APPROXIMATE FRACTURE

1 PROJECT:PREPARED BY:SHEET:DATE:REDI-ROCK INTERNATIONAL1 / 7 BARRIER WALLS WITH REDI-ROCK RETAINING HOLLOW CORE (R-41HC) BLOCKS,FREESTANDING HOLLOW CORE (F-HC) BLOCKS, AND CAST-IN-PLACE CONCRETE INFILLWERE CONSTRUCTED AND TESTED AT THE ASTER BRANDS TEST LAB IN CHARLEVOIX,MICHIGAN. COMPLETE DETAILS ARE PROVIDED IN TEST REPORTS AVAILABLE ON THEWEBSITE, VIEW OF TESTFRONT VIEW OF TESTAPPROXIMATELIMITS OFFRACTUREREDI-ROCK R-41HC AND F-HC BARRIER WALLAPRIL 15, 2021 PROJECT:PREPARED BY:SHEET:DATE:LOADBARRIER WALL STEM(F-HC BLOCKS WITHCAST-IN-PLACECONCRETE INFILL) "14"#6 BENT BARTYPICAL, (3) BARSEVERY 46 18"#6 STRAIGHT BARSTYP., (4) BARS EVERY 46 18"BAR ROTATEDAS SHOWNR-41HC BLOCK WITHSTONE INFILLR-41HC BLOCK WITHCIP CONCRETE INFILL#6 ( mm) STRAIGHT BARDOES NOT EXTENDINTO R-41HC BLOCKAVERAGE EDGE OFPRECAST BLOCK / CIPCONCRETE7"CROSS-SECTIONTOP VIEW(1 BLOCK LENGTH OFWALL SHOWN)#6 ( mm) BARSCONTINUOUS ALONG WALLSPACED 18" (457 mm)VERTICALLYREDI-ROCK INTERNATIONAL2 / 7 COMPRESSIVE STRENGTH OFCAST-IN-PLACE CONCRETEINFILL AT TIME OF TEST,f 'c = 3,779 psiALL STEEL REBAR WASA615 GR 60/AASHTO M31,fy = 60 ksiREDI-ROCK R-41HC AND F-HC BARRIER WALLAPRIL 15, "10"10"6"4"PROJECT:PREPARED BY:SHEET:DATE.

2 REDI-ROCK INTERNATIONAL3 / 7 DETERMINE Mc (FLEXURAL RESISTANCE OF THE STEM WALL ABOUT AN AXISPARALLEL TO THE LONGITUDINAL AXIS OF THE BARRIER)TO DETERMINE Mc, THE NOMINAL FLEXURAL STRENGTH OF THE STEM WALL IS CALCULATEDAT THE BASE OF THE STEM, WHICH IS LOCATED AT THE JOINT BETWEEN THE TOP ROW OFRETAINING HOLLOW CORE (R-41HC) BLOCKS AND THE BOTTOM ROW OF FREESTANDINGHOLLOW CORE (F-HC) BLOCKS. STRENGTH IS CONSIDERED TO BE PROVIDED BY THECAST-IN-PLACE CONCRETE CORE WITH NO CONTRIBUTION FROM THE TEXTURED FACEPANELS OF THE FREESTANDING HOLLOW CORE (F-HC) CAPACITY OF THE BARRIER CAN BE CALCULATED BY THE YIELD LINE PROCEDUREDETAILED IN AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS, NINTH EDITION, 2020,APPENDIX A13, - CONCRETE REINFORCEMENT IS PROVIDED BY (3) #6 BENT BARS EVERY 46 18" OF WALL (LENGTHOF A REDI-ROCK BLOCK).

3 A 4TH #6 STRAIGHT BAR WAS CAST INTO THE CORE BUT DID NOTEXTEND ACROSS THE JOINT AT THE BASE OF THE STEM AND DOES NOT CONTRIBUTE TO = inAs = 3 x = in2d = ina = HT OF THE COMPRESSIVE BLOCK =As f 'c b= x 60, x 3,779 x inb = inad = inMc = As fy (d - a/2) = x 60,000 x ( - ) = 533,232 lb * in / inMc = 11,560 lb * ft / ft = kip * ft / ftOUTSIDE EDGE OF F-HC BLOCKCAST-IN-PLACE CONCRETE CORE(f 'c = 3,779 psi)A SIMPLIFIED SKETCH OF A (1) BLOCK LONG SECTION OF WALL FOR ANALYSIS IS AS SHOWN:LAB TESTING PRODUCED LOADS OF 18,574 AND 17,978 lb, WHICH CORRESPONDTO FLEXURAL STRENGTHS (Mc) OF AND kip * ft / ft FOR A (1) BLOCKLONG SECTION.

4 REFER TO OUR PHASE 1 BARRIER TEST R-41HC AND F-HC BARRIER WALLAPRIL 15, 2021 PROJECT:PREPARED BY:SHEET:DATE:REDI-ROCK INTERNATIONAL4 / 7 DETERMINE Mw (FLEXURAL RESISTANCE OF THE STEM WALL ABOUT ITS VERTICAL AXIS)TO CALCULATE Mw, THE NOMINAL FLEXURAL STRENGTH OF THE STEM WALL PARALLEL TOTHE BARRIER IS CALCULATED. STRENGTH IS CONSIDERED TO BE PROVIDED BY THECAST-IN-PLACE CONCRETE CORE WITH NO CONTRIBUTION FROM THE TEXTURED FACEPANELS OF THE FREESTANDING HOLLOW CORE (F-HC) REINFORCEMENT IS PROVIDED BY (2) #6 BARS THAT ARE CONTINUOUS ALONG THELENGTH OF THE BARRIER = 36 inAs = 2 x = in2d = ina = HT OF THE COMPRESSIVE BLOCK =As f 'c b= x 60, x 3,779 x 36= inMw = As fy (d - a/2) = x 60,000 x ( - )A SIMPLIFIED SKETCH OF THE WALL CROSS SECTION FOR ANALYSIS IS AS SHOWN.

5 LAB TESTING PRODUCED FIRST YIELD AT LOADS OF 14,402 AND 12,772 lb,WHICH CORRESPONDS TO FLEXURAL STRENGTHS (Mw)OF AND kip * WALL WAS TESTED IN AN UPRIGHT POSITION. IF FRICTION ISCONSIDERED BETWEEN THE TEST SUPPORTS AND THE WALL (ASSUMEDm = ) AND FRICTION LOADS ARE SUBTRACTED FROM THE MEASUREDLOADS, FLEXURAL STRENGTHS AT FIRST YIELD WOULD BE AND kip * TO OUR PHASE 2 BARRIER TEST CONCRETE CORE (f 'c = 3,779 psi)b = 36 inad = in= 315,306 lb * in = 26,275 lb * ft = kip * ftREDI-ROCK R-41HC AND F-HC BARRIER WALLAPRIL 15, 2021 PROJECT:PREPARED BY:SHEET:DATE:REDI-ROCK INTERNATIONAL5 / 7 DETERMINE Lc (CRITICAL LENGTH OF YIELD LINE FAILURE PATTERN)Lc CAN BE CALCULATED WITH AASHTO EQUATION AS FOLLOWS.

6 LAB TESTING PRODUCED WAS PERFORMED ON (2) FULL SIZE CRITICAL LENGTH OF THE YIELD LINE FAILURE IN BOTH TESTS WASAPPROXIMATELY 8 ft. THE MEASURED FAILURE LOADS WERE AND TO OUR PHASE 3 BARRIER TEST HEIGHT OF BARRIER = 3 ftLt = LENGTH OF DISTRIBUTION OF FORCE = ft (FROM TEST)Mb = FLEXURAL RESISTANCE OF A BEAM AT THE TOP OF THE WALL (IF ANY) = 0 kip * ftMc = FLEXURAL RESISTANCE OF THE STEM WALL ABOUT AN AXIS PARALLEL TO THELONGITUDINAL AXIS OF THE BARRIER = kip * ft / ft (CALCULATED)Mw = FLEXURAL RESISTANCE OF THE STEM WALL ABOUT ITS VERTICAL AXIS= kip * ft (CALCULATED)Lc =DETERMINE Rw (TOTAL TRANSVERSE RESISTANCE OF THE RAILING)Rw CAN BE CALCULATED WITH AASHTO EQUATION AS FOLLOWS.

7 Lt2Lt228H(Mb + Mw)McLc= * 3(0 + ) ftRw =22 Lc - Lt8 Mb + 8 Mw +Mc LcH2Rw =22 * - * 0 + 8 * + * = kipsREDI-ROCK R-41HC AND F-HC BARRIER WALLAPRIL 15, 2021 PROJECT:PREPARED BY:SHEET:DATE:REDI-ROCK INTERNATIONAL6 / 7 EVALUTATE OVERTURNING10,000 lb(EQUIV. STATIC LOAD)REDI-ROCK R-41HC AND F-HC BARRIER WALLAPRIL 15, 2021 OVERTURNING REISTANCE PROVIDED BY (1)R-41HC BLOCK AND (2) F-HC BLOCKS WITHINTERNAL CORES AND SPACE BETWEEENADJACENT RETAINING BLOCKS FILLED SECTION WAS DRAWN IN ARE AS FOLLOWS:VOLUME OF CONCRETE = cft / ftWEIGHT = 145 x = 1,435 lb / ftDISTANCE FACE OF BLOCK TO CG OF BARRIER = inOVERTURNING RESISTANCE,MR = W x d = 1,435 x = 1,973 lb * ft / ftPER NCHRP 663 DESIGN OF ROADSIDE BARRIER SYSTEMS ON MSE RETAINING WALLS,A 10,000 lb EQUIVALENT STATIC LOAD IS USED TO SIZE THE STRUCTURE FOROVERTURNING MOMENT FOR AN IMPACT AT THE TOP OF THE BARRIER CAN BECALCULATED AS FOLLOWS.

8 MO = 10,000 x (54) / 12 = 45,000 lb * ftSETTING OVERTURNING RESISTANCE EQUAL TO OVERTURNING MOMENT TIMES AFACTOR OF SAFETY, THE MINIMUM LENGTH OF BARRIER CAN BE MR = g x (1,973 x LENGTH) = x 45,000 LENGTH = ft = BLOCKSA BARRIER WALL CONSTRUCTED WITH JOINT WIDTHS AT LEAST 7 BLOCKS APARTHAS THE CAPACITY TO RESIST OVERTURNING PRODUCED BY A 10,000 lbEQUIVALENT STATIC LOAD WITH A RESISTANCE FACTOR OF "54"PROJECT:PREPARED BY:SHEET:DATE:REDI-ROCK R-41HC AND F-HC BARRIER WALLREDI-ROCK INTERNATIONAL7 / 7 APRIL 15, 2021 SUMMARYCALCULATED YIELD LINE FAILURE PATTERNS AND TRANSVERSE RESISTANCE OFBARRIER WALLS WITH REDI-ROCK RETAINING HOLLOW CORE (R-41HC) BLOCKS,FREESTANDING HOLLOW CORE (F-HC)

9 BLOCKS, AND CAST-IN-PLACE CONCRETE INFILLCLOSELY MATCH VALUES MEASURED IN FULL SCALE LAB ON THE VALIDATED STRENGTH CALCULATIONS, A BARRIER WALLCONSTRUCTED ACCORDING TO THE SAME DETAILS IS CAPABLE OF RESISTING ANAASHTO TEST LEVEL TL-4 DESIGN FORCE OF BARRIER SHOULD EXTEND AT LEAST 2 BLOCKS BEYOND THE REQUIRED ZONE TOPREVENT THE STRENGTH REDUCTION AT THE END OF A WALL FROM CONTROLLINGPERFORMANCE OF THE VEHICLE PERFORMANCE IMPACT TESTING WAS COMPLETED. NO ATTEMPT WASMADE TO CONSIDER BARRIER SHAPE OR FACE TEXTURE. THIS BARRIER SHOULD ONLYBE USED IN LOW SPEED APPLICATIONS, OR IN APPLICATIONS WHERE IT WILL NOT BESUBJECT TO DIRECT IMPACTS FROM HIGH SPEED TRAFFIC, SUCH AS BEHIND A CURBOR SIDEWALK.