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REPORT DOCUMENTATION PAGE 2 4 AUG pno. /u fr/dAxpluy Pubkc reporting burden for the cotection of «ilwmation B estmated lo average 1 row per response, nduotog the tm for reviewing ã ga*ermg and inainianngihe data neeo d and Semfcomments regarding S» 1215 Jefferson Davis Highway. Suite 1204. Artngton. VA 22202-«302. and to tneOffice of Management and Budaet Paperwork Reduction Project
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  REPORT   DOCUMENTATION   PAGE   4   UG   pno.   /u fr/dAxpluy   Pubkc   reporting   burden   for the cotection   of   «ilwmation   B   estmated   lo   average   1   row   per   response,   nduotog   the   tm for   reviewing   ã ACDr   C r   r»r   „,   ga*ermg   and inainianngihe   data   neeo>d   and   emfcomments   regarding   S»   ^ r ^ L-oK-BL-TR-00 1215   Jefferson   Davis   Highway.   Suite   1204.   Artngton.   VA   2202-«302.   and   to   tneOffice   of   Management   and   Budaet   Paperwork   Reduction   Project   <07O«)188)   Washington.   DC   0503.   Mnageinen.   aw   Buogfi.   PLEASE   DO   NOT   RETURN   YOUR   FORM   TO   THE   ABOVE   ADDRESS.     REPORT   DATE   (DD-MM-   YYYY)   30-06-1999   4.   ITLE   AND   SUBTITLE   REPORT   DATE   6/30/99   Dynamic   Strength   Enhancement   of   Conventional   Concrete   3.   ATES   UUvcricu   ,,   .„...   Nov.   1   7   ov. 31   5a.   ONTRACT   NUMBER   98   6. AUTHOR(S)   H.D.   Kang,   Y.S.   Roh,   K.J.   Willam   and   Y.   Xi   5b.   GRANT   NUMBER   F49620-98-1-0159   5c   PROGRAM   ELEMENT   NUMBER   5d.   PROJECT   NUMBER   5e.   TASK   NUMBER   7.   ERFORMING   ORGANIZATION   NAME(S)   AND   ADDRESS(ES)   CEAE   Department   CU-Boulder   Boulder,   CO   0309-0428   5f.   WORK   UNIT   NUMBER   9.   PONSORING/MONITORING   AGENCY   NAME(S)   AND   ADDRESS(ES)   US   FOSR   Boiling   ir   orce   ase   Washington,   DC   0332-6448   8.   ERFORMING   ORGANIZATION   REPORT   NUMBER   SESM   esearch   eries   Report   U/SR-99/6   10.   PONSOR/MONITOR'S   ACRONYM(S)   12.   ISTRIBUTION   AVAILABILITY   STATEMENT   Unrestricted 11.   PONSORING/MONITORING   AGENCY   REPORT   NUMBER   13.   UPPLEMENTARY   NOTES   19990927   47   14.   BSTRACT   ~   .   «f   . ♦   ^   K   t0   m ^ estlga * e   the   Performance   of   conventional   concrete   at   different   loading   rates,   experimental   results   LTSl IS^TTAT   T   JeDSi0n   aDd   COmpression   tested   ™ d «   diff «^ oading   speeds.G-mix   specimens   prepared   at   the   Tyndall   Air   Force   Base   were   used   to   determine   the   range   of   loading   rates   of   the   servo-hydraulic   equipment   at   hand   and   to   obtain   expenmental   results   with   a   series   of   indirect   tension   and   uniaxial   compression   tests   ^JlTZü^i°V   ^f eri r ntal   «Nervations,   a   comprehensive   triaxial   concrete   model   was   extended   from   rate   indepen-   dent   elasto-plasticity   to   rate   dependent   vosco-plasticity   using   the   Duvaut-Lions   overstress   formulation.   he   visco-plastic   concrete   mode,   was   adopted   to   exp   ore   the   dynamic   strength   enhancement   in   tension,   compression   and   shear   in   terms   of   a'single   visccSy   foadnJTh   IT T   T   D   C r Tete   thC   failUrC   Pr0PertieS '   ie   hC   triaXiaI   mna ^   Md   the   fail ™ »ode,   depend   not   only   on   the   Z Ü   f   T ° n   t* rate   T ^ at   high   SpeCd   impaCt -   In   this   Paper   » effort   was   undertaken   to   assess   the   diffuse   and   localized   failure   modes   of   the   triaxial   concrete   model   and   its   visco-plastic   extension.   15.   UBJECT   TERMS   Rate Effects of   Concrete   Materials,   Viscoplastic   oncrete   Model,   Dynamic   Strength   Enhancement   in   ension,   Compression   nd   Shear   16.   ECURITY   CLASSIFICATION   OF:   a.   EPORT   b.   BSTRACT   c.   THIS   PAGE   17.   IMITATION   OF   ABSTRACT   18.   UMBER   OF   PAGES   19a.   AME   OF   RESPONSIBLE   PERSON   19b.   ELEPONE   NUMBER   {Include  area code)   ^WWwsr^ Standard   Form   298   Rev.   8-98)   Prescribed   by   ANSI-Std   Z39-18    Dynamic   Strength   Enhancement   of   Conventional   Concrete   Hong   D.   Kang   ,   Young   S.   Roh 2 ,   Kaspar   J.   Willam   3   and   Yunping   Xi 4   Abstract   In   order   to   investigate   the   performance   of   conventional   concrete   at   different   loading   rates,   ex-   perimental   results   of strength   enhancement   were   obtained   under  tension   and   compression   tested   under   different   loading   speeds.   -mix   specimens   prepared   at   the   Tyndall   Air   Force   Base   were   used   to   determine   the   range   of   loading   rates   of   the   servo-hydraulic   equipment   at   hand   and   to   obtain   experimental   results   with   a   series   of   indirect   tension   and   uniaxial   compression   tests.   For   interpretation   of the   experimental   observations,   a   comprehensive   triaxial concrete   model   was   extended   rom   rate   independent   elasto-plasticity   to   rate   dependent   visco-plasticity   using   the   Duvaut-Lions   overstress   formulation.   he   visco-plastic   concrete   model   was   adopted   o   explore   the   dynamic   strength   enhancement   n   ension,   compression   and   shear   n   terms   of   a   single   viscosity   or   rather   relaxation   time.   n   concrete   the   failure   properties,   .e.   he   triaxial   strength   and   the   failure   mode,   depend   not   only   on   the   load   path,   but   also   on   the   loading,   rate   especially   at   high   speed   mpact.   n   this   paper   an   effort   was   undertaken   to   assess   the   diffuse   and   ocalized   failure   modes   of   the   triaxial   concrete   model   and   its   visco-plastic   extension.   Keywords:Duvaut   Lions   visco-plasticity,   Concrete,   Rate   sensitivity,   Dynamic   strength   en-   hancement,   Regularization.   'Post-doctoral   Fellow,   CEAE   Dept.   University   of   Colorado,   Boulder,   CO   309-0428   2 Doctoral   Student,   CEAE   Dept.   University   of   Colorado,   Boulder,   CO   309-0428   3   Professor,   CEAE   Dept.   University   of   Colorado,   Boulder,   CO   80309-0428   assistant   Professor,   CEAE   Dept.   University   of   Colorado,   Boulder,   CO   80309-0428    1   Introduction   Mechanical   oading   initiates   micromechanical   failure   of   concrete   materials   due   o   nterface   debonding   among   the   cement   paste   and   the   aggregate   particles.   hereby,   the   heterogeneous   constituents   of   materials   alter   material   rate   effects   due   o   different   mass   densities.   he   dif-   ferent   failure   mechanisms   of   particle   interaction   and   the   interface   layers   determine   the   surface   roughness   which   may   be   used   as   a   measure   of   fracture   energy   release   during   failure.   s   the   fracture   energy   presumably   remains   constant   when   the   surface   area   of   fracture   zone   does   not   change,   the   strength   enhancement   under   fast   oading   will   be   accompanied   by   increasing   brit-   tleness   unless   the   fracture   surface   area   changes.   The   experimental   exploration   of   the   dynamic   strength   enhancement   in   concrete   materials   is   limited   to   the   loading   range   of the   servo-hydraulic   MTS   testing   systems   in   the   Materials   Lab-   oratory   of   the   University   of   Colorado   at   Boulder   which   is   capable   of   loading   up   to   strain   rate   .   of   e   =   0 -1   at   the   fastest.   Thus   only   a   limited   amount   of   strength   enhancement   is   expected   in   the   experimental   test   program.   hereby   previously   tested   results   collected   by   Bischoff   (1988)   and   Bachmann   1993)   are   used   to   compare   experimental   and   numerical   results   conducted   or   the   project   sponsored   by   AFOSR   under   grant   F   49620-98-1-0159:   Dynamic   Performance   of   Conventional   and   Non-conventional   Concrete'.   To   compare   predictions   of   rate   independent   with   rate   dependent   concrete   behaviors   under   different   loading   rates,   the   triaxial   elasto-plastic concrete   formulation   by   Kang   (1997)   is   adopted   which   has   been   implemented   in   the   3-D   FE   program   FEAP 5 .   A   single   eight   noded   brick   finite   element   is   used   to   study   the   difference   of   viscous   effects   in   uniaxial   tension,   shear   and   uniaxial   compression   assuming   uniform   conditions.   or   shear   loading,   equibiaxial   tension-compression   (T-C)   is   applied   to   evaluate   the   dynamic   strength   enhancement   of   concrete   subject   to   in-plane   shearing   under   plane   stress.   A   literature   survey   shows   that   the   increase   of   strength   in   concrete   materials   is   not   very   significant   for   loading   rates   up   to   e   =   1   x   10 2   (mm/mm/sec).   owever,   for   oading   rates   higher   than   =   x   10 1   (mm/mm/sec),   specially   the   dynamic   strength   enhancement   of   tensile   strength   becomes   very   significant.   2   Experiments   A   eries   of   tests   under   splitting   tension   and   uniaxial   compression   were   performed   on   G-mix   specimens   which   were   prepared   at   the   Tyndall   Air   Force   Base.   ingle-sized   imestone   aggre-   gates   were   sed,   he   diameter   of   which   was   smaller   than   m   3/8   n.).   he   aggregates   were   retained   on   a   #   4   3/16   n.)   ieve.   oncrete   was   mixed   with   more   water   than   he   amount   of   regular   concrete   mix   ratio   o   minimize   air   void.   t   s   ype   Portland   cement,   5 Finite   Element   Analysis   Program   developed   by   R.   Taylor   and   G.   Simo,   University   of   California,   Berkeley    C   S   G   =   3.6   4.6,   /c   =   .0   by   weight,   and   6.1   %   of   type   T'   lyash.   hree   differ-   ent   G-mix   specimens   were   provided:   a)   eight   5cm   x   30cm   6m   x   I2in)   cylinders,   b)   welve   10cm   x   10cm  x   20cm   (4m   x   Ain   x   8in)   prisms,   and   (c)   nine   10cm   x   10cm   x   10cm   (4m   x   4m   x   4m)   cubes.   Axial   deformation   was   measured   by   wo   LVDTs   Linear   Variable   Differential   transducer)   attached   on   both   sides   of   the   specimen   as   depicted   in   Figure   1.   For   compression   testing,   some   grease   was   applied   to   the   oading   surface   i.e.   op   &   bottom)   to   minimize   friction   between   loading   platen   and   specimen.   n   the   case   of   the   indirect   Brazilian   tension   test,   the   test   method   described   in   ASTM   C496   (1996)   was   followed   for   the   cylindrical   specimen   geometry.   n   contrast,   for   ension   testing   on   cubical   specimen,   circular   oading   device   diameter,   0   =   60   mm)   depicted   n   Figure   ,   was   used   according   to   RILEM   recommendation   TC14-CPC   1994).   or   both   splitting   tension   and   compression   tests,   stroke   control   was   used   by   maintaining   constant   stroke   with   various   oading   rates.   uring   the   test,   the   response   behavior   of   vertical   oad   vs.   stroke   was   monitored   and   recorded   by   the   data   acquisition   system.   2.1   ompression   Test   Four cylindrical   and   twelve   prismatic   specimens   were   used   for  uniaxial   compression   testing.   The   moderate   strain   rate   was   e   =   1   x   10~ 3   mm/mm/sec)   and   the   low   strain   rate   was   i   =   x   10~ 6 .   The   irst   cylindrical   specimen   GCR1)   under   uniaxial   compression   was   tested   with   a   wrong   parameter   setup   of the  data  acquisition system,   so   the   compressive   strength,   f ofthat   specimen   underestimates   the   actual   strength   as   shown   in   Table   .   n   contrast,   the   compressive   strength   values   obtained   from   the   prismatic   specimens   were   significantly   higher   than   the   ones   of   the   cylindrical   specimens,   ee   Table   2.   here   was   40   %   difference   n   strengths   which   can   not   be   fully   explained   by   shape   and   ize   of   the   wo   different   geometries.   s   indicated   n   Figure   2,   the   dynamic   strength   enhancement   of   the   cylindrical   specimens   hows   about   5   %   ncrease,   while   the   strength   values   of   the   prismatic   specimens   exhibit   slightly   more   enhancement.   he   stress-strain   responses   of   the   experiments   are   shown   or   various   oading   rates   n   Figures   3   a   and   b).   2.2   ndirect   Splitting   Tension   Test   Four   cylindrical   and   nine   cubical   specimens   were   used   or   indirect   Brazilian   ension   esting.   Figure   4   exhibits   the   relative   ncrease   of   tensile   strength   at   different   oading   rates,   and   Fig-   ures   5   a   and   b)   illustrate   the   nominal   stress   versus   axial   strain   i.e.   stroke   over   the   specimen   height,   D 0 )   of   cubical   and   cylindrical   specimens,   respectively.   he   tensile   strength   of   G-mix   concrete   was   evaluated   by   the   standard   formula   in   Eqn.   1)   based   on   inear   elasticity   Tim-   oshenko   and   Goodier,   970)   considering   the   pecific   geometry   of   the   cylindrical   and   cubical  
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