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Canadian Geotechnical Journal
Revue canadienne de geotechnique
Published by Publike par THE NATIONAL RESEARCH COUNCIL OF CANADA LE CONSEIL NATIONAL DE RECHERCHES DU CANADA
Volume 13 Number 2 May 1976 Volume 13 numkro 2 mai 1976
Use of the static penetration test in frozen soils
B. LADANYI Depnrttnenr of Mineral Engineering, Ecole Polytrctlniqu~~, C.P. 6079, Stntion A , Montreal, Quebec H3C3A7
Received May 9, 1975
Accepted January 13, 1976
Within the scope of a study on the use in frozen soils of some geotechnical field investigation methods, a series of deep, static and quasi-static, penetration tests was carried out in July 1974 at a permafrost site near Thompson, Manitoba. The field study included stress - and penetration rate - controlled tests, performed with an electric penetrometer, as well as several short-term and stage-loaded pressuremeter tests. The study shows that a static penetration test can furnish valuable information on the time-dependent strength of frozen soil, provided the test is conducted either with a very accurate control of the penetration rate, or as a stage-loaded test. It is considered that a comparison of frozen soil strengths deduced from such a test, with those determined by pressuremeter tests or triaxial compression tests, can only be made at comparable strain rates. An attempt was, therefore, made in the paper to find a relationship between the penetration rate and an equivalent time to failure for the soil surrounding the penetrometer tip, which enabled this comparison to be carried out.
Dans le cadre d'une etude sur I'utilisation en sols geles de certaines methodesd'investigation in situ des sols, une serie d'essais de penetration statiques et quasi-statiques fut effectuke en juillet 1974 sur un site de pergelisol pres de Thompson, Manitoba. Cette Ctude de chantier a comport6 des essais de penetration effectues avec un penitromktre Clectrique, avec contr8le de la charge ou de la vitesse d'enfoncement, ainsi que plusieurs essais pressiom'Ctriques, rapides ou it chargement par paliers. Les resultats de cette Ctude montrent que I'essai de pknitration statique peut fournir des renseignements valables sur la resistance en fonction du tempsd'un sol gel.6, B condition qu'il soit effectue avec un contrble tres precis de la vitesse de penetration, ou qu'il soit execute comme un essai de chargement par paliers. On considere que les resistances mtcaniques d'un sol gel6 tirkes d'un tel essai de penetration ne peuvent se comparer avec celles deduites des autres types d'essais, tels les essais pressiomCtriques et les essais de compression triaxiale, qu'a une vitesse de deformation semblable. Par consequent, afin de permettre cette comparaison, on a essay6 d'etablir dans cette etude une relation theorique entre la vitesse de penetration et le temps de rupture equivalent pour le sol en proximite de la pointe du penetrometre.
Can. Geotech. J . , 13.95 (1976)
Introduction pling equipment is available and when proper Because of the presence of ice in its pores, a measures are taken to minimize the thermal
frozen soil is generally much stronger and disturbance of the soil during drilling and therefore much less susceptible to mechanical sampling, good quality samples can be ob- disturbance than the same soil when unfrozen. tained from practically all kinds of frozen soils As a result, when convenient drilling and sam- with the exception of those containing coarse
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96 CAN. GEOTECH. J . VOL. 13, 1976
gravel and rock debris. In principle then, one would expect laboratory investigations to be the main source of data for foundation design in frozen soils. In fact, however, this is not so, and preference is actually being given more and morc to the field methods. The main reason for this is the fact that the majority of large projects involving frozen soils, such as the pipelines in permafrost regions, are located in remote northern areas and usually cover long stretches of terrain. Conservation of frozen samples and their transport to specialized laboratories, which are still rather scarce, pre- sent considerable difficulties and are often very expensive. Moreover, laboratory determination of certain basic properties of frozcn soil, such as its creep parameters, may take quite a long time.
There is, therefore, a growing interest at present in the development of certain field methods that would be able to furnish quickly certain basic parameters necessary in founda- tion design in permafrost areas. It should, however, be kept in mind that the parameters used in the design of foundations in frozcn soils are not necessarily the same as those in unfrozen soils. For example, in frozcn soils one is morc interested in creep than in con- solidation, while all the strength parameters make sense only when expressed as functions of time and temperature. For that reason, any ficld method. conventional in unfrozen soils, will require reappraisal and often modification before it can be used with success in frozen soils.
One such field method, the use of which in frozen soils has been investigated recently, is the pressuremeter test (Ladanyi and Johnston 1973). After a certain modification of the test- ing procedure and introduction of an appro- miate theoretical treatment of data, the test proved to be a very promising mcthod for determining in situ, not only the usual short- term deformation and strength parameters, but also the creep parameters of the frozen soil.
The pressuremeter test, however, although based on a very simple principle, requires, nevertheless, experienced personnel and great care in the preparation of the borehole and the ~erformance of the tests. if consistent and h i ab l e results are to be obtained. Moreover, it is sometimes objected that the test furnishes
information only on the soil properties in the horizontal direction, which may not be suf- ficient for the design of vertically loaded foun- dation elements in anisotropic soils.
Another test, coming to mind immediately, which is still simpler to perform and is not subject to the latter objection, is the quasi- static penetration test. The test, known orig- inally as the 'Dutch Cone' or the 'Deep, quasi- static, cone penetration test' has been in con- tinuous use in ordinary soils for the last 40 years and has shown excellent results as a means for rapid determination of short-term strength parameters of various types of soils, (Sanglerat 1972; Schmertmann 1975).
While the test has probably been used be- fore in frozen soils the author knows of no account in the literature of any systematic study of the use and interpretation of the static penetration test in such soils. There is no reason, obviously, why the test could not fur- nish short-time strength data for a frozcn soil in the same manner as for an unfrozen soil, provided the frozen ground can be penetrated with the available equipment. However, in order to become useful for foundation design in frozen soils, the test should, in addition, be able to furnish some information on the creep properties of the soil, enabling a reasonable prediction of the time-dependent behavior of the foundations to bc made. In other words, similarly as in the case of the pressuremeter test, the use of the static penetrometer test in frozen soils requires the establishing of an optimum testing procedure and an appropriate method for interpretation and extrapolation of test results.
With that purpose in mind, a field study of the test was carried out in July 1974 at a permafrost site near Thon~pson, Manitoba. In addition to a series of load- and penetration- rate controlled tests performed with an electric penetrometer, several short- and long-term pressuremeter tests were also carried out for comparison purposes.
This paper describes the testing procedures and presents the results of the test program eonductcd on that permafrost site.
Test Site Conditions The selected permafrost site at Thompson is
adjacent to the test site that has previously
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ICE LENS THICKNESS INCHES MOISTURE CONTENT, %
0 0.1 0.2 0.3 0 10 20 30 40 50
I I ,
- I- I NOT SAMPLED 1 1 3'
0
A 7 3
0
A-(I 0
0
A-(I
0
A-(I 0
0
0 A-0
* MOISTURE C O N T E N T - N O VISIBLE ICE A PLASTIC LIMIT 0 MOISTURE C O N T E N T - W I T H ICE LENSES U LIQUID LIMIT
FIG. 1. Soil profile at the permafrost test site, Thompson, Manitoba, (after Johnston and Ladanyi 1974).
been used by the National Research Council of Canada for performing a program of perma- frost anchor tests and a series of pressuremeter tests, the results of which have been published in three preceding papers (Johnston and La- danyi 1972, 1974; Ladanyi and Johnston 1973). Since a detailed description of the site was given in the first of the three papers, only a short general outline will be given here, simi- lar to that shown in the second previously men- tioned paper.
Thompson lies within the discontinuous permafrost zone. Stratified sediments (varved clays) of low to medium plasticity occur at the test site to a depth of about 19 ft (6 m).
In the boreholes made in connection with the installation of anchors (Johnston and Ladanyi 1972), it was found that the thickness of the silt layers varied from 1 to 12 in. (2.5 to 30.5 cm) and of the clay layers from 0.5 to 1 in. (1.3 to 2.5 cm). The varved clay was under- lain by a dense silt. Ice lenses were mainly horizontal and varied in thickness from hairline to about 0.5 in. (1.3 cm) in the top 13 ft (4 m) . Very little ice was noted between 13 and 19 ft ( 4 and 6 m) and none was visible in the silt between 19 and 30 ft (6 and 9 m) . Soil and ice conditions are shown in Fig. 1.
Ground temperatures at the test site, from about 5 to 30 ft (1.5 to 9 m) were between
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98 CAN. GEOTECH. J. VOL. 13, 1976
31.5 and 31.8 O F (-0.3 and -0.1 "C), and they were essentially isothermal throughout the year.
Apparatus and Procedure All the penetration tests at the site were per-
formed with a 10 ton (89 kN) capacity Fugro electric penetrometer without friction sleeve. The penetrometer, which has originally a 60" conical point and contains a force transducer, enables a continuous recording of the point resistance on a moving graph paper to be made. A detailed description of the pen- etrometer is given in a paper by de Ruiter (1971).
The diameter of the penetrometer is about 1.4 in. (3.57 cm), i.e. so that its projected end-bearing area is exactly 1.55 i n 2 ( 10 cm2). The penetrometer has a straight cylindrical shaft above the tip with the same diameter as the tip. It should be noted that in the present tests the original conical tip of the penetrometer was replaced by a flat disc. This was done essentially in order to make it more similar to a plate-loading test, and to enable a clearer interpretation of the test results in terms of representative strain rates. The modification, however, is not considered essential in practice.
The thrust for pushing the penetrometer into the ground and the corresponding dead weight was provided by a Mobil Drill mounted on a tracked Bombardier Muskeg Carrier. Since the total weight of this equipment was only about 3 tons (27 kN), the vehicle had to be anchored during the tests by a couple of screw anchors. Nevertheless, due to the high cohesive resis- tance of the frozen soil and its adhesion to the rods, it was found difficult to push the pen- etrometer more than about 2 ft (60 cm) below the bottom of the borehole. The tests were, therefore, carried out at various levels but always starting from the bottom of a predrilled borehole.
Since the strength of a frozen soil is highly dependent on the rate of strain, i.e. much more than that of an ordinary unfrozen soil, special care was taken to control very accurately the rate of penetration of the penetrometer. This was achieved by means of a 4 in. ( 10 cm) long linear potentiometer fixed to the rods and bearing against a reference frame anchored in the soil. In that manner, both the end-bearing
force and the amount of penetration were simultaneously recorded on a 2-pen recorder.
The penetration tests carried out at the site were of two different kinds: (1) quasi-static tests, carried out at a constant rate of penetra- tion, and (2) static or incremental loading penetration tests carried out at constant load increments.
The tests of the first type are similar to con- ventional quasi-static penetration tests in that they record the resistance of the soil to a con- stant rate of penetration. The difference in the present tests was, however, that the rate of penetration had to be much slower and con- trolled much more accurately than in unfrozen soils. This was achieved by tracing, before each test, on the recording paper, a set of inclined straight lines, the slope of which was calcu- lated so that, if any of the lines was followed by the penetration recording pen at a given speed of the paper, the rate of penetration would be constant and equal to the predeter- mined value. Obviously, in order to keep the rate constant, the thrust had to be continuously varied, which was achieved without difficulty by adjusting occasionally the pressure valve on the drill. In this manner, it was possible to carry out the sounding tests at various rates, even down to very slow rates (0.021 in./min = 0.053 cm/min), comparable to those used in performing triaxial compression tests.
It should be noted, however, that the de- scribed system for performing slow penetra- tion tests was devised on the basis of the equip- ment available on the site, and is clearly not the only or the best possible solution for prac- tice. For example, a very efficient and rela- tively inexpensive system for performing such tests, even on full scale piles at well-controlled rates of penetration as low as 0.01 in./min (0.25 mm/min), was recently described by Garneau and Samson ( 1974).
The second type of test is similar to an ordinary incremental loading test in which the load is increased in small increments and, at each load, the settlement is recorded as a function of time. The difference in the present tests, however, was that the main interest was concentrated not in the total settlement but in the rate of penetration at each load. The total penetration during such a test is, therefore, not kept within a fraction of the diameter as in
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LADANYI 99
usual plate loading tests, but the penetrometer can be let to penetrate the depth of several diameters, provided the soil is reasonably homogeneous within the penetrated depth.
One to two tests per borehole were per- formed in 12 different boreholes, all drilled within an area of the site of about 30 ft x 30 ft (9 m X 9 m). Of the total of 16 tests, only the results of those carried out within the depth interval of 9 to 12 ft (2.75 to 3.65 m) , will be shown here, because only these tests were con- sidered to be within a reasonably isothermal permafrost zone. In total, the results of 4 static and 5 quasi-static tests will be shown in the following. It should be noted that, before each test, a 3 in. (7.5 cm) diameter hole was first drilled down to about 4 in. (10 cm) above the level of the start of the test. True deep penetration resistances were, therefore, re- corded only several base diameters below the bottom of the borehole. The rates of penetra- tion used or observed during the tests varied from about 0.001 to 1.0 in./min (0.0025 to 2.5 cm/min) .
Penetration Test Results The main purpose of the whole penetration
testing program was to find the relationship be- tween the penetration rate and the resistance of frozen soil penetration, that would eventu- ally enable conclusions to be made on the be- havior under load of foundation elements em- bedded in such a soil. It was considered that, in practice, this information could be obtained by combining the two described types of pen- etration tests in the following manner:
(1) At a given area of the site, first several closely spaced quasi-static (rate controlled) penetration tests, should be performed, each of them at a different penetration rate. If the soil within the area covered by the tests does not show much lateral variation, a set of such tests should, in principle, be able to furnish a strength vs. penetration rate relationship for each traversed soil layer.
(2) Second, a series of static (incremental loading) tests are carried out in the same area, each of them confined to a single representa- tive soil layer, that has been identified pre- viously in the quasi-static tests.
soil strata at very low penetration rates, the quasi-static tests will usually be limited to rela- tively high penetration rates exceeding about 0.1 in./min (0.25 cm/min) . At penetration rates lower than that value the time-dependent strength of frozen soil can much more conveni- ently be determined by means of static pen- etration tests.
Figure 2 shows the point resistance profiles obtained in two closely spaced quasi-static penetration tests conducted at two different penetration rates, of 0.067 and 0.5 in./min (0.17 and 1.27 cm/min) , respectively. In spite of somewhat erratic profile due to the presence of the varves, a clear increase in penetration resistance with increasing rate can be seen from these two tests, which were about 3 ft (90 cm) apart. The resistance increase in the two tests was rather large, i.e. up to about 50%. It should be noted, however, that at such relatively high penetration rates, the penetration rate effect tends otherwise to be smaller in the average than at very low rates attainable in the static tests. This can be seen in Fig. 7 where the results of 9 penetration tests are plotted together.
Figure 3 shows the results of three addi-
q , ksi 0 1 2 3
Penetrometer size :
".-. 0 10 q. MPa 20
FIG. 2. Results of two closely spaced penetration tests in permafrost, performed with accurate control It is clear that. in ~ractice. because of the , .
length of time necessary for traversing thick of penetration rate.
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100 CAN. GEOTECH. J. VOL. 13, 1976
4 , ksi 1 2 3 I I I
'.
T e s t , s-15 inth
I I 0 10 q. MPa 20
FIG. 3. Results of three closely spaced quasi-static penetration tests in permafrost.
tional quasi-static tests performed in the samc area and depth intervals. Two of them (No. I1 and 14) were strictly rate controlled tests con- ducted at the samc rate of 0.25 in./min (0.63 cm/min) and they showed an average resis- tance of about 1.5 ksi (10 MPa) with a variation of about 20% about the mean value. On the other hand, Test 12 was conducted as a con- ventional quasi-static test, i.e. with only a rough manual control of the penetration rate. As a result, its rate varied considerably around the mean value of 1 in./min (2.5 cm/min), which produced large variations in the re- corded soil resistance, as can be seen in Fig. 3, but the variations are still more visible in the original recording. This result shows that in frozen soils a proper control of penetration rate is essential for obtaining consistent results in quasi-static penetration tests.
Compared with the quasi-static tests, the static or incremental loading tests, were easier to perform with the available equipment which was well adapted for keeping the load at a constant level. As mentioned before, an essen- tial condition for the success of such tests when
used for evaluating the effect of the rate on the penetration resistance, is that each of them should be performed within a reasonably homogeneous soil layer.
In the present investigation, because of the varved soil character, with larger (silt) varves about 5 in. (12.5 cm) thick, in order to meet this requirement, i.e. to remain within one single varve, it was necessary to start the test at the top of the varve and keep total displace- ments within about 1 in. (2.5 cm). In addition, in order to get several load increments neces- sary for the analysis, each increment had to be kept very small. In spite of these strict require- ments, several successful tests of this kind were carried out at the site. Figure 4 shows the results of two such tests performed at two different levels of the borehole No. V (Test 8-1 at -116.2 in. = -295 cm, and Test 8-2 at -1 17.8 in. = -299 cm), while Fig. 7 shows the rates measured in these two tests, as well as in two additional tests performed in bore- hole No. X I (Test 15-1 at 117 in. = 296 cm, and Test 15-2 at 119 in. = 301 cm). All the four tests were conducted up to high rates which could be termed as soil failure. The depth range of the four tests is shown also in Fig. 3.
The results of such static load tests can be plotted in several different manners. In un- frozen soils the results are usually shown in the form of a load vs. settlement plot, where the latter corresponds to the cumulative settlc- ment observed at the end of a particular con- stant load interval. This method clearly makes sense only if one can reasonably assume that the settlement at the end of each stage has practically stabilized. If, on the other hand, the settlement docs not show stabilization at the end of each interval but continues to in- crease at a steady rate, one can either increase the length of time for each stage so that the settlements can be stabilized, or, alternatively, onc can attempt to extrapolate the results to longer times by using the rates of settlement observed at the end of each loading stage.
Figure 4 shows that, within the load interval used in the two tests, the settlement after a 15 min period at each stage was not attenuating but showed rather a steady increase with time.
On the other hand, the instantaneous portion of settlement is seen to be practically nonexis- tent, while the primary creep portion, on the
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80 Time, min 120 I I 0
1.85 T...8-2 - 1
FIG. 4. Results of two static (incremental-load) penetration tests in permafrost.
settlement curves, is so small that it can be neglected in comparison with the steady state settlement when extrapolation is extended to longer intervals of time of interest in practice.
In frozen soils, therefore, where such be- havior is usually observed (e.g. Johnston and Ladanyi 1972), it seems logical to represent the results of such static penetration tests in a plot relating the applied loads with the result- ing penetration ratcs observed at the end of each stagc. Since, however, such a plot should serve as a means for extrapolating the mea- sured data beyond the range of direct obser- vation, the choice of the plotting method may have a considerable importance. In the follow- ing, it will be shown how the extrapolation of the results of such tests can bc affected by the choice of the plotting method.
Extrapolation of Static Penetration Test Results to Lower Rates
In order to be able to use the results of a static penetration test for predicting the be- havior of a foundation element under load, one should be able to reprcsent the results in such a graphical or analytical form that would enable a realistic extrapolation to be made to the rates that are much smaller than those used in the tests. Eventually, by using such a method, one can then also attempt to establish from the test results a general relationship between the strength and the rate of strain for the frozen soil, as will be shown later.
Since no theroetical relationship has so far been established between the penetration rate
and the frozen soil resistance, three different empirical formulations will be considered for representing the test results and for cxtrapolat- ing them to lower rates. They are a logarith- mic, a hyperbolic, and a power law, respec- tively.
The logarithmic law is, obviously, thc one that has been used most frequently in the past for representing the rate dependence of strength in unfrozen soil mechanics. The same law was used by Thomas (1965) for showing the rate dependence of static penetration resistance in the London clay. The usual method for finding experimental pararnetcrs of such a logarithmic law consists in plotting on a semi-log plot the resistances (on the linear scale) against the rates (on the logarithmic scale). For an or- dinary saturated unfrozen clay, deformed under unclrained conditions such a plot usually shows that a tenfold increase in rate gives about 10% increase in strength or penetration resis- tance. (Thomas 1965; Ladanyi and Eden 1969; Dayal and Allen 1975). Compared to other possible sources of strength variation, this rate effect in unfrozen soils is considered to be small and is usually neglected. It may, nevertheless, become important when large differences in scale are involved, as will be shown later.
In order to see the usefulness of such a rep- resentation for frozen soils, the final rates of penetration observed at the end of each load- ing stagc in the tests 8-1 and 8-2 have been plotted in Fig. 5 against the applied pressures in a semi-log plot. The resulting plot is seen to
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FIG. 5. Point resistance vs. penetration rate rela- tionship from the tests 8-1 and 8-2, shown in semi- logarithmic plot.
be nonlinear, which shows that the rate effect does not follow a logarithmic law in that soil. In addition to that, the rate effect on the strength in frozen soil is so high that this kind of plot would lead one to conclude that the soil would lose all its resistance if the penetra- tion rate falls down to about 10-"0 lo-" in./min (2.5 x lo-* to 2.5 x cm/min). Since this concIusion is clearly unrealistic, the use of a semi-log plot for extrapolating the penetration resistance of frozen soil to much lower rates cannot be recommended.
Another method for representing the same experimental data is based on the assumption that the load versus penetration rate relation- ship follows a hyperbolic law (Johnston and Ladanyi 1974).
In terms of the applied pressure on the tip, q, and the related terminal penetration rate, S, such a hyperbolic law has the form
The values of the two experimental param- eters (s/q), and q,,, respectively, can be ob- tained by plotting the ratio S/q against 3, as in Fig. 6. If a straight line can be drawn through the points, the value (S/q) is then equal to the intercept of such a line at the origin, while the asymptotic failure load q,, is equal to the slope of the straight line, a/b, Fig. 6 (Kondner 1963).
Figure 6 shows that the experimental points for the two tests fall fairly well on straight lines, at least at higher rates, which enables the follow- ing relationships to be deduced: For test 8-1 :
For test 8-2:
where q is in ksi and S in in./min (1 ksi = 6.9 MPa and 1 in./min = 2.54 cm/min).
This apparently good straight-line fit may lead one to conclude that a hyperbolic law is very convenient for representing the penetra- tion rate vs. strength relationship in frozen soils at all rates. A closer inspection of Fig. 6 reveals, however, that this is only true for rates higher than about 0.004 in./min (0.01 cm/min). For lower rates, the points start, in fact, falling more steeply towards the origin which can be better seen from the enlarged plot superimposed on Fig. 6. Consequently, it would be clearly too conservative to use [2] and [3] for extrapolating the experimental resistances to rates lower than about 0.005 in./min (0.0125 cm/min). If this is, nevertheless, done, it is found that the resistances fall off quickly to very low values, which do not seem realistic. The.reason for this discrepancy from the hyper- bolic law is, obviously, the fact that, at low rates, the hyperbolic relationship becomes prac- tically linear, implying the validity of a linear- viscoelastic behavior for frozen soil, which does not correspond to the reality (Ladanyi 1972). On the other hand, the constant slope of the lines in Fig. 6 at higher rates shows that the penetration resistance of the frozen soil does not increase indefinitely with increasing rate, but seems to tend to a finite asymptotic value of the order of 2 ksi (1 3.8 MPa) .
Figure 7 shows finally the same experimental results from the tests 8-1 and 8-2 plotted in a log-log plot. It is known that in such a plot a power law relationship appears as a straight line. As it will be seen in Fig. 1, each of the two tests can be approximated by two straight lines with a change in slope at about 0.01 in./min (0.025 cm/min) . In addition, the test results from two other static tests (15-1 and 15-2) and five quasi-static tests performed at the site are also shown in Fig. 7 for comparison.
A general power-law relationship for the rate dependence of penetration resistance has the form
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.-
---- (10 times enlarged scale)
FIG. 6. Point resistance vs. penetration rate relationship from the tests 8-1 and 8-2, shown in Kondner's plot.
FIG. 7. Log-log plot of the point resistance vs. penetration rate relationship, obtained in static and quasi-static tests in the depth interval of 116 to 120 in. (295 to 305 cm).
where
is the slope of the straight line in the log-log plot, while qo and So are co-ordinates of any reference point on that line. Applied to the lines obtained for the tests 8-1 and 8-2 in the interval 0.001 < S < 0.01 in./min, [4] and [5] yield
For test 8-1 :
for test 8-2:
where q is in ksi and S in in./min. At rates over 0.01 in./min (0.025 cm/min), the slope becomes much smaller with l / n -- 0.06 to 0.07 (n -- 14.3 to 16.7).
The power law relationship is usually found very convenient for extrapolating the creep data in frozen soils to very low rates (Vialov 1962; Ladanyi 1972; Johnston and Ladanyi 1972). According to this law, the strength decreases slowly with the decrease in rate and becomes zero only at zero rate.
Figure 7 shows, in addition, the results of two more static penetration tests, 15-1 and 15-2, made at the same depth and in the same general area. Both are seen to follow the same trend as the tests 8-1 and 8-2, i.e. they seem to tend towards an asymptotic value of the penetration resistance located somewhere be- tween 1.5 and 2.2 ksi (10.4 and 15.2 MPa). The same trend is shown by the results of five quasi-static tests shown on the right-hand side of the figure. It should be noted that, for this comparison, only the range of penetration re- sistances observed in the depth interval of 116 to 120 in. (2.95 to 3.05 m) was plotted in Fig. 7, which corresponds to that in which the incremental load tests were made. The fact that the penetration resistance at the rates over about 0.01 in./min (0.025 cm/min) increases much more slowly (in logarithmic sense) than at lower rates leads to the conclusion that, on the basis of conventional, high-speed, penetra- tion tests, it will always be very difficult, if not
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104 CAN. GEOTECH. J . VOL. 13, 1976
impossible, to predict the long-term behavior of a footing or pile embedded in frozen soil.
As far as the short-term frozen soil strength is concerned, thc quasi-static penetration test may bc used successfully for its determination, provided one can properly transform the pene- tration rate into an equivalent strain rate and find the strength parameters of frozen soil from the measured penetration resistance. A method for carrying out this transformation is shown in the following.
Determination of an Equivalent Time to Failure for Quasi-static Penetration Tests
When quasi-static penetration tests are per- formed in unfrozen soils, it is usually found that large variations of penetration rate result in only rclatively small variations of the pene- tration resistance. Typical values for that varia- tion found in clays are of the order of 7 to 10% increase in point resistance for a tenfold increase in penetration rate (Thomas 1965 ; Ladanyi and Eden 1969; Dayal and Allen 1975). This is clearly a small effect, as far as the performance of penetration tests is con- cerned. However, even this rate effect in clays may become important when the results of penetromcter tests have to be used for the design of large piles. This is due to the fact that the observed rate dependence of soil resis- tance to penetration is actually not a function of the penetrating rate but rather of an average strain rate to which the soil is subjected during the penetration. Since this average strain rate is proportional to the ratio between the penetra- tion rate, S, and the penetration diameter, B, any comparison of the penetration resistances obtained in penetration tests carried out with penetrators of different diameters can only be made on the basis of the scaled-down penetra- tion rates (i.e. at the same i /B ratios), or, alternatively, at the same times to failure, as shown by Marsland ( 1974).
For example, for a penetrometer of 3.57 cm (1.4 in.) diameter, penetrating into clay at the usual rate of 2 cm/s = 120 cm/min, the value of B/B = 120/3.57 = 33.6 min-l. On the other hand, in a full scale pile test with a 16 in. (40 cm) diameter pile, the penetration rate may be of the order of 0.032 in./min (0.08 cm/min), which gives S/B = 0.08/40 = 0.002 min-l. The scaled-down rate in the pile
test is, therefore, in fact, not only 1500 times but 16 800 times smaller than in the penetra- tion test, which would result in about 30 to 40% decrease in penetration resistance for the pile in the same clay. For some reason, this not so small strain rate effect due to scale was not mentioned in some fundamental papers on the subject (KCrisel 1967; De Beer et al. 1974).
In frozen soils, where the strain effect is much more pronounced, for any test to be ac- ceptable, it should be able to furnish a clear relationship between the observed strength and a representative rate of strain in the soil.
Finding the latter relationship is not an easy task because both the strain and the strain rate around the penetrating tip of a penetrometer vary continuously from point to point, decreas- ing rapidly with the distance, similarly as around an expanding cavity. So far, very few attempts have been made to establish this rela- tionship, and only one, known to the author, was based on the expanding cavity model (Peck 1966).
In the following, this relationship will be established on the basis of assumptions which are considered to be more acceptable than in some previous similar attempts. It is now gen- erally recognized that the penetration of a cylindrical punch deep into an elastic-plastic material such as an unfrozen or frozen soil, produces in the soil a state of stress and strain very similar to that resulting from the expan- sion of a spherical cavity. There are differences obviously at the contact with the penetrator base, but the resemblance improves quickly with the distance from the base (Ladanyi and Johnston 1974).
The similarity between the penetration by a cylindrical punch and an expanding spherical cavity at the tip level is, however, only valid for the soil elements located below the level of the base. Once the base of the punch has pen- etrated below the level of a particular soil element, the element will attain a state of stress and strain more similar to that resulting from the expansion of a cylindrical cavity, equal in size to the penetrometer shaft. In other words, a straight-shaft cylindrical pen- etrator starts deforming the soil as an expand- ing spherical cavity but ends by deforming it up to the level of an expanding cylindrical
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LADANYI 105
cavity, as correctly observed by Roy et al. (1974).
Nevertheless, there is little doubt that a major portion of the strain rate effect is gov- erned by the behavior of the soil elements located directly below the tip of the penetrom- eter, along the line of its penetration.
As the penetrometer advances continuously into the soil, it is always preceded and sur- rounded by a plastic front, which may have a shape similar to that shown in Fig. 8. For any soil element located on the line of penetration, failure occurs as soon as the element is at- tained by the advancing plastic front, which moves at the same speed as the penetrometer. The time to failure for any such element is then approximately equal to the time necessary for the strain in it to increase from a negligible initial value to the failure strain.
If for any soil element on the penetration line, such as A in Fig. 8, it is assumed that a spherical cavity rCgime is valid, the shear strain y to which it is subjected when the penetrator is at a distance r, can, for a volume constant case, be calculated from the formula (Ladanyi
p l a n d a r y 1 1 spher~cal cavity
A'
A . r t V'
FIG. 8. Soil response to penetration by a flat cylin- drical punch, assumed in the eval~lation of the penetration rate effect.
I I
I i
where a is the penetrometer radius and r is the radial distance of the soil element measured from the center of the base, which is assumed to coincide with the center of the expanding cavity.
On the other hand, the radius of the plastic zone, r,,,s,l,, can be calculated by substituting the failure strain, yilf (under axial symmetry conditions) for 7 in [8]:
Elast~c-plastic
boundary, cylin-
drical cavity 4
If such a plastic front penetrates into the soil together with the penetrometer at a rate S, the time to failure, tf, for a soil element located in its way can be calculated from
where r , denotes the distance at which the strain is still negligible with respect to thc failure strain. A reasonable assumption for the latter may be to take this negligible strain to be equal to 1% of the failure strain y,,. With this asumption one gets:
and
[12] r,. - rp,sgll = 3.65 n yj,f-1/3
The time to failure is then from [lo] and [12]
where B = 2n denotes the diameter of the pen- etrometer tip.
For example, for a standard size penetrom- eter with B = 1.4 in. (3.57 cm), penetrating into a soil with = 0.05, at a rate of 2 cm/s (0.8 in./s), one would get from [I31 an equivalent time to failure of about 9 s. This agrees with the usual assumption about the time to failure in such a test (Meigh and Cor- bett 1969).
Determination of Strength Parameters In order to determine from the measured
point resistance q the value of soil strength parameters, the following bearing capacity for- mula is normally used:
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106 CAN. GEOTECH. J. VOL. 13, 1976
where p, is the average ground pressure at the level of the penetrometer point, c is the co- hesion, and N,," and NcO are the bearing capa- city factors for a very deep circular footing, the former being related to the latter through the well known relationship
[151 NqO = 1 + NcO tan + In unfrozen soils the quasi-static penetration
tests are usually made either under drained (in sands) or under undrained conditions, (in saturated clays). In the first case, with c = 0, one gets from [14]: N,," = q/po, from which one can determine the corresponding value of the angle of shearing resistance +, if the rela- tionship between N," and 4 is known.
In the second case, since in terms of total stresses +,, = 0, one gets N,," = 1 and NcO = constant, which enables an easy determination of the undrained shear strength c, from [14], because the value of NC0 for +,, = 0 is known to be about 9 to 10.
While the second case can also be applied to frozen clays at relatively high frost tempera- tures, this simplification cannot be made for the frozen soils other than clays because the strength of most frozen soils contains usually both a frictional and a cohesional component. This is due to the fact that, at relatively high strain rates such as produced in an ordinary quasi-static penetration test, the failure en- velope of most frozen soils, and of pure ice, has a parabolic shape with the uniaxial com- pression strength about 3 to 5 times higher than the uniaxial tensile strength (Vialov 1962; Kaplar 1971; Sayles 1973).
In other words, in frozen soils, not one but two strength parameters usually have to be determined from the results of a deep penetra- tion test. Since [14] alone is insufficient for that purpose, one must either find another independkt ;elationship, or be able to make a reasonable assumption on one of the two pa- rameters. The first case is applicable, for ex- ample, to normally consolidated unfrozen clays whose cohesion increases linearly with depth due to consolidation under gravity forces.
Since it is unlikely that a similar relationship could be found for frozen soils, the only re- maining solution is then to determine from [14] the value of cohesion c of frozen soil after making a reasonable assumption on the value of its short-term angle of friction 4. Unfor-
tunately, very little experimental evidence is still available on that angle which is a function of the type of frozen soil, its density, degree of saturation, temperature, and the applied strain rate. At present, on the basis of limited infor- mation supplied by some more recent investi- gations (Vialov 1962; Neuber and Wolters 1970; Kaplar 1971 ; Alkire and Andersland 1973; Sayles 1973), one can expect to find the following range of values of the short-term angle of friction for different types of frozen soils: for frozen sands: 4 -- 29 to 37'; for frozen silts 4 -- 15 to 25'; for frozen clays 4 -: 0 to lo0.
As far as the bearing capacity factor NcO in [15] is concerned, its value can be determined approximately as in unfrozen soils, i .e. by mul- tiplying the corresponding Prandtl's Nc-factor, valid for a strip footing on the surface, by a shape factor sc and a depth factor dc, as pro- posed by Brinch Hansen ( 196 1 ).
where, according to Brinch Hansen ( 196 1 ) , for a very deep circular footing
and 0.35
'la' dc = 0.6/(1 + 7 tan4 4) The values of NcO and NqO according to [15]
to [IS] are shown in Table 1 and represented graphically in Fig. 9.
For example, in the present case of a frozen varved silt with + -- 15 ', from Table 1 : NqO = 6.7 and NcO = 21 .l. Taking into account that at the level of the tests the average total ground pressure po was about 8.5 psi (59 kPa), [14] would give for a penetration resistance of q = 2000 psi (13.8 MPa) :
92 psi (0.635 MPa)
It should be noted that bearing capacity factors that may correspond better to frozen soil behavior, i.e. which are valid for a non- linear-elastic-plastic material, have recently been determined for a deep circular footing by Ladanyi and Johnston (1974). As, in addition to strength, the factors take into account also the soil deformability, they are usually lower than those shown in Table 1 and Fig. 9, and
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LADANYI
TABLE 1. Bearing capacity factors for a deep circular footing
0, degrees
FIG. 9. Bearing capacity factors N,,O N2 for a very deep circular load, according to Brinch Hansen (1961).
are therefore considered to be more appropri- ate for estimating the bearing capacity of a deep foundation in frozen soil.
On the other hand, use of higher bearing capacity factors in Table 1 and Fig. 9 seems more appropriate in connection with the evaluation of field penetration test results, be- cause it will furnish lower and safer values for the frozen soil cohesion.
Use of [13] and [14], respectively, will make it possible to transform any given penetration resistance vs. penetration rate relationship obtained from a static or quasi-static penetra- tion test into an equivalent stress vs. strain rate relationship, such as may be obtained from a triaxial compression or a pressuremeter test.
Comparison With the Results of Pressuremeter Tests
In addition to the quasi-static penetration tests, several pressuremeter tests were also carried out at the site for comparison purposes.
Since the testing procedure and the interpreta- tion of the tests has been the same as described in the paper by Ladanyi and Johnston ( 1973), no details will be given here.
In total, four pressuremeter tests were per- formed at the site. Of the four tests two were of the short-term type (i.e. 2 min per load increment), and the remaining two stage- loaded with several 15 min stages at constant pressure. As the results of the tests were very consistent, only the average values of the de- termined parameters and their range will be presented here.
The limit pressure in the four tests varied between 300 and 360 psi (2.1 and 2.5 MPa).
From the two short-term tests, the following data were deduced: plain strain cohesion: c,, = 130 t 12 psi (0.9 & 0.08 MPa); total angle of friction (assumed) : 4 = 15"; shear strain at failure: Y , , , ~ = 0.05; approximate time to failure: (peak of stress-strain curve) : tf = 20 min.
From the two stage-loaded pressuremeter tests, the following average creep rate equation was established:
where U, is the equivalent stress in psi, re is the equivalent strain rate in min-l, and t is the time in minutes. The equivalent stress and strain rate are defined as in Ladayi (1972).
As indicated in the foregoing, in the two short-term pressuremeter tests the failure strain in the soil, Y , , , ~ = 0.05, was attained in about 20 min. Taking into account that shear strains under axial symmetry and plane strain conditions are related by
one gets: yae = 0.0433. The equivalent pen- etration rate is then according to [13]:
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108 CAN. GEOTECH.
o r , forB= 1.4in. (3.57cm),S=0.364in./min (0.924 cm/min) .
For that rate, which is rather high, the pen- etration resistance would according to Fig. 7 be in the range of about 1200 to 2200 psi (8.3 to 15.2 MPa). With the same assumptions as in [20], ( i .e . 4 = 15O), one gets from [14] the corresponding range of frozen soil cohesion under axial symmetry conditions: c = 54 to 102 psi (0.37 to 0.70 MPa). The correspond- ing plane strain values are c,, = 62 to 117 psi (0.44 to 0.83 MPa). The cohesion so deter- mined is seen to be lower than the peak co- hesion of 130 psi (0.9 MPa) found from pres- suremeter tests, which is thought to be due mainly to the use of high values of bearing capacity factors in [14].
On the other hand, the creep exponent of stress in [21], n = 1.2, deduced from pressure- meter creep tests is much lower than that found in static penetration tests (n = 3.3 to 5.7), which appears in [6] and [7]. This difference is likely due to the natural anisotropy of the varved soil. It should be noted that still higher values for that exponent (n = 7.5 to 8.0) have been obtained from creep tests on rod anchors performed earlier at the same site (Johnson and Ladanyi 1972), in which the soil was also deformed in the vertical direction rather than in horizontal direction as in pressuremeter tests.
Discussion and Conclusions On the basis of this investigation on the use
and interpretation of static and quasi-static penetration tests in frozen soils, the following conclusions can be made:
(1 ) In the relatively warm permafrost soil such as found in the Thompson area (31.5 O F
= -0.3 OC), the penetration tests can be per- formed with the same equipment as in or- dinary unfrozen soils. In the tests, the total point load did not exceed about 4000 lb (17.8 kN). However, due to very large lateral bond in the frozen silty soil, total load on the rods was much higher and exceeded the thrust capacity of the drill when the penetrometer descended about 2 to 3 ft (0.60 to 0.90 m) below the bottom of the predrilled borehole. This leads to the conclusion that the per- formance of deep penetration tests in perma-
frost soils will require very heavy equipment, unless the tests are made from the bottom of a predrilled hole, or unless the rods have a slightly smaller diameter than the penetrom- eter.
(2 ) The results of both static and quasi- static penetration tests performed at the site show that the resistance of frozen soil to pen- etration increases with increasing penetration rate. The rate of resistance increase was, how- ever, found to decrease with increasing pen- etration rate, which made extrapolation beyond the tested range difficult. In particular, while quasi-static penetration tests furnish valuable information on the in situ short-term strength of frozen soil, their results obtained at rela- tively high rates of penetration are very difi- cult to extrapolate to very low rates which are of interest in the foundation design. For the latter purpose a much better information can be obtained from static penetration tests. The static tests, which can be performed with the same equipment as quasi-static tests, should be carried out in such a manner that they will fur- nish a clear relationship between the applied pressure and the resulting penetration rate, that may serve as the basis for extrapolating the results to much longer intervals of time.
( 3 ) In frozen soils, the strength of which is highly sensitive to the rate of strain, the results of penetration tests can bc compared with those obtained in other types of tests only at comparable equivalent strain rates or times to failurc. In the paper, a relationship bctween the penetration rate and an equivalcnt time to failure was established from a simple thcoreti- cal analysis. According to this theory, the rate of penetration of 0.8 in./s ( 2 cm/s) used in ordinary soils would correspond to an cquivalent time to failure of about 9 s, which agrees with the expectations.
(4 ) Using the same rclationship, the results of penetration tests were comparcd with those obtained by pressuremeter tests at thc same site. It was found that, at the same equivalent rate of strain, the short-term cohesion of the frozen soil determined by both types of tests was quite similar. However, the strength in- crease with strain rate in pressuremeter creep tcsts was much higher than that observed in static penetration tests, which is thought to be due to the soil anisotropy.
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LADANYI 109
Acknowledgments The work described in this paper forms part
of a general program of research on the be- havior of frozen soils being carried out at the Northern Engineering Centre of Ecole Poly- technique, Montreal, under operating grants from the Department of Education of Qutbec, and the National Research Council of Canada. The author would like to thank the Geotech- nical Section of the NRCC for their field sup- port in Thompson and, in particular, for active help in the field and valuable comments re- ceived from Mr. Harry Baker. The author is grateful to Mr. Jean Paquin, Research Assis- tant and Mr. Florent Gauvin, Technical As- sistant, both at Ecole Polytechnique, for their help in preparing the equipment and carrying out the field tests.
ALKIRE, B. D. and ANDERSLAND, 0. B. 1973. The effect of confining pressure on the mechanical properties of sand-ice materials. J. Glaciol. 12, pp. 469-481.
BRINCH HANSEN, J. 1961. A general formula for bearing capacity. Bull. No. I I. Dan. Geotech. Inst., Copen- hagen, Den.
DAYAL, V. and ALLEN, J. H. 1975. The effect of penetra- tion rate on the strength of remolded clay and sand samples. Can. Geotech. J . 12, pp. 336-348.
DEBEER, E. E., LOUSBERG, E.. WALLAYS, M., CARPEN- TIER, R., DE JAECER, J . and PAQUAY, J. 1974. Scale effects in results of penetration tests performed in stiff clays. Proc. Europ. Symp. Penetration Test., Stock- holm, Swed. vol. 2.2, pp. 105-1 14.
DE RUITER, J . 1971. Electric penetrometer for site inves- tigations. ASCE, J . Soil Mech. Found. Div. 97 (SM2), pp. 457-472.
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anchors in permafrost. Can. Geotech. J. 11, pp. 348-358. KAPLAR, C. W. 1971. Some strength properties of frozen
soil and effect of loading rate. U.S. Army Cold Regions Res. Eng. Lab., Hanover, N.H., Spec. Rep. No. 159.
K ~ R I S E L , J. 1967. Scaling laws in soil mechanics. Proc. 3rd Panamerican Conf. Soil Mech. Found. Eng., Caracas, Venez., vol. 111, pp. 69-92.
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penetration test in sensitive clays, Proc. 7th Int. Conf. Soil Mech. Found. Eng., Mexico, Sess. I, pp. 225-320.
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MARSLAND, A. 1974. Comparisons of the results from sta- tic penetration tests and larae in-situ plate tests in Lon- don Clay. Proc. Europ. -symp. penetration Test., Stockholm, Swed., vol. 2.2, pp. 245-252.
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List of Symbols penetrometer radius 2a = penetrometer diameter frozen soil cohesion intercept depth factor creep exponent bearing capacity factors for a deep circular footing average total pressure at the test level point resistance of the penetrometer (end bearing resistance) asymptotic (calculated) point re- sistance
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110 CAN. GEOTECH. J . VOL. 13, 1976
r = radial distance from the center of the U, = equivalent stress (as defined in penetrometer base Ladanyi 1972)
S = rate of penetration 4 = angle of friction of frozen soil (in SC = shape factor terms of total stresses) t = time Y = shear strain = - c3 NOTE: Dot over symbols denotes time rate.
c3 = principal normal strains Subscripts a,ps, and f denote 'axial symmetry', % = equivalent strain rate (as defined in 'plane strain,' and 'failure' respectively.
Ladanyi 1972)
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