Centrifuge modeling of rapid load tests with open-ended piles

Centrifuge modeling of rapid load tests with open-ended piles

Civil Engineenng & Geosciences Faculty', Delft Universil}' ofTechnolog}', the Nelherlands van L o t t u m , H . & H ö l s c h e r , P.

Dellares, Ihe Netherlands van T o l , A . F.

Civil Engineering & Geosciences Faculty, Delfl University of Technolog}' and Deltares, the Netherlands

Kejavords: centrifuge modeling, rapid load, open-ended pile, close-ended p i l e , silt, sand

A B S T R A C T : Rapid and static load tests were conducted on open-ended and close-ended piles i n the Deltares GeoCentriflige. hi f l i g h t , a pile was dnven into the soil. B o t h fme-grained sand and silt beds were tested. B o t h the rapid and static soil resistances o f a close-ended p i l e were higher than the soil resistance o f an open-end pile i n both sand and silt. For the rapid load test, the higher the penefration rate, the higher the m a x i m u m soil resistance. The rado o f m a x i m u m soil resistance between a rapid load test and static load test does not depend on pile type but on soil type: less than 1.0 f o r sand and higher than 1.0 f o r silt. The results show that centrifiige modeling can be applied f o r open-ended piles but then silt must be used as the soil material.

1 I N T R O D U C T I O N

Pile load tests are a standard procedure f o r the verification o f pile load-displacement behavior as w e l l as f o r prediction o f the static bearing capacity o f the pile. The methods used are the static load test ( S L T ) , the dynamic load test ( D L T ) and the r a p i d load test ( R I . T ) . The tests vary i n terms o f the dunensionless wavelength A,,, = ^J^ x c ^ j / I , i n w h i c h Tf is the loading duration, Cp is the pile wave velocity and L is the p i l e length. N„ < 10 f o r the D L T , 10 < A„, < 1000 f o r R L T and N„ > 1000 f o r the S L T ( H ö l s c h e r and van T o l , 2008). A l t h o u g h the S L T is the most reliable method, i t is o f t e n too expensive and t i m e consuming to apply routinely. The R L T is increasingly used because it is better i n terms o f execution, elaboration and quality assurance than the D L T (Middendorp et al. 1992) and is more suitable f o r use i n offshore foundation engineering than the S L T .

Open-ended piles generally behave as though f u l l y plugged during static loading but they can behave i n a partially plugged w a y during rapid or dynamic loading, especially w h e n loading rates are h i g h (Bruno and Randolph 1999). The degree o f p l u g g m g depends o n several factors such as pile depth, pile diameter, loading rate and soil type... D i f f e r e n t degrees o f p l u g g i n g are expected to result i n different levels o f soil resistance. A n understanduig o f p l u g g i n g d u r i n g an R L T is important f o r the application o f R L T s to open-end piles: i f a pile plugs during an S L T but does not p l u g

during an R L T , the R L T w i l l be um-eliable and may underestimate pile capacity.

Scale modeling o f pile load tests offers a good opportunity to investigate this area. It avoids the h i g h costs o f field testing and offers additional possibilities compared w i t h field testing. Centiifiige m o d e l i n g is considered to be a reliable method due to the accurate representation o f the stress state, especially the self-weight sti'ess gradient, around and inside the model pile at a reduced scale. A n experimental study o f R L T s and SLTs w i t h open-ended piles was p e r f o n n e d w i t h d i f f e r e n t soil types to examme p l u g g i n g behavior i n silt and sand, especially during R L T s , and to compare soil resistance i n rapid and static conditions. Results fi-om open-ended piles test are also compared w i t h those fi'om close-ended piles tests. This paper presents the results fi'om f o u r test series comprising several R L T s and SLTs.

2 D E S C R I P T I O N O F R E S E A R C H 2.1 Centrifuge modeling

G i v e n the requirement o f sttess s i m i l a r i t y between the m o d e l ( w i t h the centrifiige length L,„odei and the c e n ü i f l i g e acceleration o f a„,oded and the prototype ( w i t h the length Lp,-o,ot)pe and the earth's gravity Uprotoi)pe), the scale factor is d e f m e d b y means o f Equation ( 1 ) .

j y _ ArP'otype _ "model _ "model

Table 1 shows the scale factors o f some parameters on the basis o f dimensional analysis, summarized by Taylor ( 2 0 0 5 ) . I t should be noted that, by using centrifuge modeling, the dynamic event and the consolidation event have t w o different time scale factor, N and respectively. This different w i l l be discussed later.

The experimental study was carried out in the GeoCentrifuge at Deltares (The Netherlands). Figure 1 shows the f a c i l i t y w h i c h consists o f sand f ü l container, loading system o f t w o hydraulic actuators... M o r e detail on the facilit>' o f the centrifuge tests setup can be f o u n d in H u y ( 2 0 0 8 ) .

Table 1. Scale factors in centrifiij ;e testo Parameters Model Prototype Length/Displacement 1 N Acceleration N 1 Time (dynamics) 1 N Time (consolidation) 1 N -Mass 1 Velocity 1 1 Force 1 Stress 1 1 Strain 1 1 Hydraulic achiator 1 / Pile Listallation Hydraulic actuator 2

Pile Loading L o a d cell

,pile

Figure 1. Centrifiige test setup (Huy, 2008). A l l dimensions in m m . 2.2 Model piles

The model pile was made t r o m steel w i t h a length o f 3 0 0 m m , a diameter o f 1 1 . 3 m m (£>), w a l l thickness o f 0 . 5 m m and mass o f 8 7 5 gram f o r an open-ended p i l e and 1 0 3 5 gram f o r a close-ended pile (jW ) ; this mass includes the pile mass and the m o u n t m g gear on the pile head. A load cell was mounted on the p i l e head to measure the applied force.

2.3 Model materials

Baskaip sand {dso = 1 3 0 p m ) and sih {dso = 5 8 p m ) were chosen f o r the tests. Table 2 lists the basic parameters f o r the soils (the quoted values f o r f r i c t i o n angle and permeability are at 6 5 % relative density) and Figure 2 shows the grain size distribution curves.

To m i n i m i z e tlie scale effects, the ratio o f pile w a l l thickness to the mean grain size d^o needs to be larger than 10 and the ratio o f the inner diameter o f pipe pile to dso must be larger than 200 (de N i c o l a and Randolph, 1997). The silt almost sadsfies this condition (8.6 and 178). h i the sand, the ratios are 3.9 and 79. h i prototype terms, the test w i t h s i h coiresponds to the n o m i a l use o f open-end piles i n sea-bed sand, w h i l e the test w i t h sand is an exfreme case i n a f i n e gravel layer w h i c h is sometimes to be found i n reality.

The soil sample was prepared b y drizzling sand into water, f o l l o w e d b y densification using impact loading ( R i e t d i j k et al., 2010). This method made it possible to achieve a reasonably homogeneous and reproducible sample o f 6 5 % relative density ( f o r these types o f soils).

Table 2 . Properties o f soilSp

Parameters Units Sand Silt Grain vol. mass k g / m ' 2 6 4 7 2 6 5 0 d50 l-im 130 58 M i n . porosity % 3 4 4 2 . 2 Max. porosity % 4 6 . 9 5 3 . 9 Internal fi-iction angle* degree 4 0 ° 3 8 ° Permeability m/s 1 2 x 1 0 ' ^ 1 . 5 x 1 0 - '

detemiined by tria.xial tests

10" Grain size [mm]

Figure 2 . Grain size distribution curves.

10

As mentioned on Section 2 . 1 , the scale factors o f dynamic event and consolidation are different (A'' and N'^) hence i f the same soil type as i n reality is used, the pore f l u i d must be A'' times more viscous to have a u n i f i c a t i o n o f the scale factors (Taylor, 2005). However m the authors' research group, i t is still not feasible to saturate the silt bed w i t h viscous f l u i d . Beside, the m a i n idea o f this research is investigation and comparison o f the open-ended p i l e i n sand and s i h therefore water was selected as the model pore f l u i d f o r a l l tests. Based on the results o f H u y (2008), the response o f the p i l e under r a p i d loading w i l l be drained, w i t h water as the pore f l u i d i n both cases (Baskarp sand and silt) then the effects o f excess pore pressure can be ignored.

2.4 Test programme

Three tests were p e r f o i m e d at the gravity level N = 40 w i t h the same loading programme: t w o tests i n silt, one w i t h an open-ended pile (OEP) and one w i t h a close-ended pile (CEP); and one test w i t h an OEP m sand. D u r i n g the tests, the pile was f i r s t pushed f r o m the pre-embedded depth o f 10£) to a depth o f 20D using the large hydraulic actuator. T w o R L T s w i t h average velocity o f 23.5 m m / s ( S l o w test) were then p e r f o i m e d w i t h displacements o f 1 % D (Rapid 1%) and 10% D (Rapid 10%) respectively (duration 10 ms) and t w o other R L T s w i t h average v e l o c i t y o f 125.6 mm/s (Fast test) and, f m a l l y , an S L T w i t h a displacement o f 10% D (Static) was performed. The results f r o m one test conducted previously (also at Dehares) w i t h a CEP i n sand ( H u y et al., 2008) are also s h o w n here f o r the purposes o f comparison.

3 R E S U L T S O F T H E C E N T R I F U G E T E S T Figure 3 shows t w o typical results f o r measured pile head force and applied p i l e displacement. The pile head forces have been corrected f o r the s e l f - w e i g h t o f the pile. 0.5 L-0.5 -1.5 + Rapid 1% • Rapid 10% • Static -Ö.2 0 0.2 0.4 0.6 Pile tiead force [l<NJ

(a) Average velocity o f 2 3 . 5 0 mm/s

0.5r 0.8 È . - 0 . 5 -1.5; + Rapid 1% • Rapid 10% • Static -Ö.2 0 0.2 0.4 0.6 0,8 Pile tiead force [kN]

(b) Average velocity o f 125.60 mm/s Figure 3 . Measured load-displacement curves.

The apphed force can be considered rapid, even though, compared w i t h a field test (e.g. Matsumoto and Nishimura, 1996), the generated force has v e i 7 h i g h gradients at the beginning and at the end o f loading and a l o n g duration o f m a x i m u m force, especially in the Fast test. The mfluence o f this force generation w i l l be discussed further on Secdon 4 .

O n Figure 3(b), there are loops at the end o f loading i n the Rapid 10% o f Fast test. This is the overshoot o f the loadmg actuator when i t is controlled to achieve the fastest loading duration o f 10 ms. As the overshoot is caused by the mechanics o f loading system and happens after the considered loading duration o f 10 ms, this overshoot was not taken into account.

D u n n g an R L T , the pile can be seen as a r i g i d body, h i that case, the force on the pile head {F„,easwecd is squal to the sum o f the soil resistance {Fsoii) and the inertia force {Fi„„iia) o f the pile (Middendorp et al. 1992). The soil resistance can therefore be calculated fi'om:

where M is the pile mass and a is the pile acceleration. The acceleration is calculated numerically as the second derivafive o f the measured pile displacement at all tune steps.

z^ = [z/,,z/2,...,z/p...z/„] (3) . , = " - - ' V " - ' (4)

Figure 4 shows an example o f the measured pile head force, inertia force and resultmg soil resistance and prescribed pile displacement fi'om the R L T w i t h silt. This soil resistance still includes velocity effects due to rapid loading. In Figure 4, the velocity and acceleration o f the pile are also presented.

n n ! I • I 1 -1 I ' ' ' '

0 0 05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 Time [s] Time [s]

(c) Pile velocity i n time (d) Pile acceleration in time Figure 4 . Example o f measured and calculated signals.

4 D E S C R I P T I O N S A N D D I S C U S S I O N O F T H E M O D E L P I L E T E S T R E S U L T S

This section describes the comparison o f SLTs and RLTs i n silt and sand i n detail. I t should be noted that, fi-om this p o i n t on, the soil resistance force durmg the R L T w i l l be the calculated pile head force after elimmating the mertia force o f the pile, and that all the numbers and quantities are m terms o f model scale ( N = 40 g).

4.1 Pile installation

As described above, the m o d e l piles were pushed into the soil m e d i u m w i t h the large hydraulic actuator fi-om the mitial depth o f l O D to the f m a l depth o f 2 0 D (fi'om distance o f 250 m m to distance o f 140 m m f r o m the contamer base) w i t h a d r i v i n g velocity o f 10 m m / m m . A t this very l o w d r i v i n g speed, the installation process can be considered as static j a c k i n g and the pore pressure does not b u i l d up.

Figure 5 shows the pushmg records f r o m the installation phase o f open-ended pile m sand and s i h beds. I t is clear that the installation o f the model pile m sand requires about 3 0 % more force than i n silt. A possible explanation is the grain size o f sand, w h i c h is 2.5 tunes larger than the gi-ain size o f silt and quite large compared to the thickness o f the pile w a l l .

140 I ' ' ' ' ' '

-0.2 0 0.2 0.4 O.B 0 8 1 1.2

Pile iiead force IkU]

Figure 5. Load-Displacement curve f o r installation phase o f open-ended pile.

4.2 Soil resistance and penetration rate effect Figures 6 and 7 show the soil resistance-displace-ment curves f o r d i f f e r e n t m a x i m u m displaceresistance-displace-ment values. Smce the duration o f the loading was the same i n a l l tests, the loadmg speed and then the penetration rate also varies between these tests. Figure 6 shows the resuhs o f the tests m silt and Figure 7 shows the results o f the tests i n sand. Part a) shows the resuhs f o r the OEP and part b ) shows the resuhs f o r the CEP. The test f o r the CEP i n sand

can be f o u n d m H u y et al. (2008). The average velocities i n a l l o f these tests are 23.50 nun/s. Table 3 presents soil resistance values o f t w o rapid loadings at 10% D displacement and corresponding static loadings i n a l l f o u r tests.

Generally, the soil resistance-displacement curves o f R L T s have quhe shnilar patterns: the force f n s t rises q u i c k l y to its m a x u n u m value, then stays h i g h at about the m a x u n u m value before finally f a l l m g rapidly. This steep loading pattern deviates from the loadmg pattern observed i n field tests w i t h a shallower increase to the m a x i m u m load and a shallower decrease to zero. This is a l ü n i t a t i o n o f the hydraulic loading system, as seen i n Figure 4.

There is almost no hnprovement i n the S L T values o f static loadings m each tests although between them there is several rapid loadmg.

The s o i l resistance observed d u r i n g the SLTs m sand was higher than m silt: soil resistance w i t h the OEP was 1.5 tmies higher; a factor 2 was f o u n d f o r the CEP. These differences could possibly be explained b y the properties o f the soil materials. Fhstly, the fi'iction angle o f Baskarp sand is 1-2° higher than the f r i c t i o n angle o f silt (at a relative density o f 6 5 % ) . Based o n Brinch-Hansen (1970), the difference between 38 and 40 degree leads to a 3 0 % higher bearing capacity o f a strip foundation, this is another observation but i t can give some suggesfion. Secondly, the dso o f the sand is 2.5 times larger than the dso o f the silt. The dso governs the thiclcness o f the shear band along the pile shaft, at the outer surface f o r the CEP pile and at the outer and mner surface f o r the OEP pile ( W o l f et a l , 2003; W o o d , 2002), and at the pile t i p w h i c h is normally about 8-12 dso. I t is w e l l k n o w n that m the shear band, soil is loosen and the shear sfress reduces hence the shaft resistance reduces also. This explains w h y the static resistance o f CEP pile i n sand is factor 2 higher than that i n silt but this factor is o n l y 1.5 f o r OEP pile.

The m a x m i u m soil resistance o f the close-ended pile is higher than the m a x i m u m soil resistance o f the open-ended pile i n both the R L T and S L T : about 3 0 % f o r the sand sample and 10% f o r the s i h sample. For the R L T , the higher the penefration rate, the higher the m a x u n u m soil resistance, about 10% difference between the slow test and the fast test i n silt test and 5% difference m sand test. This holds f o r both close-ended and open-ended piles.

T o compare the s o i l resistance during static and rapid loadmg, t w o factor RM and Rup are d e f m e d as:

^ ^ ^ ^ ^ ^ W t e a d . ( 5 )

-Static

i n w l i i c l i p M a x load IS the m a x k n u m soil resistance during rapid load test, F y p i o a d is the soil resistance at the unloading point o f rapid load test, Fstatic is the m a x i m u m soil resistance at the static load test. I t should be noted that p M a x i o a d , Fstatic are calculated at the same displacement.

W i t h the sand sample, the m a x u n u m soil resistance during the R L T , o f both CEP and OEP, is comparable w i t h the m a x i m u m soil resistance during the S L T : RM~ 0.95 ( 5 % lower) f o r the slow tests and Rj\i ~ 1 f o r the fast test. W i t h the silt sample, RM ~ 1.07 ( 7 % higher) f o r slow test and RM ~ 1.19 ( 2 0 % higher) for fast test, these differences apply to both the close-ended and open-ended piles.

4.3 Unloading-point in ethod

The ratios o f soil resistance at the unloading point durmg the RLTs to m a x i m u m soil resistance during the SLTs were quite different i n all tests. W i t h slow tests, except the CEP i n sand has RUP = 0.78, three other tests has Rup ~ 1 as expected fi-om the d e f i n i t i o n o f unloading-point method (Middendorp et al. 1992). W i t h fast test, Rup is significantly less than 1. This strange phenomenon can be explained f r o m Figure 3, either o f the steep loading pattern or o f the high inertia force, especially the parts o f after m a x i m u m load.

Because o f very high acceleration, fast test reaches maxunum prescribed displacement at only 2 0 % m a x i m u m load; w h i l e slow test reaches m a x u n u m prescribed displacement at 92-98% m a x i m u m load. As pointed out by M c V a y et al. (2003) and Paikowsky (2006), m order to have good prediction o f pile bearing capacity b y U P method, the assumption o f " s o i l resistance at the U P coincides w i t h static capacity o f the p i l e " is considered as significant. From this point o f view, w i t h the hydraulic loading system used i n this research, the U P method is only applicable w i t h slow rate test only.

4.4 Plugging

A f t e r installation and all loading phases, the pile was dug out. The final pluggmg length o f the soil inside the model piles was 55 m m {5D) w i t h sih and 22 m m ( 2 0 ) w i t h sand. The total displacement o f each pile was 122 m m (10.8Z)), w i t h the total embedded length o f each pile being 241 m m (20.8Z)). Plugging length as a percentage o f the total embedded length o f pile was about 2 3 % f o r silt and 9% f o r sand. These are relatively extreme values f o r plugging length when compared to those generally obsei-ved m reahty (10-20% o f the embedded length o f the pile) (Randolph et al., 1991).

A close inspection o f Figure 6 shows that the SLTs f o r the OEP and the CEP are ahnost identical. The R L T s f o r all piles show that the force declines after reaching the m a x i m u m . W i t h the OEP, the force decreases slightly more than f o r the CEP and is slightly more perturbed. The soil column inside the pile in sand tests may have slipped during the R L T s as the increasing bearing capacity exceeds the p l u g capacity. Figure 7(a); this does not happen m silt tests, Figure 6(a). However, the differences are small and the soil resistance o f the open-end pile was quite comparable to the soil resistance o f the close-ended pile. This suggests that the piles p l u g during both SLTs and R L T s . The m o t i o n o f the p l u g w o u l d have to be measured directly to obtain more accurate information.

Since the measured p l u g g m g length as w e l l as the plug behavior during SLTs and R L T s o f OEP is h i g h l y dependent on the material, it is important to use a correctly scaled material to avoid potential influence fi-om scaling effect, especially i n respect o f the interaction between the pile annulus and the soil (de N i c o l a and Randolph, 1997). I n this research w i t h A = 40, silt must better be used than sand.

Table 3. Soil resistance in R L T and SLT at displacement o f 10% D .

Ranidload testof 1 0 % D Max. velocity

Average

velocity Rapid loading

Static load Ru displacement [mm/s] [mm/s] Max load [kN] u p l o a d \m [ k N ] Ru Close-ended Sand 1 57 23.50 1.27 1.05 1.35 0.94 0.78 2 335 125.60 1.33 1.22 1.35 0.99 0.90 Close-ended Silt 1 54 23.50 0.71 0.65 0.66 1.07 0.98 2 124 125.60 0.79 0.24 0.66 1.19 0.37 Open-ended Sand 1 51 23.50 0.90 0.86 0.93 0.96 0.92 Open-ended Sand 2 121 125.60 0.95 0.43 0.96 1.00 0.45 Open-ended Silt 1 53 23.50 0.63 0.57 0.59 1.06 0.98 Open-ended Silt 2 116 125.60 0.70 0.30 0.61 1.15 0.50

0.2 0.4 Soil resistance [kN] (a) Open-ended 0.2 0 -0.2 -0.2 men t -0.4 OJ ro o. -0.6 _w Pil e -0.8 -1 • Rapid u : Rapid u = • Stètic _ * _ U P . . L o a d . l . @ Max Load • Static Load -Ö.2 0.2 0.4 0.6 Soli resistance [kN] 0.8 1.2 (a) Open-ended Soil resistance [kN] (b) Close-ended

Figure 6. Load-Displacement curve for pile in silt.

Soil resistance [kN]

(b) Close-ended ( f r o m Huy, 2008)

Figure 7. Load-Displacement curve for pile i n sand.

5 C O N C L U S I O N S

This paper described experimental w o r k investigating soil plugs i n open-ended piles i n a geotecluiical centrifiige. B o t h static and rapid load tests were studied i n t w o types o f soil: fme-grained sand and sih.

The conclusions can be summarized as f o l l o w s : 1 Centrifuge testing is a feasible and e f f i c i e n t

approach to studying the behavior o f open-end piles.

2 The soil resistance i n tests w i t h sand was higher than i n tests w i t h s i h and was higher f o r close-ended p i l e than f o r open-ended pile. This holds f o r both rapid l o a d tests and static load tests. W i t h m r a p i d load tests o f the same s o i l type, the higher the penetration rate the higher the m a x i m u m soil resistance.

3 The unloadmg point m e t h o d d i d not w o r k w e l l w i t h loading tests w h i c h have steep increase o f loading force or h i g h inertia forces.

4 The proper scaling o f an open-end pile requires proper scaling o f the grain size. Silt must be used for a 1:40 scale.

The research is s t i l l ongoing. T o unprove out understanduig o f plugging behavior and the hnpact o f p l u g g m g on open-end pile capacity d u r m g R L T s , the p r e l i m m a r y tests can be improved by:

1 Increasing the number o f test to investigate the repeatability.

2 Measuring the p l u g g m g length d u r m g mstallation and a l l successive static and rapid loading steps; 3 E x a m i n i n g the mfluence o f other factors as

generated excess pore pressure, drainage c o n d i t i o n and i n h i a l s o i l density.

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