Suppi 7 (1996) REMR Technical Nte CS-ES-4.6 Flw-Net-Cputed Uplift Pressures Alng Cncrete Mnlith/Rck Fundatin nterface ntrductin One f the key stages in a stability evaluatin f navigatin and fldcntrl structures is the calculatin (r assignent) f uplifi pressures alng the base f the hydraulic structure and/r alng a critical rck jint r jints within the fundatin. Using accurate piezetric instruentatin data at a site alng with knwledge f the site gelgy is the preferred ethd fr establishing uplift pressures. Hwever, when instruentatin data are nt available r when the reservir levels t be analyzed exceed thse fr which the piezetric easureents were ade, ther prcedures ust be used t establish the distributin f flw and the crrespnding uplift pressures. Three prcedures are widely used by engineers t establish the uplift pressures alng an iaginary sectin r sectins thrugh the structure-fundatin interface and/r alng a sectin r sectins within the rck fundatin. These three prcedure are (1) a prescribed uplift distributin as given, fr exaple, in an engineering anual specific t the particular hydraulic structure; (2) uplifl pressures cputed fr flw within rck jints; r (3) flw-net-cputed uplift pressures. Purpse This technical nte presents the results f a study invlving twdiensinal (2-D), steady-state flw thrugh a pereable rck fundatin. The results shw the ipact f hgeneus, anistrpic pereabilities (i.e., KX # Ky) and the ipact f base separatin n the uplift pressures alng the base f a rck-funded retaining nlith. Steady-State Seepage Analysis Tday, analytical tls such as the finite-eleent ethd (FEM) are available t cpute the distributin f heads and flw within pereable fundatins. Mst prbles invlve the analysis f steady-state seepage given prble-specific geetry and bundary cnditins. An FEM del f twr threediensinal steady-state seepage can cnsider hgeneus r hetergeneus regins cprising the flw regie as well as istrpic r anistrpic pereability within each f these regins. The Windws versin f Cncrete and Steel Applicatins
SUPP[ 7 (1996) the Crps FE seepage prgra (X822 in the CORPS Library) called FASTSEEP (Engineering Cputer Graphics Labratry used in this analytical investigatin f 2-D steady-state seepage. (Tracy 1983), 1993), was Seepage Prble Analyzed The case f a cncrete gravity lck retaining wall funded n pereable rck was used in this study. Figure 1 shws the cncrete nlith t be 82.7 ft high and 45 ft wide. This nlith has a base-t-height rati f.54, which is within the range (.33 t.7) that is typical fr gravity earthretaining nliths (Ebeling et al. 1992). This particular nlith was chsen fr further study because its geetry (e.g., base-t-height rati) is typical f gravity retaining nliths and because this nlith has been extensively analyzed in the REMR Research Prgra fr separatin alng the base f the nlith under extree lading. The nlith was analyzed by eans f (1) the cnventinal equilibriu ethd f analysis as well as the FEM with three different crack/crack prpagatin dels; (2) a base separatin analysis with the use f interface eleents; (3) a base separatin analysis with the seared crack apprach; and (4) a linear elastic fracture echanics discrete crack analysis. n the case f the extree lading (e.g., n lck pl) and a cnservative assignent f aterial prperties, all fur analytical prcedures shwed that as uch as 5 percent f the base f the nlith ay separate hrn its rck fundatin alng their interface. All nine seepage analyses assued that the nlith was ipereable and that the pereable fundatin was hgeneus. N drainage was included within the fundatin in these prbles. A typical set f diensins is shwn in Figure 1, alng with a suary f the paraeters that were varied in the nine seepage analyses. Three cases f nlith-t-fundatin cntacts were cnsidered: (1) fill cntact alng the interface (BJB = 1 percent), (2) an interediate case f three-quarters cntact alng the interface (B&B = 75 percent), and (3) the extree case f nly half f the nlith in cntact with the fundatin (13JB = 5 percent). Fr each case, three sets f fundatin pereabilities (KX = KY, KX = 1KY,and KX = KY/1) were cnsidered. Flw Nets fr Anistrpic Pereabilities with Full Cntact Alng the nterface Figures 2 thrugh 4 shw the steady-state flw nets fr the pereable fundatin with KX= KY, KX= 1KY,and KX= KY/l, respectively, fr a nlith in full cntact with the rck fundatin (BJB = 1 percent). The water table in the backfill is assued t be at elevatin (cl) 396 ft, and the head in frnt f the nlith is assued t be at el 34 ft. 2 Cncrete and Steel Applicatins
SUPP 7 (1 996) A cparisn f the flw net in Figure 3 fr KX = 1O$ with that shwn in Figure 2 fr KX = $h s ws that alng any given flw le belw the nlith, there is less f a change in elevatin between flw channels than that fr the istrpic case (Figure 2). That is t say, the re pereable hrizntal directin rients the flw channels in a re hrizntal directin. The cnverse is true when the flw net in Figure 4 fr KX = K+1O is cpared with that shwn in Figure 2. n this case, the re pereable vertical directin rients the flw channels in a re vertical directin. Flw Nets fr strpic Pereabilities with Partial Cntact Alng the nterface Figures 2, 5, and 6 shw the steady-state flw nets fr the case f istrpic pereability (KX = KY)and 1, 75, and 5 percent, respectively, f nlith-t-rck base cntact. n all analyses f nliths with partial cntact (i.e., a crack extending fr the heel), full hydrstatic water pressures within the backfill (crrespnding t a water table at el 396 ft) were assigned alng the cracked prtin f the interface. Cparisn f the three figures shws that the syetry f the flw channels is preserved abut a vertical line lcated idway between the te and the crack tip (which is the heel in Figure 2). Uplift Pressures Alng the nterface The distributins f uplift pressures alng the nlith-t-rck interface are shwn in Figures 7, 8, and 9 fr BJB = 1 percent (i.e., full cntact), 75 percent, and 5 percent, respectively. Each figure shws the resulting uplift distributin fr the cases f KX= KY, KX= 1KY,and KX= KY/1. The linear uplift distributins crrespnding t flw cnfined alng the interface (i.e., nediensinal (1-D) flw) are als included in these figures. The three figures shw fur iprtant results. First, 2-D seepage within the istrpic fundatin alters the resulting distributin f uplift pressures when cpared t uplift pressures resulting fr 1-D flw. Secnd, the distributins f uplift pressures fr the three ratis f pereabilities are nearly the sae. Third, the distributins f uplift pressures fr the 2-D analyses are antisyetric t the distributin f uplift pressures fr 1-D flw abut a pint idway between the tip f the crack and the te f the wall. Finally, the pint f antisyetry is aintained idway between the crack tip and the te fr all crack lengths. The resultant uplift frce, equal t the area under each f the uplitl pressure distributins, is the sae value fr each f the fur analyses shwn in Figure 7. This is als the case fr the results shwn in Figures 8 and 9. The resulting frce fr the linear uplift pressure distributin in Figure 7 (l-d flw) acts at a pint alng the interface that is tw-thirds the distance Cncrete and Steel Applicatins 3
SUPP 7 (1996) fr the te t the heel, acting at a pint 3 ft fr the te (B. = B = 45 ft). The resultant uplift frces cputed fr the results f the ther three 2-D analyses shwn in Figure 7 act at pints that are between 4 and 5 percent clser t the te f the wall than the pints fr the linear uplifi distributin. This difference is even less fr the results shwn in Figures 8 and 9. Cnclusins The principal results f this study are as fllws: a. b. c. Anistrpic pereabilities (i.e., KX # KY)rient the flw channel in the directin f larger pereabilities. Tlus effect is bserved in the resulting 2-D steady-state seepage flw net. Given a prescribed crack length, the agnitude f the resulting uplift frce is equivalent fr the 1-D analysis t the uplift frces cputed fr the three 2-D analyses (KX = KY, KX = 1O$, and KX = KY/lO). The distributins f uplift pressure alng the nlith-t-rck interface calculated using 2-D FE seepage analyses are siilar but nt exactly equivalent t the distributin fr 1-D seepage analyses. Even thugh the resultant uplift frces are equal in agnitude differences in the distributins f uplift pressures between the tw analyses result in the uplift frces acting at different pints alng the interface. The authrs cautin against aking generalities based n the results f this study t re cplicated seepage prbles. They attribute any f the siilarities in the previusly stated 1- and 2-D study results t the fllwing features f the nine idealized prbles: The distance fr the te f the nlith t the left extent f the finiteeleent esh (i.e., a lcatin f a flw r head bundary cnditin) was large and equal t the distance fr the heel t the right extent f the esh (anther flw r head bundary cnditin). The base f the nlith was parallel t the priary flw channels in all fur seepage analyses The pereable fundatin was deled as hgeneus The priary flw channel iediately belw the nlith was nearly hrizntal as was the rck-t-nlith interface. N drainage features were included in the fundatin. Cncrete and Steel Applicatins
SUPP 7 (1996) Any ne f these factrs will ipact the cnclusins stated previusly and will cntribute t larger differences in the results between the different types f seepage analyses when cpared t the results f this study. References Ebeling, R. M., Clugh, G.W., Duncan, J. M., and Brandn, T.L. 1992. Methds f evaluating the stability and safety f gravity earth retaining structures funded n rck, Technical Reprt REMR-CS-29, U.S. Ary Engineer Waterways Experient Statin, Vicksburg, MS. Engineering Cputer Graphics Labratry. 1993. FASTSEEp. Brigha Yung University, Prv, UT. Tracy, F.T. 1983. User s guide fr a plane and axisyrnetric finite eleent prgra fr steady-state seepage prbles, nstructin Reprt K-83-4, U.S. Ary Engineer Waterways Experient Statin, Vicksburg, MS. Acknwledgents The fllwing WES Research Tea Mebers are acknwledged fr their cntributins t this prject: Dr. Rbert M. Ebeling and Mr. Michael E. Pace. Pint f Cntact Nae: Dr. Rbert M. Ebeling Phne N.: (61) 634-3458 Address: Directr U.S. Ary Engineer Waterways Experient Statin ATTN: CEWES-M-D/Dr. Rbert M. Ebeling 399 Halls Ferry Rad Vicksburg, MS 3918-6199 Cncrete and Steel Applicatins
RENR TN CS-ES-4.6 %PP[ 7 (1996) r=- : d- d c G.x n Y? Y?.-4 @ l Yx d i-) t ii-l d- d x Y -1 Y?.\ 4 ~~ ii 6 Cncrete and Steel Applicatins
.x /\ REMR TN CS-ES-4.6 SUPP 7 (1996) h (-u (u i-7 d- h R- (-r L L1 Cncrete and Steel Applicatins 7
SUPP[ 7 (1996) d ih l (u /. Yx (% d d Cncrete and Steel Applicatins
).4 ~.... 4 Be_ ~7. ~.. B.. 4 Fund ~tin: Kx = $ Ky i% u r-i+--- -- - -.- --- -- 1 *. EL 422.7 = EL 396 225 1 ( 145 igure 4. Results f Be/B = 1 percent, Kx = ~ KY
SU@ 7 (1 996) (-u 7 t- 3 4 x Yx Ll- Y 1, 1 Cncrete and Steel Applicatins
~r - i-) (u l REMR TN CS-ES-4.6 Suppi 7 (1 996).\~ -K! \ (WQ l.j- Yx i Cncrete and Steel Applicatins 11
SUPP[ 7 (1996) :., 1 t 1 1 : Ln aj c-) 1- E G R w 12 Cncrete and Steel Applicatins
L REMR TN CS-ES-4.6 S(JPP 7 (1996) u-) -c : -l_ + U) 1 1 l : Ln r- w u-) * 1 U-1 T -+ u-) u-) (-u E u-) r--l aj t- Cncrete and Steel Applicatins 13
SUPP[ 7 (1996) c u c -i- U-1 T E u-) (u f) 1 E E (-u u E E k- 14 Cncrete and Steel Applicatins