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THE MENARD PRESSUREMETER

Interpretation

and

Application

of Pressuremeter Test Results to Foundation Design

GENERAL MEMORANDUM

D.60.A N

OUR RESEARCH CENTRES IN FRANCE

,}:

Longjumeau (Essonne)

Granville (Manche)

SOLS SOl LS N° 26 - 1975

Contents Introduction

3,

Analysis of results obtained

10

Ca lculation of the bearing capacity

19

Calculation of the seulement foundation

at a

Evaluation of differentiai settlement. Allowable values for structures Conclusions

SOLS SOl LS No 26- 1975

34

41

1ntroduction This general note is a review of the technical ru les adopted by specialist engineers employing pressuremeler methods. lt has been edited for incorporation in sail investigation reports th us allowing the reader a full understanding of the pressuremeter analysis.

independant cells and consequently exerts at the central cell level a strictly uniform pressure against the borehole walls. The pressure is increased in equal increments of time and pressure and the resulting borehole expansions recorded (fig. 2).

The notice first describes the practical procedures that must be respected by the geotechnicians and drilling personnel in carrying out the borings and the pressuremeter tests . The drilling equipment and test method used will vary in function of the nature of the sail encountered and the type of study undertaken .

The instruments currently in use are the types G and GC. The monitoring deviee is connected to the probe by what appears to be a single flexible plastic tubing but which is in tact two tubes one inside the ether. The inner tube carries the water to the central cell and the space between the two tubings allows the gas to reach the guard celts; this prevents the possible expansion of the inner tubing which would lead to erroneous readings of the amou nt of water injected.

Then foll ow the ru les for the interpretation of the results, based on the pressuremeter theory as weil as the experience gained from a large number of full -scale tests. These ru les relate to the most usual cases, from the point of view of sail mechanics : appartment buildings, bridges, reservoirs, etc ... Special notices are also available for studies of a particutar nature : sheet pile or diaphragm walls, piles subjected to horizontal forces, stabitity of slopes and excavations, transmission towers, foun· dations subject to alternating loads orto vibrations, foundations on rock, tunnels, dams, roads, etc ... lt is reminded that the pressuremeter test is essentially an in-situ load test carried out within a borehole on the actual site being investigated. Analysis of the stress/ deformation diagrams obtained for each metre of penetration permits the evaluation of the mechanical properties of the sail on which are based the calculations for the foundations.

Pressure is applied to the water through pneumatic control equipment and the resutting sail deformations are indicated by volume changes which are read on a sight tube. Each instrument can be supplied with a series of prob!'!s which corresPond to the most usual bore· hele dimensions.

OCOMA code

l

EX

Diameter of the probe

Borehote diameter (mm)

(mm)

mini.

32

34

1. 1.

Performance of the pressuremeter test

Equipment

The pressuremeter (fig. 1) consists of two main elements : a radially expandable cylindrical probe which is ptaced inside a borehole at the desired test elevation and a monitoring unit which remains on the grou nd surface. The probe is made up of three SOLS SOILS N" 26- 1975

8X NX

38

44

46

58

60

66

74

76

80

AX

1.

maxi .

521

The standard metallic probecovers will allow testing the majoritv. of soils.

Type GB pressuremeter ln service since 1973; particularly adapted for tests in rock ( 100 bars) - ali cells pressurized by water.

Type GC pressuremeter Modern version replacing the older type G in service since 1962

Fig. 1

8

- normal pressure range : up to 40 bars - guard cells pressurized by gas - measuring celles pressurzied by water

SOLS SOl LS N' 26- 1975

For very loose compressible soils characterized by limit pressures of less than 1.5 bar, very flexible membranes and covers with an overall inertia of 0.6 bar should be used. On the ether hand, for very high moduli (above 20.000 bars), stiff covers and membranes shall be used, previously calibrated ; these exhibit a much reduced and more uniform compressibility. When the volume variation, for a pressure increment of 1 bar, becomes less than 0.5 cm3 (modulus above 4 .000 bars), the volumetrie shunt must be used, magnifying 50 times the sensitivity of the volume readings. Finally, it is appropriate ta record the recent introduction of a simpler apparatus known as the minipressuremeter which is adapted forcompaction control and sail investigations at shallow depth. ln this case, the probes employed are shorter, their diameters being 22 and 32 mm.

1.2.

or rock bits. A rotary percussion wagon drill may be used provided the drilling fluid is a bentonite slurry. The traditional sounding equipment used for obtaining labo ra tory samples is not al ways sui· table for pressuremeter drilling as it often leads ta disturbance of the borehole walls due to the slow rate of advancement, the circulation of water under pressure betweerï the walls of the ho le and the core barrel and the vibratiOn of the drill rads. The tests should be carried out after each pass of the drill which itself must be limited to a length varying from 3 to 30 m according to the nature and sensitivity of the ground.

1.2.3. Very compact deposits of sand or sand and gravel require a mixed method of driving and drilling: il a large diameter casing is driven and the inside washed out; a srilall pilot hele is then drilled ahead over a short distance and an ordinary «slotted casing» driven into it. The tests are carried out as dril ling advances, or

General notes on placing the pressuremeter probe

1.2. 1. ln submergee! loose granular soils (sand, sand and gravel below water), the probe must be driven ta the required elevation either by driving as in the «Standard Penetration Test», or by static pressure such as in the Dutch cane soundings, or aga in by vibration ; in this case, the probe is protected by a casing with longitudinal slits which allow radial expansion. This method results in sail particle movement and slight compaction n~ar the point, but as long as the sail is granular, the effects on the test results are negligible. On the contrary, silty or clayey soils, especially below the water table, are not completely insensitive to driving, ta static penetration or even to vi bration ; it is therefore recommended that the probe should not be placed by these methods for very precise investigations of settlements as this may result in altering the elastic properties of the sail. These methods nevertheless re main val id for the majority of foundation studies and do nOt alter the failure characteristics.

1.2.2. ln many cases, the probe can be lowered in boreholes pre-drilled with flight augers, raller bits

SOLSSOILS N° 26-1975

ii) an open ended «slotted casing» attached ta a casing of the sa me diameter is driven into the sail following the path of a pilot ho le drilled through the casing and slightly a head of it. The tests may th en be car· ried out after completion of the drilling operation as the casing is being extracted.

1.3.

Soif identification

As will be seen later, the shape of the pressuremeter curves, the values of limit and creep pressures, the moduli E and the relations between moduli E and li mit pressures (see para. 2.4), give precise indications of the nature of the investigated layers. These results are complemented by visual examination of sail samples whether they be augered, from a sam pler or cuttings from wash boring. The rate of drilling advancement and/ or the driving records supply additional information as ta the layers encountered. When particularly delicate geological conditions are encountered, an additional borehole with near continuous sampling should be provided for.

1.4.

Carrying out the test

1.4.1. The standard test must be· carrièd out less than 24 hours after the drilling operation except in the case of driven-in probes where there is no risk of alteration of the soit due t o water absorption. However, tolerances of several days are admissible for boreholes carried out without water (hand augering, drilling with air scavenging) above the water table. Whatever the investigation, the tests must be carried out systematically, metre by ·metre in arder to record accurately the variations of strength parameters in function of depth. Discontinuities in the test spacing are not allowable ; the measurements are thus practically continuous and enable complete information to be obtained concerning the various lay ers. Emphasis is placed on the necessity for continuous pressuremeter testing from the ground levet, whatever may be the depth previously prescribed for the foundations. This is to 'ensure a better understanding of the site by a complete study of the different layers and an exact determinatio n of the «equivalent embedment» and the possible active earth pressures.

1.4.2. The test itself is standardized and shou ld be carried out with ten equalloading increments (5 to 14 increments will be tolerated) up to the point of failure . Readings of deformations with respect to time are taken for each pressure increment at . 15 seconds, 30 seconds and one minute after the appliCation of this increment (fig. 2) . 1.4.3. To obtain as complete a load deformatio n curve as possi ble, the measured volume should 3 reach 700 cm if pl < 8 bars and 600 cm if 8 < ~ < 15 bars. ln ether cases the test must be carried up to 20 to 25 bars pressure in soils and up to 50 to 70 bars in rocks. 2.

Analysis ·o f results obtained

2.1.

Characteristics measured

From the load deformation diagrams thus obtained at each elevation, the main mechanical characteris-

10

tics of the soil are calculated ; these are : the deformation modulus E and the limit pressure p~ at failure.

2. 1.1. The pressuremeter modulus Eisa distortion modulus of the soil measured in a deviatoric stress field. lt characterizes the pseudo-elastic phase of the test . Obviously i(must not be confused with the oedometer modulus (measured in an isotropie or spherical stress conditions). although precise experimental relationships exist between them as will be seen later. The distortion modulus plays an essential role in the calculation of the settlement of foundations and is generally more important than the oedometer modulus . The limit pressure Pt by definition corresponds to the limiting state of failure of a soit subjected to an increasing uniform pressure on the wall of a cylindrical cavity. This fundamental mechanical characteristic enters into ali the analysises of foundation stability carried out in accordance with pressuremeter methods.

2.1.2.

The test also permits the ca lcul ation of ether characteristics of the soil : the creep pressu re or elastic limit (fig. 2-cl. creep coefficient, the natural «at-rest» pressure. These characteristics on ly enter into very special studies and do not appear in the usual reports.

2.1.3.

2.2.

Calculation of modulus E and limit pressure p~

2.2.1. Computation of the modulus E

ln an elastic media , the radial expansion of a cylin· drical cavity is related to the pressure by the equation :

~ E or

E = (1 + ~1 ~

Llp

(1)

(2)

Llr

where a

is Poisson's ratio, arbitrarily assigned a value of 0.33.

SOLS SOILS N" 26-1975

,----

Prtssufl

,----

,----,----

,----

Pi

~ Vi(u)

a) pressure and volumetrie expansion against

"l

Vi (~)

ti me

Ti me

"'- '\...

Vi f.o)

'\... ~ Vol umtHic

'\...

Expansion

~

Volumelrit Expansion pseudo-elastic phase

b) the pressuremeter curve

Pl Pressure ( limlt pressure)

"~'"' )..___.,._,.---L,i,L---L--L---,~~ 1

c) the creep curve

- P l

(creep pressure)

Prtssu rt

Fig 2

SOLS SOILS N' 26- 1975

Plotting a pressuremeter test

11

When expressed in function of volume instead of radius, equation (2) becomes ~ (1+o) 2V ~

!3 1

Probe

D1ameterof borehole

is the volum}i of the cavity at the ~stant when ~is measured, provid~d ~ is measu red in the pseudo·elastlc p~ase of t he test (fig. 3·al

Va (c·mJ)

EX

34

AX

44

535

BX

60

535

NX

76

790

"' v where V

(mm)

-

K (cm'l

535 2000

2700

The modu lu s derived from equation (3) is referred to as the «pressuremeter modulus». ln a pressuremeter test, the vo lume V depends on the size of the probe used ; it is the sum of two components

where V0

is the initial or «at rest» volume of the measuring cell

vm

is the mean additional volume injected (read directly on the sight tube of the instrument).

and

Equation (3) can the refere be expressed as E ~ K~ /', v

where K

is a dimensional coeffic ient of · the probe K = (1 + a) 2 (V 0 + = 2.66 (V 0 + vml

Vm)

(The arbitrary value of 0.33 assigned to Poisson's ratio has no influence on the estimation of settle· ments. The same value has been assigned in the term (L.±..E:l which appears in the settlement for· mulae). E The value of K for vm """' 200 cm 3 are as fo ll ows for standard probes (these do not apply to special BX and NX probes with longer centra l cells for greater accuracy).

12

The nomogram fou nd on the fol lowing page yields immediately the va lu es of the modulus E for stan da rd EX, AX, and BX probes.

2.2.2. Computation of the !imit pressure Pt By definition, the asymptote be determined conventionally ponding to a initial vo lume

the limit pressure is the abscissa of to the pressuremeter curve. lt can directly from the curve but more it is taken as the pressure carres· volume increase b.V equa l to the of the borehole V (ô V/ v = 1).

Since the initial vo lume for a standard AX or BX probe is in the arder of 600 cc {535 cm 3 + volume injected to contact the borehole walls) b. V/ v may be assumed to occur for a reading of V = 700 cc. If, during a test, the vo lu metrie increase attained is less than specified above, it is still possible to extrapolate with precision the value of the limit pressure provided the creep pressure has been exceeded during the test. This extrapo lation is based on the relative or reciprocal volumes theories. ln the latter case, the last few readings corresponding to the plastic phase are plotted on a p, 1/V scale paper; these should plot as part of a straight line; the point at whi ch the extension of the straight li ne intersects the 700 cc ordinate corresponds to th e limit pressure.

SO LS SO ILS No

2S- 1975

(volur'fleter

read1ngs) 700

1 1

~1

1i

~t '

1

'1

pu

l>p

{Pressure gouge

reading)

E = K ( vm) />p_ l>pj

CO'

f:J.v

K l>p llv

K ! v m) can be derived from the next chart as Jang as water level is at 0 mark in the sight tube of the volumeter when the probe is «at rest>>

P~ =Pu-

pi

+Water head

v

ER=K ~

"L-Vi

EA.AVG•K~

v2_v;

p

SOLS SOILS N" 26-1975

Fig 3

13

1000

(cm•)

iii! 500

-

400

250

1 1

200 _190

1

180 170 160 150 4

1

1 1 1 1

'

1

1

j 130 120

1

110

1

100

i

pl

Pressure seo 1e _..,...

How to plot the plastic JJhase curve on a p, 11v graph paper to obtain the limit pressure

14

SOLS SOl LS N" 26 - 1975

0

~

51

~'"

~

~

.D

~ ] w

"~

~

!l' 3

.i

~

1

w

g ~

d

~

"

"Il 1~

~

Ill ,;

~

E

~

'ii .:l

w

] ~~~

~

E

~ :;:E

L

·f

~

~ 1'5

6

~

/!' m~ ~

j~

~

i"

~

1

c

~

~

'l'

§

~

~

"'

~

[;; b

~

i5

u

SOLS SOl LS N° 26- 1975

15

An approximate value of the li mit pressu re can also be obtained considering the following statistical results: · the creep pressure (or the end of the elastic phase) is equal to a half or two thirds of the li mit pressure ;

2.4.

Indicative values of E and p 1

2.4.1. lt may be useful, for readers unfamiliar with pressuremeter techniques to list the usual ranges of E and p1 for the principal types of sail s. Sail

· for every geological formation, there is a constant relationship between E and p1 according to the type of sail.

22.3. The pressure and volume readings recorded on the site must be adjusted to compensate for : - the head of water in the central cell tubing; - the inertia of the assembly consisting of the membrane + caver + possibly a slotted tube (6 Pi ou

p;l; - the expansion of the central cell tubing under pressure. The first two essentially affect the value of the limit pressure and the third, which is minimal, the pressuremeter modulus.

2.2.4. When the sail investigation relates to foun dations subject to cyclic loadings or vibrations, it is of interest to carry out a number of loading and unloading cycles in the pseudo-elastic phase of the test . These cycles yield : - a rebound modulus ER ; - a cyclic modulus EA which is a mean of repetitive loading and rebound cycles.

mud, peat soft clay medium clay stiff clay mari loose silty sand silt sand and gravel sedimentary sands limestone recent fill old lill

~

P• in bars

21o 15 0 .2 to 1.5 0.5 to 3 51o 30 30 to 80 3 10 8 80 to 400 6 to 20 50to600 6 to 40 lo 5 51o 20 to 15 20 to 100 80 to 400 12 lo 50 75 to 400 10 10 50 800 to 200.()(X) 30 toover 100 0.5 to 3 51o 50 4 to 10 40to150

2.4.2. The ratio E/ p1 of the modulus and the li mit pressure is a characteristic of the type of sail under exélmination; the higher values of E/ p 1 (12 to 30) are encountered amongst over-consolidated soils such as the London clay ; the law values of E/ p 1 (5 to 8) are more prevalent with alluvial soils (sands and gravels, silty sands under water). This ratio should be systematically studied in arder to follow the sail variations with precision and bring tc light any accidentai remoulding during the drilling operation which could result in a decrease of 20 tc 30% of Ei p,. The examination of the driving records are aise useful for detecting local variations although these have no absolute meaning, whatever may be the opinion of seme who believe in their adequacy.

These are of particular value for any study related to motorways or vibrating machinery.

2.5.

2.3. Presentation of results

lt is recalled that the point resistance Rp of the static penetrometer is proportional tc the modulus E and the limit pressure p1• The ratios Rplp 1 are constant for a given geological layer but vary with the grain size distribution of the soit and its water content. The following relationships have been established, deduced from the pressuremeter theory and checked experimentally.

The modu li and li mit pressure values are presented graphically in function of depth in parai lei with the logs and driving records. The simultaneous presentation of ali these results greatly facilitates the analysis of the sail conditions.

16

Correlation between point resistance Rp (static penetrometer) and p 1

SOLS SO ILS N' 26- 1975

DRIV ING RECORDS

Blows

per

10 c.m

pendrchon

10 11

: sttonds For 30cm

12

Fig 4

SOLS SOILS N° 26- 1975

17

Type of soli

Rpi P,

clay silt

2.5 io 4 5 to 6 to 9

sand

2. 6.

2.7.1. The study of differentiai seulement int'roduces the concept of specifie settlement of the ground (the seulement of a foundation of one metre square loaded at one bar) at each sounding location and the percentage variations of the specifie settlements between the different locations. lt is desirable, from the general study stage onwards, to utilize this same idea of standardized specifie settlement for a typical case of loading (a case of . three imaginary parai lei strip footings 1 m wide at 4.5 m centres loaded at 1 bar. This seulement ws is calculated for each sounding location using the formula below (to be explained in paragraph 4.6.1 .). which takes into account the decrease of the stresses and the variations of moduli with depth by applying a weighting factor. The ground has been divided into layers 1 m thick (except the first one which is only 50 cm) over a depth of 25 m to obtain

Influence of the water-table leve/

The influence of the water·table leve! on the measured characteristics is appreciable and increases with the ratio E/ p 1 of the sail. Thus the saturation of an initially dry sail characterized by E/ p 1 = 20 may result in a decrease of up to 40 % of the E values. This ph enomenon must be taken into ac· count when dealing with work founded on silts situated in areas subject to flooding or large watertable leve! variations. 2.7.

General features of the site investigated

c

Before proceeding with the actual calculations for the foundations, it is necessary to study the general features of the site by a statistical analysis of the geotechnological results obtained. lt will be seen later that the settlements (and the differentiai settlements in particular) rather than bearing capa· city limit the loads that can be supported by a sail.

i

where E1

The site will therefore be defined not only by the average characteristics encountered but also, and above ali , by their variation in plan and depth.

0

is the pressuremeter modulus at depth i,

ni

is the weighting factor at the same depth, the values of which are given below:

0

1

2

3

4

5

6

7

8

9

10

11

Alluvium Clay Fi li

11 16 21 34.5

10 13 18 30

5.3 7.8 10.3 18.0

3.7 5.8 7.5 15.0

2.9 4.6 6.0 13.3

2.2 3.5 5.0 11.6

1.7 2.8 4.0 10.0

1.2 2.2 3.3 8 .6

0.9 1.7 2.8 7.3

0.7 1.4 2.3 6.3

0.5 1.1 1.9 5.5

0.45 0.9 1.6 4.7

Depth (ml

12

13

14

15

16

17

18

19

20

21 22

23 24

25

.0.4 0.8 1.4 4.1

0.4 0.7 1.2 3.5

0.35 0,65 1.1 3.1

0.35 0'.6 1.0 2.7

0.3 0.55 0.9 2.3

0.25 0.45 0.65 1.7

0.25 d.45 0.65 1.6

0.2 0.4 0 .6 1.5

0.2 . 0.35 0.55 1.5

0.2 0.3 0.5 1.4

Dept h lm) Sand

Sand

Alluvium Cl ay

Fi li

18

=

0.3 . 0.25 0.5 0.5 0.8 0.7 2.1 1.9

SOLSSOILS N° 26-1975

The seulement is obtai ned in centimetres for moduli expresSed in bars. Given that for the majority of soils, the seUlement of a footing varies according to the levet of the foundation, it is proper ta specify the leve! selected for the calculation of the specifie settlement ( 1 m depth is often chosen). Thus n values w 1 , w2, ... wi' .... wn of the specifie seulement are obtained for n soundings F 1 , F2 , F1, ::. F" : one sentence is lacking obviously ! «which can be anlyzed by the statiscal method. consequently derive» : - the mean value of specifie seUlement :

Cwi j

=1 n

- the value of the standard deviation :

r

j = 1 n -

1

o ld river, developing caVings, underground river, etc ... ). Thi s is particularly valuable for estimating the possibility of extension or aggravation of any such weakness between soundings. Seme complementary soundings may then appear necessary in arder ta clarify a local uncertainty and ta eliminate risks of geotechoical nature. 3.

Calculation of the bearing capacity

The pressuremeter test is a type of Joad test which in particular yields the limit pressure p 1 which corresponds to the failure of the sail. Exper ience and theory have shawn that the ultimate bearing capacity of a foundation is proportional ta Pp the factor proportiona l ity being fu net ion of the relative depth and of the foundation shape. This factor, called the bearing factor, has been the abject of very many theoretical and experimental research works, a large number of which have been ca rried out at the Soils Stud ies Centre of Paris and published in th e Sols-Soi ls magazine. Whatever the type of foundations or nature of the sail involved, the direct pressuremeter method of foundation calculation presents the advantages of simplicity and greater accuracy over the conventional analysis which takes into account various parameters such as cohes ion and internai angle of friction.

- whence the variation index :

e

i

=---;;-

An ana lysis, in plan, of the values of the specifie seUlement may indicate clearly defined zones (weaker or stronger) deserving detailed consideration. Final ly , for very large investigations covering a large number of soundings, it is advisable ta plot the curves of equal specifie seulement : study of this «contou r map» simplifies the evaluation of the site as a who le.

Full sca le loading tests carried out at the Soils Studies Centre, on footings, caissons and piles, have brought out the concept of critical depth of embedment: for a deep foundation (embedment greater than the critical embedment) the sail displaced by the vertical movement of the foundation is absorbed by elastic displacement of the surrounding sail whilst for a surface foundation (embedment less than the critical value), heave of the surrounding sail can be observed at the moment of failu re, heave Which is al i the more pronounced than the embedment is the lesser.

3.1. 2.1.2. Examination of each of th"e pressuremeter soundings in relation ta the geological conditions often makes possible a determination of the causes of local weaknesses (water table leve!, branch of an

SOLS SOILS W 26- 1975

fundamental. formula R·O

Th e ultimate bearing capac ity of a foundation q 1 is related ta the limit pressure p1 of the sa il by a linear fun ction :

19

where k

q0

Po

is the bea ring factor vayring from 0.8 to 9 according to the embedment, the shape of the foundation and the nature of the sail,

which will be used in particu'tar in the calculati.on of the end bearing resistance of pites and/or caissons. This simplification is obviously not val id for investigations in very soft soils (silt, peat) below the water table, especiaUy if the depth is great.

is the overburden pressure at the periphery of the foundation levet after construction,

When the grou nd levet is submerged, the ultimate bearing capacity is

is the «at rest» horizontal earth pressure at the test level (at the time of the test).

where h

q1· Yh

The stresses Po and q 0 are «total stresses» (in particular Po can be measured with a Geocell stress captor). 3.2.

(in a sail with no strength p1 = p0 ' i.e . Pa' = 0)

is the buoyant density of the soit

K0

is the coefficient of horizontal earth pressure at rest

[ P, - h]

is the li mit pressure with no correction for the water held in the tubing.

Usually K0 y' = 0.55 (when h is expressed in metre and pressures in tfm2) : experience shows that when Y'-.. 0.55 (very loose soit) K0 ,...1, and wh en Y' .... 1.1 (compact soi!) K0 - 0.5. 3.3.

Further, it has often been the custom in dealing with pressuremeter results to tabulate the value p1 - h, h being the head of water in the tu~ing above the probe. The calculation and presentation of results is greattv simplified by identifying p1 with p1 - h, the error introduced being Jess than 2 % for most dry sites. Similarly, one can define the net ultimate bearing capacity q' of the grou nd as equal to the surcharge it can withstand before failure; q' = q, . Qo

(in a soil w'ith no 'strength q 1 = q 0 and q' arriving at the simplified formula :

20

= 0) thus

K0 Y' h]

Y'

Termina/ogy

Often the net li mit pressure p 1' is used which is equal to the difference between the li mit pressure Pt effectively attained and the horizontal earth pressure at rest :

= k [lp, · hl·

is the difference in elevation between the probe and the pressure gauge

Values of the bearing factor k

lt has already been indicated that the value of k depends on the type of soil, the embedment and the shape of foundation. 3.3.1.

Soi/ categories

From a practical point of view, the soils can be divided into four categories, according to the table below. lt must be noted that recent fills and underconsolidated soils are not listed in this table; these will be examined in a later chapter (paragraph 4.9) dealing with the self-bearing boundary. One must keep in mind that the allowable bearing capacity is not only a function of the ultimate bea ring capacity of ~he soit, but also. of the allowal;>le settlements for the analysed st ructure.

SOLS SOILS N" 26- 1975

BEARING FACTOR AGAINST EMBEDMENT . FOR ISOLATED FOOTINGS, PIERS AND PILES

k

--- --

9 /

SOIL

~

8

t"

~

'

--

/

7

/

/v

6

5

- --

--

/

/

v/ ;/ -;Y /,- /

-

-- --

3

1

---

-

0,8

--- --- --- ---- ---

~

H ~

H

H

" "~ u

4 -

SOIL

f ~

ffi

} CA TEGORYI!

/

~

0

SOIL

}CATEGORY

1/,?

Ir

Fig 5a

/

/ /

4

2

-- --- ---- --

/// :/

v

TEGORYIDA

~

H

"

0

"

~

u

~

8

footing s , pier s and bored piles

12

16

"~ u

SOIL

CA TEGORYl

H N

" ~

. 20

~

~ u

he 'If

driven piles, displacemcnt caissons

Bearing factor values

SOLS SOILS N" 26 - 1975

21

BEARING

FACTOR

AGAINST EMBEQMENT

FOR STRIP FOOTINGS AND CAST-IN-SITU DIAPHRAGM WALLS

k

5 SOIL CATEGORY

4 ~~---4--~--~--4---+---+ . ---+---~ ~--4=--illA

--- -

--~ -

-

3

2

/

-- --- ---

~/

' / '. ~~---:-: 1--- 1--- -t---t--

'-V

--- -

--rn

---- ----- n

-r:-

H

t---

r-- ~. . -

t - - 1:::::

H

~~-0~,84---+-o:~~~--~-4--~:~~~~--~.:~~~~·+--~~: f 0

4

8

12

16

20

he

If

Fig 5b

22

SO LS SOILS N' 26- 1975

Ranges of pre~ures li mit Pt

0. 0. 18 . 12 . 4. 10.

3.3.2.

Nature of soil

12 bars 7

Soil categories

Clay

category 1

Silt

40 30 8

Firm clay or mari Compact silt Compressible sand Soft or weathered rock

30

10. 20 40 . 100

Sand and gravel

30 .

Very compact sand and gravel

category Il

category Ill

Rock

60

Critical embedment he

Below a certain depth, an embedded foundation maintains a constant ultimate bearing capacity cq 1 • q 0 J. This critical embedment is a function of the soil category : relative values (i.e. related to the half width of the foundation) are tabulated below according to the shape of the footing :

category IliA

of plasticity would imply). The set of graphs show that, in a soil homogeneous with respect to depth , the bearing capacity increases with embed· ment until it reaches an asymptotic value characte· , ristic of deep foundations. The lowest value of k corresponds to a foundation placed on the surface :

k Foundation Soil

Category Category Category Category

3.3.3.

Circular or Continu eus square 1 Il Ill Ill A

4 10 16 20

'6 12 18 22

Soil categories

Variations of k:

The nomograms on fig. 5 page 19 give the values of k in function of the equivalent depth of embed· ment for the various types of soil. The more resistant the soil situated above the level of the foundation, the greater its effect on the bearing capacity of the foundation (it is not just dead load as the rather too elementary theories

SOLSSOILS N° 26-1975

= 0.8

The maximum values of k which are obtained for a depth greater than the critical depth of embedment are given below and are used for calculating the end bearing capacity of foundations (rules R1 for piles, R2 for cast in-si tu walts).

Ill

Ill bis

Bearing factor Drilled pile

1.8 3.2 5.2

Driven Cast in· pile situ walts

3.6 5.8 9

1.4 2.1 2.9

The values used for shallow foundations (rule R3) will .be explained in detaillater.

23

"' ~

,. ~

0>

Bo l~ 1,1 3 1

1,'2 5

1

Vf~l

C1RCULAR OR SQUARE FOOTI NG

....!::._: 1 2R

1, 50 1 175

!,_

2R

(M0 )~ 2,50

1~

1

;---1

STR1P

_..!:.__0) 2R

10 20

Ao

h•

R

en

0

r

en en Q

[;;

"'"' 0>

1

~

"'

The graduated scale U2R permits graphicat calcula tion of the bearing factor of a rectangular footing by interpo lation between a strip f1Joting and a square footing. Example : ta calculate the value of k for he/ A = 1.5 U2R = 2 (usual ratio for an isolated footing) and a sa il of category Ill . Draw the straight tine he/ A = 1.5 which cuts the two category Ill curves at A and B. T he ordinate k of M is calculated so that M divides the segment AB in the same ratio as M0 divides the segment A0 8 0 . Then Ao A and 8 0 B are drawn converging at C from which point a straight line is drawn passing through M0

.

3.4.

Analysis for heterogeneous conditions ·

As a preliminary, it is approPriate to define the

concepts of the equivalent Jimit pressure Pte and of the equivalent depth of embedment he· 3.4.1.

Equivalent limit pressure (rule 4)

3.4.2.

Equivalent depth of embedment (Rule RS)

When the ground exhibits characteristics wh ich vary with depth, it is necessary to defi ne the equi valent depth of embedment he relative to the sail ofthe founding elevation. Thisdepth he is calculated bV applying the following formula (Rule AS) :

1;h

When the foundation rests on strata whose strengths are variable with depth , the equivalent li mit pres· sure Pte is defined as the geometrie mean of the values obtained near the level of the foundation :

he = - ,P1 e

p 1' (z) dz

o

where p 1'e has already been defined.

where p; 1

geometrie mean of values measured in the section from + 3R ta + R above founding leve!

p( 2

geometrie mean of values measured in the section from + R to - R

p 1' 3

geometrie mean of values measured in the section from - A to - 3R.

For a shallow foundation, the value p ~ 1 is not introduced, and the equivalent limit pressure be· cames 2

P(e

=V

P1' 2 x P( 3

This rul e assumes that in ali cases, the variations between p( 1 , p( 2 , p( 3 do not exceed ± 30 % of Pte·

Thus, in the case of a caisson founded on sandy soil with a limit pressure of 16 bars, the equivalent embedment and consequently the ultimate bearing capacity have the same values in the three foll ow ing cases of overburden : 8 m of fiJI with pt = 2 bars or 2 m of sandy silt with p 1 = 8 bars or 50 cm of stabilized sail with p 1 = 32 bars. ln these three cases the effective depth of embedment is 1 m (embed· ment of an imaginary homogeneous sail with a , limit pressure of 16 bars constant from the surface) . 3.5.

Calculation of foundations for stnP footings

Excavation works have a tendency, when carried out under rainy conditions or when cons· truction is delayed for sorne months, to reduce the mechanical properties of sensitive soils to a depth of 0.5 ta 2 m (case of fine slightly cohesive sand, clay with high liquid limit etc ... ). As an example on a site where the excavations are tô be a few metres deep, it is recommended, when calculatinQ the bearing capacity, to reduce by 20 % the values of p 1 measured before the earthworks and corresponding to the layer sit uated 1 or 2 m below the excavation floor . 3.5.1.

> 30 %, it is advisable ta examine Poe the problem in more detail. lt is recommended ta plot p 1'e in function of the depth of the founding leve! and to smooth out ali the peaks in the graph before use. The ether concept (determination of hel will have to be considered at the same time.

3.5.2.

When dealing with very soft soils below the water table, it is more accurate to carry out the analysis with the (p 1 • p0 ) values.

On the contrary, in the case of footings poured within forms with the remainder of the excavation being blackfilled, it is appropriate for the calculation

If

[~]

SOLS SOl LS N° 26 - 1975

The equivalent depth of embedment is calculated with the general leve! of excavat ion (basement level) ta ken as grou nd leve!, but it must be remembered to take into account the beneficiai influence of concrete slabs resting on the sail (adopt p 1 = 100 bars over the total thickness of the slab).

25

of embedment to consider only the back fi li and not the natural soil (adopt p 1 = i to 4 bars for the fill according to the compaction obtained). The presence of neighbouring foundations has a generally favourable influence on the bearing capa· city of surface footing {except in the case of foot· ings very close to each ether, which then behave as a continuous footing or a raft). For the calculation of k, the nomogram in figure 6 is used ; this is a partial enlargement of figure 5. The method of using the nomogram is explained on the graph. 3.5.3. ln the case of shallow foundations, isolated but closely grouped, the bearing k factor is limited by the following relationships: L

k < l+-

k

3.5.5.

Excentric loads

ln this case, it is usual to represent the stress distribution as trapezoïdal with a minimum pres· sure Pm on one side and a maximum pressure PM on the ether. Failure may occur either by general sinking of the footing or by localized failure in the zone of highest loading with tilting of the foundation. The two conditions must be satisfied to ensure stability : 1) the general stability is assured if

Pm

+

PM