Evaluation of the Humboldt GeoGauge TM on Dry Cohesionless Silica Sand in a Cubical Test Bin. Lary R. Lenke, P.E. Matt Grush R. Gordon McKeen, P.E.

Transcription

1 Ealuatin f the Humbldt GeGauge TM n Dry Chesinless Silica Sand in a Cubical Test Bin Lary R. Lenke, P.E. Matt Grush R. Grdn McKeen, P.E. ATR Institute Uniersity f New Mexic December 1999

2 Intrductin The GeGauge TM manufactured by the Humbldt Manufacturing Cmpany is a prtable instrument priding a simple and rapid means f measuring the stiffness f cmpacted subgrade, subbase, and base curse layers in earthen cnstructin. The GeGauge TM measures stiffness at the sil surface by imparting ery small displacements t the sil n an annularly laded regin ia a harmnic scillatr perating er a frequency f 100 t 196 Hz. Apprpriate transducer technlgy is incrprated t measure bth frce and displacement frm which stiffness can be cmputed. The cmputed stiffness is determined based n an aerage f 25 stiffness alues btained at 25 discreet frequencies in the frequency band cited abe. The GeGauge TM weighs apprximately 10 kg (22 lb). The annular ring which cntacts the sil has an utside diameter f 4.50 in. (114 mm) and an inside diameter f 3.50 in. (89 mm); hence, with a ring thickness f 0.50 in. (13 mm). Humbldt claims that the magnitude f the ertical displacement induced at the sil-ring interface is less than in. (1.3 x 10-6 m). The annular ft bears directly n the sil, supprting the weight f the GeGauge TM. Attached abe this annular fting is a shaker, which excites the fting in a ertical mde. Sensrs attached t the shaker and fting measure the frce and displacement time histries. The ertical excitatin prduces a small ertical harmnic excitatin resulting in a small harmnic deflectin at the sil-fting interface. The measured sil deflectin δ and the applied frce F can be in turn used t calculate the stiffness f the underlying granular media. The prblem f a rigid annular ring n a linear elastic, hmgeneus, istrpic half space has been cnsidered by Egr (1965). The static stiffness K f such a sil-structure interactin prblem has the functinal frm F ER K = = (1) 2 δ (1 ν ) ω( n) where E and ν are the mdulus f elasticity and Pissn s rati f the elastic media, respectiely, R is the utside radius f the annular ring, and ω(n) is a functin f the rati f the inside

3 diameter and the utside diameter f the annular ring. Fr the ring gemetry f the GeGauge TM, ω(n) is equal t Recall that the mdulus f elasticity and the mdulus f E rigidity G are relate thrugh G =, hence, the abe equatin fr static stiffness can be 2 1+ν expressed as ( ) F 3.54GR K = = δ 1 ν ( ) (2) The ATR Institute at the Uniersity f New Mexic has been recently asked, by the New Mexic State Highway and Transprtatin Department (NMSHTD), t ealuate nn-nuclear methds fr the ealuatin f cmpactin cntrl f subgrade, subbase, and base curse materials used in highway and transprtatin cnstructin. The Humbldt GeGauge TM was a identified as a ptential alternatie fr such nuclear methds. While smewhat utside the scpe f this paper, it can be argued that sil stiffness is a mre fundamental prperty f the sil s ability t supprt surface lads than density measurements btained by cmpactin methds. Mst ratinal paement and fundatin design methds use stiffness r elastic mdulus fr the thickness determinatin f each layer f a paement system. The fundamental questin that arises with any new technlgy is whether the new technlgy truly measures what the manufacturer claims. T this end the ATR Institute has embarked n an ealuatin prcess f the GeGauge TM. This paper describes a simple labratry experiment t determine if the GeGauge TM truly measures stiffness as adertised. Experiment Dynamic sil-structure interactin experiments were cnducted by Lenke, et al (1991), at the Uniersity f Clrad, using mdel ftings in an enhanced graitatinal field using the getechnical centrifuge mdeling technique. Because f the inability t truly mdel an elastic half space experimentally, they ealuated numerus cntainer shapes and bundary materials t minimize reflected wae energy in an attempt t apprximate true radiatin damping f a

4 ertically excited circular fting. One f the principal cnclusins frm their research was that cubical cntainers with a cmpliant energy absrbing bundary material allwed reasnable apprximatin f an elastic half space. In rder t ealuate the GeGauge TM, a similar apprach was taken, albeit, n a larger scale than the experiments cnducted by Lenke, et al. A relatiely large steel bx was btained f apprximate cubical shape. This steel cntainer is lined with steel plate and reinfrced externally by steel channels sectins, resulting in a fairly rigid cntainer. The nminal dimensins f this cntainer are 24 in. (610 mm) deep with a lateral crss sectinal area f 30 in. by 30 in. (760 mm by 760 mm). The lateral and bttm surfaces f this cntainer were lined with 3/4 in. (19 mm) styrfam panels as an energy absrbing material. A dry granular chesinless silica sand was btained frm U.S. Silica s Ottawa, Illinis manufacturing facility. The sand selected is designated as F-52. The prduct infrmatin prided by U.S. Silica state that this sand has a specific graity f 2.65 (typical f silica sand) with a rund grain shape. The mean grain size is apprximately 0.26 mm (0.010 in.) based n a tabulated particle size distributin. This silica sand was then pluiated thrugh air frm a height f 18 in. (460 mm) int the famed lined steel test bin described abe. This raining peratin tk apprximately 20 hurs t accmplish in rder t ensure a unifrm, highly cmpact granular media within the test bed. Upn cmpletin f the raining peratin, the surface f the sand media was carefully screeded leel with the tp f the test bin. During this peratin the ttal weight f material placed was carefully tracked. Based n careful measurement f the test bin dimensins prir t pluiatin f the sand, the resultant density f the media within the test bin culd be calculated. The aerage density (unit weight) cmputed was lb/ft 3 ( kg/ m 3 ). Based n this unit weight and the knwn specific graity the id rati f the granular media within the test bin was cmputed as With the granular media nw in place within the test bin, measurements f stiffness were btained using the Humbldt GeGauge TM. Measurements were btained at the center f the test bin surface as well as at quarter pints alng ne diagnal f the square crss sectin. A ttal f

5 eight measurements were btained with a mean alue f 6.19 MN/m (35,300 lb/in.). The standard deiatin f these eight measurements was 0.04 MN/m. The assciated cefficient f ariatin as defined by the rati f the standard deiatin t the mean was 0.7%. Analysis Harding and Richart (1963) fund that the mdulus f rigidity (shear mdulus) culd be related t the id rati and the mean effectie ctahedral stress (i.e., aerage effectie cnfining pressure) by the fllwing empirical equatin. ( 2.17 e) ( 1+ e) G = (3) ( ) 0. 5 where G is the shear mdulus, e is the id rati f the granular media and is the mean effectie cnfining pressure. The abe equatin was deelped fr rund-grained sands using dynamic wae prpagatin experimental methds. The abe equatin is empirical and has nn-hmgeneus units. The engineering units f bth the shear mdulus and mean effectie stress are in terms f punds per square inch (psi) and apparently the numerical alue 2630 has units f (psi) 0.5. Equatin (3) can be used t calculate the stiffness defined in Equatin (2) if the unknwn parameters can be estimated with sme certainty. The id rati in Equatin (3) was ery carefully determined during the experimental placement f the sand in the sil test bin. The alue f the mean effectie stress is much mre difficult t ascertain, hweer. In additin, Pissn s rati in Equatin (2) is nt knwn. Hweer, if ne can estimate the alues f the mean effectie stress and Pissn s rati, then Equatins (2) and (3) can be used t estimate the stiffness f the granular sil in the test bin and a cmparisn can be made with the GeGauge TM experiment. The mean effectie stress can be cmputed using the fllwing definitin

6 = h = + 2K 3 = 3 ( 1+ 2K ) (4) where and h are the ertical and hrizntal effectie stress cmpnents, respectiely, and K is the cefficient f lateral earth pressure. The alue f deelped by Jaky (1944) K can be estimated by an equatin K 2 1 sin φ = 1 + sin φ 3 1+ sin φ (5) where φ is the effectie angle f internal frictin f the granular media. An estimate f this angle f internal frictin was btained by a simple experiment t determine the angle f repse f the F-52 silica sand used in the bin test described preiusly. The angle f repse measured was 33. This is cnsidered a lwer bund fr φ ; the actual alue f φ may apprach 40 but the lwer bund will be used fr further cmputatinal analysis. Using the angle f repse as an apprximatin fr the internal angle f frictin yields a cefficient f lateral earth pressure f Substitutin f this alue int Equatin (4) yields the fllwing fr the mean effectie stress = (6) fllws It can be shwn that Pissn s rati can be estimated using generalized Hke s law as ν K = 1+ K (7) Fr the cefficient f lateral earth pressure preiusly estimated, the alue f Pissn s rati is calculated t be

7 At this pint, ratinal means hae been used t estimate all ariable fr cmputing the stiffness f the silica sand used in the bin tests with the exceptin f the ertical effectie stress. The alue f this ertical effectie stress is much mre difficult t estimate. The effectie stress belw the annular fting can be cnsidered as cmpsed f tw cmpnents. One cmpnent is the gestatic, r lithstatic stress caused by the self-weight f the material. This ertical selfweight cmpnent is simply the density (r unit weight) f the material γ times the depth belw the fting, z. Essentially, the self weight cmpnent f ertical effectie stress is zer at the grund surface f the sil bin and increases in a linear fashin with depth. The secnd cmpnent f ertical effectie stress is caused by the presence f the annular fting n the surface f the experimentally mdeled half space. The analytical slutin fr the ertical stress distributin n centerline belw an annularly laded fting (r = 0) is presented in Puls and Dais (1974) as = 3 3pz a 2 2 ( a + z ) 5 / 2 (8) where a is the distance frm the center f the fting t the centerline f the ring (see Figure 1), z is the depth belw the centerline f the annular fting, and p is an annular line lad acting at a distance a frm the centerline f the fting. Fr the GeGauge TM used in the experiments Figure 1. Unifrm Vertical Ring Lading n Surface f Elastic Half Space. described preiusly, a is equal t 2.0 in. (51 mm), and the weight f the GeGauge TM was measured as lb resulting in an annular line lad p f lb/in. (306.8 N/m). Nte that

8 the abe equatin is equal t the ertical effectie stress as preiusly defined since the granular media as used in the experiments is dry and pre pressures are nn existent. Figure 2 shws a graphical representatin f the ertical stress distributin as a functin f depth fr bth the gestatic stress cmpnent and the annular ring induced cmpnent. The sum f this tw stress cmpnents is the ttal ertical effectie stress. The ttal stress distributin clearly shws that the stress leels becme fairly cnstant and unifrm fr depths f 2 t 9 inches (50 mm t 230 mm). It is well knwn that the pressure bulb belw an circular fting extends t a depth equal t abut twice the diameter f the fting. The dynamic respnse f the annular fting will als be influenced by a zne f sil t a depth f abut tw diameters as well. Based n the bsered ttal stress distributin f Figure 2 and a knwledge that the depth f influence extends t tw diameters (9 in.), an estimate f 0.63 psi is made fr the ertical effectie stress belw the annular fting. 0 Vertical Effectie Stress, psi Gestatic Effectie Stress Lad Induced Stress Ttal Stress 6 9 Depth, in Unifrm Vertical Annular Line Lad Center Line r = 0 (Line Lad = lb/in., Annular Radius, a = 2.0 in.) 24 Figure 2. Effectie Vertical Stress Distributin Belw an Annular Fting.

9 Substitutin f this estimated 0.63 psi ertical effectie stress int Equatin (6) with subsequent substitutin f the mean effectie stress int Equatin (3) yields an estimate fr the shear mdulus f the granular media within the sil test bin. This shear mdulus alng with the preiusly estimated alue f Pissn s rati and the utside radius f the GeGauge TM annular fting is then substituted int Equatin (2) yielding a static stiffness f 33,800 lb/in. Cmparisn f this cmputatinal estimate with the experimentally determined alue f stiffness results in an errr less than 5%. Based n this simple experiment and a ratinal analysis, ne wuld cnclude that the GeGauge TM is indeed measuring the stiffness f the underlying granular sil media.

10 References Egr, K.E., 1965, Calculatin f Bed fr Fundatin with Ring Fting, Prc. 6 th Internatinal Cnference f Sil Mechanics and Fundatin Engineering, Vl. 2, pp Hardin, B.O., and Richart, F.E., Jr., 1963, Elastic Wae Velcities in Granular Sils, Jurnal f the Sil Mechanics and Fundatin Engineering Diisin, American Sciety f Ciil Engineers, Vl. 89, N. SM1, pp Jaky, J., 1944, The Cefficient f Earth Pressure at Rest, Jurnal f the Unin f Hungarian Engineers and Architects, pp (in Hungarian). Lenke, L.R., Pak, R.Y.S., and K, H-Y, 1991, Bundary Effects in Mdeling Fundatins Subjected t Vertical Excitatin, Prc. Internatinal Cnference Centrifuge 1991, Balkema, Rtterdam, pp Puls, H.G., and Dais, E.H., 1974, Elastic Slutins fr Sil and Rck Mechanics, Wiley, New Yrk, p. 32.