ISGSR7 Frst Internatonal Symposum on Geotechncal Safety & Rsk Oct. 8~9, 7 Shangha Tongj Unversty, Chna Expermental Study of the Lght Dynamc Penetraton Method to Test Shallow Fll of Coarse-sand n Subsol Engneerng TIAN Qngyan, Fu Heln Cvl Engneerng College of Central South Unversty, Changsha Hunan, Guangdong Transportaton and Communcaton Testng Center, Guangdong Guangzhou, Chna ABSTRACT: In ths paper, expermental relatonshp between lght dynamc penetraton blow counts N and relatve densty Dr of coarse-sand s bult on the base of large model tests by smple statstcs. Then, the feasblty of ths mothed s proved by three-dmenson numercal calculaton and feld tests. It shows that the lght dynamc penetraton can be well appled n testng the densty of coarse sand at shallow coarse-sand back fllng subground. INTRODUCTION Lght dynamc penetratng test s a common method of n-stu test. It utlzes certan hammer force to ht the drll ple nto sol and to evaluate the sol propertes accordng to the penetratng force, whch, under certan condtons, reflects the dfferences of mechancs property of sol layer. Because the lght dynamc penetratng apparatus s handy, portable and convenent to handle, many researches n the world have launched n ths feld and ganed much achevement ever snce the 95s. Meanwhle, the applcaton of the lght dynamc penetratng test method n the sand sol has been mproved greatly. However, due to the weak httng force and the easy bendng of the ple, ths method used to be consdered applcable only n dfferentatng the sol bed and n evaluatng the sotropy of the layers n fne sand sol. At present, ts applcaton n testng the relatve densty of coarse-sand backfll has not been studed systematcally. In ths paper, n order to carry out the applcaton of the lght dynamc penetratng test n testng the relatve densty of coarse-sand backfll, four knds of sand n dfferent gran szes and dfferent denstes are used to proceed a seres of lght penetratng tests n the model trough and to dsclose the expermental relatonshp between lght dynamc penetraton blow counts (N ) and relatve densty (Dr) of coarse-sand. The relatonshp s also smulated by the three-dmensonal fnte numercal analyss, by the consstency between the sol stress obtaned n the test and the result obtaned n -D FEM analyss, ths paper vertfes the relablty of the relatve densty of coarse sand n the lght dynamc penetratng test. Otherwse, the expermental relatonshp between the lght dynamc penetraton blow counts (N ) and relatve densty (Dr) s vald by feld test. RESULTS OF THE LARGE MODEL TEST In ths study, four knds of typcal sand (Table and Fg.) are chosen n back sand fllng of subsol, and the model test s proceeded n a model snk (m m m) to collect ndex, such as relatve densty Dr, the lght dynamc penetraton blow counts N, stress of sand at dfferent depth n model test, analyze the feasblty that the lght dynamc penetraton s used to test the densty of coarse sand at shallow coarse-sand back fllng n Subsol Engneerng, and buld the expermental relatonshp between blow counts N and relatve densty Dr. Results of test are shown n Tables -5. 7
pass /% 9 8 7 6 5 5.5.5.5.75 sze of seve pore /mm, sand No. ;, sand No. ;, sand No. ;, sand No. Fg. Composton of sand n model test. Crtcal depth ( h cr ) The surface layer of sand should not be neglected to detect relatve densty of sand by lght dynamc penetraton. But because t s affected by the effect of surface layer and the dead weght of sand, the lght dynamc pentraton blow count N s ncreasng gradually wth the further depth of pentraton ng certan range of the surface depth. The paper plans to gan the regularty that the blow counts change wth depth n the range of penetraton n order to control the countructon qualty of coarse-sand back fllng reasonably and evaluate the relatve densty effectvely. So t s necessary to determne the crtcal depth of lght dynamc penetraton and research nto the regularty that the blow counts change wth depth above or below the crtcal depth. From Fgs. -5, t shows that lght dynamc penetraton blow count N ncreases wth the further penetraton, and when the cone explore nto a certan depth, t reaches the maxmum whch s called crtcal depth ( hcr ). The curves of hcr and Dr of the four knds sand as showed n Fg.6 reveal that exsts n realty and t ncreases nonlnearly wth Dr. h cr Table Physcal ndex of the testng sand Seral number of Fneness Sand M X G s e max e mn F d 5 (mm) C u C c Class [] No..7.65.9.86.58.85 5.5.76 Gravel No..7.6.9.6..56.9.9 Near fne sand No..66.65.798.96.978.6 6.8.6 Mesne sand No..6.66.97.9..5 5..59 Coarse sand Note: F=(e max -e mn )/e mn ; The mneral composton of sand s quartz. 8
survey depth h /cm 6 9 5 8 Blow count N / number /cm 6 9 5 8 Blow count N/ number/ cm 6 9 5 8 6 9 5 8, Dr=.5;, Dr=.7;, Dr=.9;, Dr=.66;, Dr=.8;, Dr=.89, Dr=.7;, Dr=.9 Fg. Results of No. sand Fg. Results of No. sand survey depth h /cm survey depth h /cm 6 9 5 8 Blow count N/ number/cm 6 9 5 8 survey depth h /cm 6 9 5 8 Blow count N/ number/cm 6 9 5 8, Dr=.9;, Dr=.59;, Dr=.9;, Dr=.6;, Dr=.7;, Dr=.9;, Dr=.76;, Dr=.9; Fg. Results of No. sand Fg.5 Results of No. sand. Blow count (N ) of lght dynamc Petrenaton Accordng to the results of model tests f bgger than the crtcle depth, N of lght dynamc petrenaton ncreases wth the petrenatng depth ( h ) and relatve densty of sand (Dr); f smaller than the crtcal depth hcr, N stays stable. As the test result showed, Dr s the most senstve factor to nfluence the blow count N L n the crtcal depth, t can be concluded that the blow count N L n the crtcal depth ncrease consderably wth the ncrease of Dr. In addton, there exsts a brdge between the blow count N L and the fneness modulus Mx of sand. When Dr<.8 but N L s fxed, the larger the fne modulus Mx s, the larger the relatve densty s, the order of Dr s as followngs: gravel, coarseness, ntermedate, and fneness.. Experental formula of Dr and N from model test On the base of the features of petrenatng curve, the analyss of the relatonshp between N and Dr may be dvded nto two knds of condtons by consderng the crtcal depth as a boundary. Above the crtcal depth ( h cr ), accordng to Krem Theorem, there exsts pluralstc and lnear relatonshp between relatve densty of sand (Dr) and fneness modulus of sand (Mx), exploraton depth (h), blow count (N, the number of blow counts per cm), as showed n formula (); at the crtcal depth and ts below, Dr s n logarthm wth N L through nonlnear analyss, as showed n formula (). 9
D r =.7+.9M x -.7h+.7N (ρ=.975). () D r =-.57+.8ln(N L ) (ρ=.968) () In the above formula, Dr---- the reltve densty of sand, N ---- the blowcount of lght dynamc penetraton above the crtcal depth, Mx ---- the fneness modulus of sand, h ---- the exploraton depth of lght dynamc penetraton, N L --- the blow counts of lght dynamc penetraton at the crtcal depth. As concluded n formula, above crtcal depth, except N, the fneness modulus of sand nfluences Dr s to the most. When other parameters are fxed, the larger Mx s, the bgger the relatve densty of sand wll be. CALCULATION ON THREE-DIMENSION- FINITE UNITS Aded by the three-dmensonal fnte elements, the testng results of the lght dynamc petrenaton are further examned. Smultaneously, the stress, stran, the features of dsplacement dstrbuton and dstrbuton curve dagram of sand n the process of dynamc exploraton are calculated n sand of dfferent relatve densty. In the model procedure, the p. V. lade model s adopted, parameter unts such as the ten-cross-pont tetrahedron are used, as shown n Fg.7. hcr /cm 8 5 9 6...6 Dr.8, sand No. ;, sand No. ;, sand No. ;, sand No. Fg.6 Test relaton between h and D cr r X Z Y 8 Fg.7 The unt cross-ponts n the whole coordnate system 5 7 9 6 For partal coordnate, functon nserton by adoptng cross-pont dsplacement amount can be drectly obtaned from the unt dsplacement functon. u = v = w = m = m = m = N ( ξ, η, ζ ) u N ( ξ, η, ζ ) v N ( ξ, η, ζ ) w In the above formula,u,v,w represents the dsplacement of unt along x,y and z reference axs respectvely, N ( ξ, η, ζ ) s shape functo, ξ, η, ζ s cross-pont coordnate n part of reference frame, u, v, w represent the dsplacement of the cross-pont. The often-used mother unt of the parameter unts such as the usual tetrahedron ncludes the four cross-pont lnear tetrahedron unt and the ten cross-pont quadratc tetrahedron unt etc. (shown n fg.5). The shape functons s:. N = ( L ) L. () ()
here, =,,,; L s the rato of a sub-tetrahedron volume formed by a random pont and one sde n tetrahedron and that of the tetrahedrom. To the cross-pont n amdst sde: N N N N N N 5 6 7 8 9 = L L = LL = L L. = LL = L L = L L (5) By deducton, the unt s stffness matrx e K s expressed as the followng equaton: K e T = B DBtdA = Ω e ξ ξ η B T DB J tdξdηdζ. (6) where:b stands for stran matrx of the unt, t s thckness; J s three-dmensonal Jacob matrx; D s elastc matrx. The general stffness matrx can be formed accordng to formula(6), then the dsplacement drecton { δ } of a unt can be obtaned by the borderary condton and ts loadng{r}. [ K ]{δ}={r}. (7) Then, the unt stress and stran can be concluded, based on the equaton { ε }=[ B ]{ δ } and {σ }=[ D ]{ε}. In the nonlnear FEM analyss, the combnaton of the elastc modulus matrx, whch s needed n the ncrement calculaton, s the key problem. As the Lade model has two yeld surfaces, the elastc-plastc modulus matrx has the followng forms: G[ X] [ D] ep = [ D]. B B Φ Φ fg fg (8) In the formula: A B = + Φ ; A fg B = + Φ ; fg ] = [ ] + [ ] G G [ X B X fg B X fg Φ [ f ] [ ] g X fg Φ fg X fg f, represent yeld functons of the frst and the second yeld face of the Lade model f hyperbolod;, g stand for plastc potental functons of the frst and the second yeld face. g
h cr /cm 8 5 9 6...6.8 Dr, sand No. ;, sand No. ;, sand No. ;, sand No. Fg.8 Calculaton relaton between h and D. Comparson of crtcal depth by calculaton and model test By computng, the relatonshp between crtcal depth and relatve densty s shown n Fg.8. As shown n Fg.6 and Fg.8, for crtcal depth, the result by calculaton s qute close to the result n the model test. When the relatve densty s between. and.8, the sxe order of crtcal depth s as followngs: sand No., sand No., sand No. and sand No... Analyss about calculatonal and testng stress and stran The testng sol stress and stran durng petrenatng process are obtaned from four sol stress boxes No., No., No., No., whch are flled respectvely n sol wth depth of 5cm, 5cm, 76cm and 55cm. Durng the process of penetraton, the maxmum stress and stran n sand take place n the place where s a lttle bt above the sol stress box. The shape os close to an ellpse. In Fg. and Fg., the comparson between the stress and stran curve ganed by fnte element method and the same type of curve ganed by test n the sol stress box s shown. It s clear that the calculaton value s close to the test value. Through fnte element calculaton, t s known that, ever snce the begnnng of the drll head penetratng nto the sand surface, sol around the drll head n sand of relatvely great densty has the tendency of flow upward, and apparent upheaval and crack can be seen on the surface. When the penetratng reaches certan depth and the depth s wthn the crtcal depth, the former stress n some parts of the two sdes of the drll head lax or dmnshes, (the testng subordnate stress should be a negatve value, shown n Fgs. 9-). Ths belongs to typcal falure mechansm. Whle sand n small relatvely densty s manly controlled by the compress and penetratng mechansm, ts surface has no apophyss or unconspcuous apophyss n drllng. Due to the dfferences of the penetratng mechansm n dfferent relatve denstes and dfferent scopes, there exsts obvous dfferences n the stress, stran and dsplacement n sand of dfferent denstes. when the penetraton beyond the crtcal depth, the crtcal stress(σ )of the sand of relatve small densty whch s controlled by the contractng mechansm s weak, and the scope the mechansm works s not wde, the cover press of sol almost doesn t work. However, for the sand of relatve great densty over the crtcal depth, ts crtcal stress s strong and ts sol press nfluence s also great. Therefore, the stress value n the crtcal depth h cr s bgger than that of small densty. cr r h cr
survey depth h/cm 8 5 9 6 6 5 7 8 survey depth h/cm 8 5 9 6 5 6 8 7 5 5 6 75 9 stress σ(kpa), Test stress of sol stress box n No. bore, Cal. stress of sol stress box n No. bore, Test stress of sol stress box n No. bore, Cal. stress of sol stress box n No. bore 5, Test stress of sol stress box n No. bore 6, Cal. stress of sol stress box n No. bore 7, Test stress of sol stress box n No. bore 8, Cal. stress of sol stress box n No. bore RESULTS OF SITU-TEST Fg.9 Comparson of calculaton and test stress of sand No. 5 stranε/(με), Test stran of sol stress box n No. bore, Cal. stran of sol stress box n No. bore, Test stran of sol stress box n No. bore, Cal. stran of sol stress box n No. bore 5, Test stran of sol stress box n No. bore 6, Cal. stran of sol stress box n No. bore 7, Test stran of sol stress box n No. bore 8, Cal. stran of sol stress box n No. bore Fg. Comparson of calculaton and test stran of sand No. In order to verfy the feasblty of the applcaton of the results of lght dynamc penetraton model test, feld tests are carred out n constructng roadbed engneerng adoptng same apparatus and smlar sand wth fneness modulus of.. Three groups of test datum of fllng sand n a culvert-back are shown n Fg.. survey depth h /cm 6 9 5 8 7 Blow count N / number/cm 6 8, pont#-;, pont#-;, pont #- Fg. Relaton between N and h of lght dynamc petrenatng Contrast of Fg. wth Fgs. -5, the curve form n feld test s consstent wth that of model test. Table lsts the testng densty of sand n deferent depth and ts correspondng calculatonal value, whch s ganed by nsertng blow counts (N ) data of feld test No. #- nto formula () and (). From table 6, error or relatve error between calculatonal and testng Dr of feld sand s less than percent can be acqured. So t proves that t s feasble and vald for the formula () and () to be appled to lght dynamc petrenaton testng relatve densty of shallow fll coarse-sand subground.
Table Comparson between Dr calculated and Dr tested of No. # - coarse sand on the spot M X h N Calculatonal Test Dfference/Rato Remark value value. 8.7.76 -./-.9%. 6.7.76 -./-.9%. 9 59.7.76 -./-5.%. 8.8.76.5/6.6%. 5 75.79.76./.9% 5 CONCLUSIONS The crtcal depth n the feld test From above, four ponts can be concluded as followngs: () Durng the lght dynamc petrenaton testng, Dr of sand s the most senstve factor to the blow counts (N ), and the fneness modulus of sand s the next one. () By analyzng model test data, above the crtcal depth ( ) of sand layer, there exsts lnear relatonshp between the relatve densty of sand (Dr) and N. By adoptng Krem prncple, t s regressed to get formula (); at crtcal depth and below t, the connecton between N L and Dr can statsfy a logarthm functon, and t s regressed to get formula (). () Smulated by the three-dmensonal FEM, the calculatonal stress and stran n sol s consstent wth that of testng value, whch confrms t verfed n theory that t s feasble for lght dynamc petrenaton detectng the relatve densty of back-fll coarse sand n subground works. () By feld test, t s clear that the relatve densty of sand ganed by adoptng experental formula () () s consstent wth the test value of t. So formula () () from model test may by appled to calculate the relatve densty of carse sand. ACKNOWLEDGMENTS Ths paper s a part of the project report of Testng Method Study of the Relatve Densty of Back Fllng Coarse Sand n Transton of Brdge and Roadbed n Hghway Constructon (No. -) sponsored by the Scence and Technology Foundaton of Guangdong Transportaton Governmemt. REFERENCES Chang Aguo, Du Ronghua, Fan Pengfe. The Applcaton of PANDA Dynamc Penetraton Devce to Hghway, Shanx Scence & Technology of Communcatons,,(): 5-55 Code for Investgaton of Geotechncal Engneerng, GB5-, PRC Standard,. De Beer, E E. Donness concarnant la resstance an osakllement declutes des en as de penetraton en profondeur. Geotechnque, 98, (): -. Deng bo,the Statstc Method of Analyzng test data, Tsnghua Unversty Press, Bejng, 997. P8~56. Durgunoglu H T, Mtchell J K. Statc penetraton resstance of sols I: Analyss. In: Ralegh N C,ed. Proc ASCE Spec Conf on In Stu Measurement of Sol Propertes, New York, ASCE, 975--6-. 5-7. Hu G.Bearng capacty of foundatons wth overburden shear. Sols-Sols, 965, (): ~8 Lu Zhaohu,. Dynamc Penetraton Test on a Brdge Base, Journal of Anhu Unversty of Scence and Technology(Natural Scence),,():~7. h cr
Mahmoud, M, Woeller D,Robertson P K. Detecton of shear zones n a natural clay slope usng the cone penetraton test and contnuous dynamc samplng. Canadon Geotechncal Journal,, 7(): 65-66. Pankn,A.K., Lunne, T., Boundary Effects n the laboratory Calbraton of a cone penetraton for sand, ESOPT- Ⅱ, 98. Robertson P K, Campanella R G. Interpretaton of cone penetraton tests Part : clay. Can Geotech J, 98, (): 7-75. Tang Xanqang, In-stu Test Technology n Foundaton Project. Bejng: Chna Ralway 996. Press, Terzagh K. Theoretcal sol mechancs. New York: John Wley & Sons, 9. The FEM smulaton of dynamc penetraton process of CPTU.Ma Shu-Zh,etc, Rock and sol mechancs,(): 78-8. Xe Shouy, Xu Weya, Lu Defu, Jang Png. A General Index of Dynamc Penetraton Test Dynamc Cone Resstance and Its Applcaton, Journal of Unversty of Hydraulc and Electrc (Ychang), 998, (): 9-. Yu H S, Mtchell J K Analyss of cone resstance: revew of methods. Journal of Geotechncal and Geoenvronmental Engneerng, ASCE, 998, (): ~9 5
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