u,) = matric suction, m&

= coefficient of volume change with respect to (uy - u,)

for KO loading conditions, and m; = coefficient of volume change with respect to (u, - u , ~ ) ) The stress state variable changes can be large and consequently, the soil properties

can vary as the stress levels change As a result, it would

be necessary to integrate Eq (12.47) between the initial

and final stress states, while making the soil properties a function of the stress state It is possible to circumvent this complexity by recognizing that the constitutive surface can

be linearized by plotting the stress state variables on a log- arithmic scale In addition, it is possible to make a further simplification by transferring the matric suction variable onto the net total stress plane

The total heave formulation will be presented with the initial and final stress states projected onto the net normal stress plane The results from a one-dimensional oedome-‘ ter test are plotted on a semi-logarithmic scale (i.e., the stress state) and the slope of the plot is used in the formu- lation for total heave This method greatly simplifies the analysis for the prediction of total heave The in situ stress state is equal to the vertical swelling pressure of the soil which is measured in a one-dimensional oedometer under Ko-loading conditions As a result, only the vertical or one- dimensional heave is predicted The vertical heave predic- tion is of importance in the design of shallow foundations

14.3 THEORY OF HEAVE PREDICTlONS 407

for light structures Two case histories dealing with highly

expansive soils in Saskatchewan, Canada, are later ana-

lyzed and presented to illustrate the application of the total

heave prediction theory

For loading configurations other than Ko-conditions, vol-

ume change can also occur in the lateral directions The

swelling pressure in the lateral direction depends on several

variables, such as the initial at rest earth pressure coeffi-

cient and the horizontal deformation moduli for the soil, as

pointed out in Chapter 1 1 In a soil with wide desiccation

cracks, substantial volume changes may occur in the hori-

zontal direction prior to the development of the lateral

swelling pressure The ratio of the lateral to vertical swell-

ing pressures can range from as low as the at rest earth

pressure coefficient, which may be zero, to as high as the

passive earth pressure coefficient (Pufahl er al., 1983;

Headquarters, U.S Department of the Army, 1983; Fourie,

1989) The lateral heave prediction is best analyzed using

the volum'e change theory presented in Chapter 12, and it

will not be further elaborated upon in this section

14.3.1 Total Heave Formulations

The procedure for the calculation of total heave or swell is

similar to that used for settlement calculations The amount

of total heave is computed from the changes in void ratios

corresponding to the initial and final stress states and the

swelling index The formulation will be visualized on the

void ratio versus the logarithm of the stress state The fol-

lowing formulation assumes stress paths which have been

projected onto the net normal stress plane, as shown in Fig

14.17 The total heave stress path follows the rebound

curve (i.e., C,) from the initial stress state to the final stress

state The equation for the rebound portion of the oedom-

eter test data can be written as,

14.17 One-dimensional oedometer test results showing the ef-

fect of sampling disturbance

rected swelling pressure (Le., Po = Pi)

final stress state

follows :

where

Au, =

Uwf =

The initial stress state, Po, or the corrected swelling pres-

sure, P i , can be formulated as the sum of the overburden pressure and the matric suction equivalent (Fig 14.15) as follows:

PO = (uy - ua) + (u, - U w ) r (14.3) where

a,, = total overburden pressure

uy - u, = net overburden pressure

u, = pore-airpressure

(u, - u,,,)~ = matric suction equivalent

uw = pore-water pressure

Equation (14.3) defines the initial stress state, Po In

practice, the value of Po is not calculated, but measured as

the corrected swelling pressure, Pi, in an oedometer test The final stress state, Pf, must account for total stress

changes and the final pore-water pressure conditions The pore-air pressure in the field remains at atmospheric con- ditions The final pore-water pressure conditions can be predicted or estimated as explained in the next section

Therefore, the final stress state, Pf, can be formulated as

Pf = uy + Au, - uwf (14.4)

change in total stress due to the excavation or

placement of fill; the total stress change can have

a positive or negative sign for either an increase

or decrease in total stress, respectively predicted or estimated final pore-water pressure The heave of an individual soil layer can be written in

terms of a change in void ratio:

Aei

1 + e, hi

where

Ahi = heave of an individual soil layer

Aei = change in void ratio of the layer under consider-

e, = initial void ratio of the soil layer

efi = final void ratio of the soil layer

hi = thickness of the layer under consideration ation (i.e., eoi - efi)

408 14 VOLUME CHANGE PREDICTIONS

The change in void ratio, dei, in Eq (14.5) can be re-

written, by incorporating the soil properties and the stress

states [Le., Eq (14.2)], to give the following form for the

heave of a soil layer:

(14.6) where

Pfi = final stress state in the soil layer

Poi = initial stress state in the soil layer

The total heave from several layers, AH, is equal to the

sum of the heave for each layer:

14.3.2 Prediction of Final Pore-Water Pressures

The final pore-water pressures below a foundation or pave-

ments can either be pdicted or estimated A prediction

must take into consideration the surface flux boundary con-

ditions (i.e., infiltration, evaporation, and evapotranspira-

tion) and the fluctuation of the groundwater table The sur-

face flux boundary conditions can vary from one geographic

location to another, depending upon the climatic condi-

tions Russam and Coleman (1961) related the equilibrium

suction below asphaltic pavements to the Thomthwaite

Moisture Index On many smaller structures, however, it

is often man-made causes such as leaky water lines and

poor drainage which control the final pore-water pressures

in the soil

There are three possibilities for the estimation of final

pore-water pressure conditions, as illustrated in Fig 14.18

First, it can be assumed that the water table will rise to the

ground surface, creating a hydrostatic condition This as-

sumption predicts the greatest amount of total heave Sec-

ond, it can be assumed that the pore-water pressure ap-

proaches a zero value throughout its depth This may appear

to be a realistic assumption; however, it should be noted

Water table

Hydrostatic

(greatest heave) pore-water pressures 3

curs in the uppermost soil layer where the change in matric suction is largest

14.3.3 Example of Heave Calculations

The following example problems are presented to illustrate the calcutations associated with total heave The first ex-

ample considers a 2 m thick layer of swelling clay (Fig

14.19) The initial void ratio of the soil is 1.6, the total

unit weight is 18.0 kN/m3, and the swelling index is 0.1 Only one oedometer test was performed on a sample taken

from a depth of 0.75 m The test data showed a corrected

swelling pressure of 200 kPa It is assumed that the cor-

rected swelling pressure is constant throughout the 2 m

layer

Let us assume that the ground surface is to be covered with an impermeable layer such as asphalt With time, the negative pore-water pressure in the soil below the asphalt will increase as a result of the discontinuance of evapora- tion and evapotranspiration For analysis purposes, let us

assume that the final pore-water pressure will increase to zero throughout the entire depth

The 2 m layer is subdivided into three layers The amount

of heave in each layer is computed by considering the stress state changes at the middle of the layer The initial stress state, Po, will be equal to the corrected swelling pressure

at all depths The final stress state, Pf, will be the over- burden pressure Equation (14.6) is used to calculate the heave for each layer The calculations in Fig 14.19 show

a total heave of 11.4 cm Approximately 36% of the total heave occurs in the upper quarter of the clay strata The calculations can also be used to show the amount of heave that would occur if each layer became wet from the surface downward

The second example shows a more complex loading sit- uation, and the results are presented in Fig 14.20 Again, the clay layer is 2 rn in thickness The initial void ratio is 0.8, the total unit weight is 18.0 kN/m3, and the swelling index is 0.21 Three odometer tests were performed, which show a decrease in the corrected swelling pressure with depth (Fig 14.20)

Suppose the engineering design suggests the removal of

1 /3 m of swelling clay from the surface, prior to the place- ment of 2/3 m of gravel The unit weight of the gravel is assumed to be equal to that of the clay The 13 m of swell-

14.3 THEORY OF HEAVE PREDICTIONS 409

2) Final pore-water pressure equals zero Equation: Ah, =

Figure 14.19 Total heave calculations for example no 1

ing clay is subdivided into three strata The thickness of

each layer is shown in the table in Fig 14.20

The initial stress state, Po, can be obtained by interpo-

lation of the corrected swelling pressures at the midpoint

of each layer The final stress state; Ps, must take into ac-

count the final pore-water pressure and changes in the total

stress The final pore-water pressure is assumed to be -7.0

kPa Equation (14.6) can be used to calculate the heave in

each layer The total heave is computed to be 22.1 cm

Two assumptions are made during the heave analysis in

the second example First, it is assumed that the indepen-

dent processes of excavation of the expansive soil and the placement of the gravel fill do not allow sufficient time for equilibrium to be established in the pore-water Therefore, the soil responds only to the net change in total stress Sec- ond, by estimating a final negative pore-water pressure, it

is assumed that as saturation of the soil is approached, the slopes of the rebound curves on the matric suction and total stress planes approach the same value This assumption is reasonable, provided the final pore-water pressure is rela- tively small

A third example illustrates the amount of heave versus