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CDP 2019-0032; TELESCOPE HOUSE; RETAINING WALL STRUCTURAL CALCULATIONS; 2023-05-05
Damascene Structural Engineering STRUCTURAL CALCULATIONS FOR LANDSCAPE IMPROVMENTS POJECT ADDRESS: 4615 Telescope Ave, Carlsbad, CA 92008 PROJECT NUMBER: 2023-84 PRINT DATE: 05/05/2023 CONTENTS: 1- Plan .................................................. Page (1). 2- Retaining Wall Design..................... Pages (2-11). LICENSE D P R O F E SS IONAL E N G I N E E R S TATE OF CA L I F O R NIACIVIL EXP. 12/31/23 C 93049 THESE PLANS/DOCUMENTS HAVE BEENREVIEWED FOR COMPLIANCE WITH THEAPPLICABLE CALIFORNIA BUILDING STANDARDSCODES AS ADOPTED BY THE STATE OFCALIFORNIA AND AMENDED BY THEJURISDICTION. PLAN REVIEW ACCEPTANCE OFDOCUMENTS DOES NOT AUTHORIZECONSTRUCTION TO PROCEED IN VIOLATION OFANY FEDERAL, STATE, NOR LOCAL REGULATION.BY: _________________ DATE: ________________ True North Compliance Services, Inc. THIS SET OF THE PLANS AND SPECIFICATIONSMUST BE KEPT ON THE JOB SITE AT ALL TIMESAND IT IS UNLAWFUL TO MAKE ANY CHANGESOR ALTERATIONS WITHOUT PERMISSION FROMTHE CITY. OCCUPANCY OF STRUCTURE(S) ISNOT PERMITTED UNTIL FINAL APPROVAL ISGRANTED BY ALL APPLICABLE DEPARTMENTS. Ali Al-Murshid 01/25/24 1 of 1 1 SCOPE OF WORK DIAMOND® 9D RETAINING WALL SYSTEM 3'-0" MAXIMUM HEIGHT (SEE SHEET S0-1) I I i I i I i I i I i ! r---x--- 1 I I 1-- ! fil ] 11 i I I I I T, I I ! I (_ ! ~Z.:::_;':::::;!._.:::_,--.,-._ ,-,.-<-.._,_,..._ __ =-,.,__ 1 7'r--,;--'--•--, • I ' --., ~•-~~•-, --80--_---so.__~= 1' : I I I 1 ' I L:,..__-.,..__ 4615 Telescope Ave, Carlsbad, CA 92008 SITE PLAN -----------2----ll!la,, -:-·-·-,-·-·-'ctt!fl 1 -ix ;.:=----,' )( ~·;; I / p----ft--1-!..__~ r ,,,,.,, , ,1' ,/ I / I ,/ I / I /' I ~---------~ \ / --\ /. \, / --sni.--:, .. \_ .,, I I I I I I I I I I I I I ___ J _____ ---~ i: I ---------.::. ----'-----x ~ I ~~ -so, <J ~ <J SCOPE OF WORK: <J THE SCOPE OF WORK IS ONLY THE 3'-0" MAX HEIGHT GABION RETAINING WALL, ALL OTHER SITE ELEMENTS ARE EXISTING ANO TO REMAIN ANO OUT OF DAMASCENE STRUCTURAL ENGINEERING, INC SCOPE OF WORK sllfa Damascene Structural Engineering Address: 7812 Vassar Avenue Canoga Park, CA 91304 Phone: (661) 803-7837, (661) 522-2262 E-mail: contact@damasoeng.oom Website: www.damasceng.com ALL IDEAS, DESIGNS, ARRANGEMENTS ANO PLANS INDICATED OR REPRESENTED BY THIS DRAWING ARE OWNED BY ANO PROPERTY OF DAMASCENE STRUCTURAL ENGINEERING AND WERE CREATED, EVOLVED AND DEVELOPED FOR USE ON AND IN CONNECTION WITH THE SPECIFIED PROJECT. NONE OF SUCH IDEAS, DESIGNS, ARRANGEMENTS.OR PLANS SHALL BE USED BY OR DISCLOSED TO ANYPERSON, FIRM OR CORPORATION FOR ANY PURPOSE WHATSOEVER WITHOUT THE WRITTEN PERMISSION OF DAMASCENE STRUCTURAL ENGINEERING. No. Description 4615 Telescope Ave, Carlsbad, CA 92008 LANDSCAPE IMPROVEMENTS SITE PLAN Date Project Number: 2023-84 Date: May 05, 2023 Drawn By: M.B. Checked By: M.M. S-1 Scale: ¾s=1·-o· Project 4615 Telescope Ave,Carlsbad, CA 92008 Job Ref. 2023-84 Section Sheet no./rev. 1 Calc. by B.J. Date 5/5/2023 Chk'd by Date App'd by M.M. Date 5/5/2023 GABION RETAINING WALL ANLYSIS & DESIGN In accordance with ASCE Tedds calculation version 2.0.02 Design summary Combination 1 Action Resistance Force FoS Allowable FoS Status Overturning, sliding and bearing at base level Overturning (kips_ft/ft) 0.2 0.1 1.825 1.500 PASS Sliding (kips/ft) 0.2 0.1 1.804 1.500 PASS Bearing (ksi)3.0 1.0 3.130 1.000 PASS Eccentricity (ft) Reaction acts within the middle third of base PASS Overturning and sliding between courses 1 and 2 Overturning (kips_ft/ft) 0.2 0.1 2.412 1.500 PASS Sliding (kips/ft) 0.2 0.1 2.585 1.500 PASS Overturning and sliding between courses 2 and 3 Overturning (kips_ft/ft) 0.1 0.0 3.430 1.500 PASS Sliding (kips/ft) 0.2 0.1 3.203 1.500 PASS Overturning and sliding between courses 3 and 4 Overturning (kips_ft/ft) 0.1 0.0 5.502 1.500 PASS Sliding (kips/ft) 0.1 0.0 4.291 1.500 PASS Overturning and sliding between courses 4 and 5 Overturning (kips_ft/ft) 0.1 0.0 11.131 1.500 PASS Sliding (kips/ft) 0.1 0.0 6.726 1.500 PASS Overturning and sliding between courses 5 and 6 Overturning (kips_ft/ft) 0.0 0.0 41.882 1.500 PASS Sliding (kips/ft) 0.0 0.0 17.163 1.500 PASS 2 of 11 mlUm Damucene Stnlctul'III Englneertng 7812 Vassar Ave, Canoga Park, CA 91304 I I I I Phone: +1(661) 803-7837 Project 4615 Telescope Ave,Carlsbad, CA 92008 Job Ref. 2023-84 Section Sheet no./rev. 2 Calc. by B.J. Date 5/5/2023 Chk'd by Date App'd by M.M. Date 5/5/2023 1 1 - 0.75ft × 0.50ft 2 2 - 0.75ft × 0.50ft 0.08 3 3 - 0.75ft × 0.50ft 0.08 4 4 - 0.75ft × 0.50ft 0.08 5 5 - 0.75ft × 0.50ft 0.08 6 6 - 0.75ft × 0.50ft 0.08 10 2. 9 9 81.10 3. 0 1 Wall geometry Width of gabion 1;w1 = 0.75 ft Height of gabion 1;h1 = 0.50 ft Width of gabion 2;w2 = 0.75 ft Height of gabion 2;h2 = 0.50 ft Step to front face between courses 1 and 2;s2 = 0.08 ft Width of gabion 3;w3 = 0.75 ft Height of gabion 3;h3 = 0.50 ft Step to front face between courses 2 and 3;s3 = 0.08 ft Width of gabion 4;w4 = 0.75 ft Height of gabion 4;h4 = 0.50 ft Step to front face between courses 3 and 4;s4 = 0.08 ft Width of gabion 5;w5 = 0.75 ft Height of gabion 5;h5 = 0.50 ft Step to front face between courses 4 and 5;s5 = 0.08 ft Width of gabion 6;w6 = 0.75 ft Height of gabion 6;h6 = 0.50 ft Step to front face between courses 5 and 6;s6 = 0.08 ft Wall inclination; = 1 deg Gabion properties Unit weight of fill;d = 150.0 pcf Friction between gabions;bg = 35.0 deg Loading Soil properties Slope of retained soil; = 0.0 deg 3 of 11 mlUm Damucene Stnlctural Englneertng 7812 Vassar Ave, Canoga Park, CA 91304 I I I I Phone: +1(661) 803-7837 __ Jr-I ~1 ◄-I I -.i r•-I I I ~ ~-I I I ~ •- ~ I -~ Project 4615 Telescope Ave,Carlsbad, CA 92008 Job Ref. 2023-84 Section Sheet no./rev. 3 Calc. by B.J. Date 5/5/2023 Chk'd by Date App'd by M.M. Date 5/5/2023 Mobilization factor;M = 1.000 Internal angle of friction for retained soil; = 35.0 deg Developed internal angle of friction for retained soil;’ = atan(tan() M) = 35.0 deg Saturated density of retained soil;s = 110 pcf Wall friction angle; = 17.0 deg Base friction angle;b = 30.0 deg Bearing capacity of founding soil;q = 3.0 ksf Wall geometry Horizontal distance to centre of gravity gabion 1;xg1 = w1 / 2 = 0.38 ft Vertical distance to centre of gravity gabion 1;yg1 = h1 / 2 = 0.25 ft Weight of gabion 1;Wg1 = d w1 h1 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 2;xg2 = w2 / 2 + s2 = 0.46 ft Vertical distance to centre of gravity gabion 2;yg2 = h2 / 2 + h1 = 0.75 ft Weight of gabion 2;Wg2 = d w2 h2 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 3;xg3 = w3 / 2 + s2 + s3 = 0.54 ft Vertical distance to centre of gravity gabion 3;yg3 = h3 / 2 + h1 + h2 = 1.25 ft Weight of gabion 3;Wg3 = d w3 h3 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 4;xg4 = w4 / 2 + s2 + s3 + s4 = 0.63 ft Vertical distance to centre of gravity gabion 4;yg4 = h4 / 2 + h1 + h2 + h3 = 1.75 ft Weight of gabion 4;Wg4 = d w4 h4 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 5;xg5 = w5 / 2 + s2 + s3 + s4 + s5 = 0.71 ft Vertical distance to centre of gravity gabion 5;yg5 = h5 / 2 + h1 + h2 + h3 + h4 = 2.25 ft Weight of gabion 5;Wg5 = d w5 h5 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 6;xg6 = w6 / 2 + s2 + s3 + s4 + s5 + s6 = 0.79 ft Vertical distance to centre of gravity gabion 6;yg6 = h6 / 2 + h1 + h2 + h3 + h4 + h5 = 2.75 ft Weight of gabion 6;Wg6 = d w6 h6 = 0.06 kips/ft Weight of entire gabion;Wg = Wg1 + Wg2 + Wg3 + Wg4 + Wg5 + Wg6 = 0.34 kips/ft Horiz distance to centre of gravity entire gabion;xg = ((Wg1 xg1) + (Wg2 xg2) + (Wg3 xg3) + (Wg4 xg4) + (Wg5 xg5) + (Wg6 xg6)) / Wg = 0.58 ft Vert distance to centre of gravity entire gabion;yg = ((Wg1 yg1) + (Wg2 yg2) + (Wg3 yg3) + (Wg4 yg4) + (Wg5 yg5) + (Wg6 yg6)) / Wg = 1.50 ft Correcting for wall inclination horiz dist;Xg = xg cos() + yg sin() = 0.61 ft Vertical change in height due to wall inclination;Hf = yg6 + h6/2 - ((yg6 + h6/2) cos() - (xg6 + w6/2) sin()) = 0.02 ft Design dimensions Effective angle of rear plane of wall; = Atan((w1 - (xg6 + (w6 / 2))) / (yg6 + h6 / 2)) + 90 deg + = 83.1 deg Effective face angle; = Atan((yg6 + (h6 / 2)) / ((xg6 - (w6 / 2)))) - = 81.1 deg Effective height of wall;H = (yg6 + h6 / 2) + (w1 sin()) - Hf + (cos(90 - ) sin( + ) w6) / sin (180 - ( + )) = 3.01 ft Height of wall from toe to front edge of top gabion;Hincl = ((yg6 + h6 / 2) cos() - (xg6 - (w6 / 2)) sin()) = 2.99 ft Active pressure using Coulomb theory;Ka = sin( + ')2 / (sin()2 sin( - ) [1 + [sin(' + ) sin(' - ) / (sin( - ) sin( + ))]]2) = 0.297 Active thrust due to soil;Pa,soil = 0.5 Ka s H2 = 0.1 kips/ft 4 of 11 mlUm Damucene Stnlctul'III Englneertng 7812 Vassar Ave, Canoga Park, CA 91304 I I I I Phone: +1(661) 803-7837 Project 4615 Telescope Ave,Carlsbad, CA 92008 Job Ref. 2023-84 Section Sheet no./rev. 4 Calc. by B.J. Date 5/5/2023 Chk'd by Date App'd by M.M. Date 5/5/2023 Horizontal forces Retained soil;Fsoil_h = Pa,soil cos(90 - + ) = 0.1 kips/ft Height of soil thrust resolved vertically;dh,soil = H / 3 - w1 sin() = 0.99 ft Vertical forces Gabion weight;Fgabion_v = Wg = 0.3 kips/ft Retained soil;Fsoil_v = Pa,soil sin(90 - + ) = 0.1 kips/ft Horizontal dist to where soil thrust acts;bv,soil = w1 cos() - (H / 3) / tan() = 0.63 ft Overturning stability - take moments about the toe Overturning moment;Mo = Fsoil_h dh,soil = 0.1 kips_ft/ft Restoring moment;MR = Fgabion_v Xg + Fsoil_v bv,soil = 0.2 kips_ft/ft Factor of safety;FoSM = MR / Mo = 1.825 Allowable factor of safety;FoSM_allow = 1.500 PASS - Design FOS for overturning exceeds min allowable FOS for overturning Sliding stability - ignore any passive pressure in front of the structure Total horizontal force;T = Fsoil_h = 0.1 kips/ft Total vertical force;N = Fgabion_v + Fsoil_v = 0.4 kips/ft Sliding force;Ff = T cos() - N sin() = 0.1 kips/ft Sliding resistance;FR = (T sin() + N cos()) tan(b) = 0.2 kips/ft Factor of safety;FoSS = FR / Ff = 1.804 Allowable factor of safety;FoSS_allow = 1.500 PASS - Design FOS for sliding exceeds min allowable FOS for sliding Pressure at base Force normal to base;Ns = N cos() + T sin() = 0.4 kips/ft Eccentricity;e = w1 / 2 - (MR - Mo) / Ns = 0.10 ft Reaction acts within middle third of base Pressure at toe;toe = Ns / w1 (1 + (6 e / w1)) = 1.0 ksf Pressure at heel;heel = Ns / w1 (1 - (6 e / w1)) = 0.1 ksf Factor of safety;FoSQ = q / max(toe, heel) = 3.130 Allowable factor of safety;FoSQ_allow = 1.000 PASS - Allowable bearing pressure exceeds max design pressure to base Check overturning and sliding between courses 1 and 2 Wall geometry Horizontal distance to centre of gravity gabion 2;xg2 = w2 / 2 = 0.38 ft Vertical distance to centre of gravity gabion 2;yg2 = h2 / 2 = 0.25 ft Weight of gabion 2;Wg2 = d w2 h2 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 3;xg3 = w3 / 2 + s3 = 0.46 ft Vertical distance to centre of gravity gabion 3;yg3 = h3 / 2 + h2 = 0.75 ft Weight of gabion 3;Wg3 = d w3 h3 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 4;xg4 = w4 / 2 + s3 + s4 = 0.54 ft Vertical distance to centre of gravity gabion 4;yg4 = h4 / 2 + h2 + h3 = 1.25 ft Weight of gabion 4;Wg4 = d w4 h4 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 5;xg5 = w5 / 2 + s3 + s4 + s5 = 0.63 ft 5 of 11 mlUm Damucene Stnlctul'III Englneertng 7812 Vassar Ave, Canoga Park, CA 91304 I I I I Phone: +1(661) 803-7837 Project 4615 Telescope Ave,Carlsbad, CA 92008 Job Ref. 2023-84 Section Sheet no./rev. 5 Calc. by B.J. Date 5/5/2023 Chk'd by Date App'd by M.M. Date 5/5/2023 Vertical distance to centre of gravity gabion 5;yg5 = h5 / 2 + h2 + h3 + h4 = 1.75 ft Weight of gabion 5;Wg5 = d w5 h5 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 6;xg6 = w6 / 2 + s3 + s4 + s5 + s6 = 0.71 ft Vertical distance to centre of gravity gabion 6;yg6 = h6 / 2 + h2 + h3 + h4 + h5 = 2.25 ft Weight of gabion 6;Wg6 = d w6 h6 = 0.06 kips/ft Weight of entire gabion;Wg = Wg2 + Wg3 + Wg4 + Wg5 + Wg6 = 0.28 kips/ft Horiz distance to centre of gravity entire gabion;xg = ((Wg2 xg2) + (Wg3 xg3) + (Wg4 xg4) + (Wg5 xg5) + (Wg6 xg6)) / Wg = 0.54 ft Vert distance to centre of gravity entire gabion;yg = ((Wg2 yg2) + (Wg3 yg3) + (Wg4 yg4) + (Wg5 yg5) + (Wg6 yg6)) / Wg = 1.25 ft Correcting for wall inclination horiz dist;Xg = xg cos() + yg sin() = 0.56 ft Vertical change in height due to wall inclination;Hf = yg6 + h6/2 - ((yg6 + h6/2) cos() - (xg6 + w6/2) sin()) = 0.02 ft Design dimensions Effective angle of rear plane of wall; = Atan((w2 - (xg6 + (w6 / 2))) / (yg6 + h6 / 2)) + 90 deg + = 83.4 deg Effective face angle; = Atan((yg6 + (h6 / 2)) / ((xg6 - (w6 / 2)))) - = 81.4 deg Effective height of wall;H = (yg6 + h6 / 2) + (w2 sin()) - Hf + (cos(90 - ) sin( + ) w6) / sin (180 - ( + )) = 2.51 ft Height of wall from toe to front edge of top gabion;Hincl = ((yg6 + h6 / 2) cos() - (xg6 - (w6 / 2)) sin()) = 2.49 ft Active pressure using Coulomb theory;Ka = sin( + ')2 / (sin()2 sin( - ) [1 + [sin(' + ) sin(' - ) / (sin( - ) sin( + ))]]2) = 0.294 Active thrust due to soil;Pa,soil = 0.5 Ka s H2 = 0.1 kips/ft Horizontal forces Retained soil;Fsoil_h = Pa,soil cos(90 - + ) = 0.1 kips/ft Height of soil thrust resolved vertically;dh,soil = H / 3 - w2 sin() = 0.82 ft Vertical forces Gabion weight;Fgabion_v = Wg = 0.3 kips/ft Retained soil;Fsoil_v = Pa,soil sin(90 - + ) = 0.0 kips/ft Horizontal dist to where soil thrust acts;bv,soil = w2 cos() - (H / 3) / tan() = 0.65 ft Overturning stability - take moments about the toe Overturning moment;Mo = Fsoil_h dh,soil = 0.1 kips_ft/ft Restoring moment;MR = Fgabion_v Xg + Fsoil_v bv,soil = 0.2 kips_ft/ft Factor of safety;FoSM = MR / Mo = 2.412 Allowable factor of safety;FoSM_allow = 1.500 PASS - Design FOS for overturning exceeds min allowable FOS for overturning Sliding stability - ignore any passive pressure in front of the structure Total horizontal force;T = Fsoil_h = 0.1 kips/ft Total vertical force;N = Fgabion_v + Fsoil_v = 0.3 kips/ft Sliding force;Ff = T cos() - N sin() = 0.1 kips/ft Sliding resistance;FR = (T sin() + N cos()) tan(bg) = 0.2 kips/ft Factor of safety;FoSS = FR / Ff = 2.585 Allowable factor of safety;FoSS_allow = 1.500 PASS - Design FOS for sliding exceeds min allowable FOS for sliding 6 of 11 mlUm Damucene Stnlctul'III Englneertng 7812 Vassar Ave, Canoga Park, CA 91304 I I I I Phone: +1(661) 803-7837 Project 4615 Telescope Ave,Carlsbad, CA 92008 Job Ref. 2023-84 Section Sheet no./rev. 6 Calc. by B.J. Date 5/5/2023 Chk'd by Date App'd by M.M. Date 5/5/2023 Check overturning and sliding between courses 2 and 3 Wall geometry Horizontal distance to centre of gravity gabion 3;xg3 = w3 / 2 = 0.38 ft Vertical distance to centre of gravity gabion 3;yg3 = h3 / 2 = 0.25 ft Weight of gabion 3;Wg3 = d w3 h3 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 4;xg4 = w4 / 2 + s4 = 0.46 ft Vertical distance to centre of gravity gabion 4;yg4 = h4 / 2 + h3 = 0.75 ft Weight of gabion 4;Wg4 = d w4 h4 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 5;xg5 = w5 / 2 + s4 + s5 = 0.54 ft Vertical distance to centre of gravity gabion 5;yg5 = h5 / 2 + h3 + h4 = 1.25 ft Weight of gabion 5;Wg5 = d w5 h5 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 6;xg6 = w6 / 2 + s4 + s5 + s6 = 0.63 ft Vertical distance to centre of gravity gabion 6;yg6 = h6 / 2 + h3 + h4 + h5 = 1.75 ft Weight of gabion 6;Wg6 = d w6 h6 = 0.06 kips/ft Weight of entire gabion;Wg = Wg3 + Wg4 + Wg5 + Wg6 = 0.23 kips/ft Horiz distance to centre of gravity entire gabion;xg = ((Wg3 xg3) + (Wg4 xg4) + (Wg5 xg5) + (Wg6 xg6)) / Wg = 0.50 ft Vert distance to centre of gravity entire gabion;yg = ((Wg3 yg3) + (Wg4 yg4) + (Wg5 yg5) + (Wg6 yg6)) / Wg = 1.00 ft Correcting for wall inclination horiz dist;Xg = xg cos() + yg sin() = 0.52 ft Vertical change in height due to wall inclination;Hf = yg6 + h6/2 - ((yg6 + h6/2) cos() - (xg6 + w6/2) sin()) = 0.02 ft Design dimensions Effective angle of rear plane of wall; = Atan((w3 - (xg6 + (w6 / 2))) / (yg6 + h6 / 2)) + 90 deg + = 83.9 deg Effective face angle; = Atan((yg6 + (h6 / 2)) / ((xg6 - (w6 / 2)))) - = 81.9 deg Effective height of wall;H = (yg6 + h6 / 2) + (w3 sin()) - Hf + (cos(90 - ) sin( + ) w6) / sin (180 - ( + )) = 2.01 ft Height of wall from toe to front edge of top gabion;Hincl = ((yg6 + h6 / 2) cos() - (xg6 - (w6 / 2)) sin()) = 2.00 ft Active pressure using Coulomb theory;Ka = sin( + ')2 / (sin()2 sin( - ) [1 + [sin(' + ) sin(' - ) / (sin( - ) sin( + ))]]2) = 0.291 Active thrust due to soil;Pa,soil = 0.5 Ka s H2 = 0.1 kips/ft Horizontal forces Retained soil;Fsoil_h = Pa,soil cos(90 - + ) = 0.1 kips/ft Height of soil thrust resolved vertically;dh,soil = H / 3 - w3 sin() = 0.66 ft Vertical forces Gabion weight;Fgabion_v = Wg = 0.2 kips/ft Retained soil;Fsoil_v = Pa,soil sin(90 - + ) = 0.0 kips/ft Horizontal dist to where soil thrust acts;bv,soil = w3 cos() - (H / 3) / tan() = 0.68 ft Overturning stability - take moments about the toe Overturning moment;Mo = Fsoil_h dh,soil = 0.0 kips_ft/ft Restoring moment;MR = Fgabion_v Xg + Fsoil_v bv,soil = 0.1 kips_ft/ft Factor of safety;FoSM = MR / Mo = 3.430 Allowable factor of safety;FoSM_allow = 1.500 PASS - Design FOS for overturning exceeds min allowable FOS for overturning 7 of 11 mlUm Damucene Stnlctul'III Englneertng 7812 Vassar Ave, Canoga Park, CA 91304 I I I I Phone: +1(661) 803-7837 Project 4615 Telescope Ave,Carlsbad, CA 92008 Job Ref. 2023-84 Section Sheet no./rev. 7 Calc. by B.J. Date 5/5/2023 Chk'd by Date App'd by M.M. Date 5/5/2023 Sliding stability - ignore any passive pressure in front of the structure Total horizontal force;T = Fsoil_h = 0.1 kips/ft Total vertical force;N = Fgabion_v + Fsoil_v = 0.3 kips/ft Sliding force;Ff = T cos() - N sin() = 0.1 kips/ft Sliding resistance;FR = (T sin() + N cos()) tan(bg) = 0.2 kips/ft Factor of safety;FoSS = FR / Ff = 3.203 Allowable factor of safety;FoSS_allow = 1.500 PASS - Design FOS for sliding exceeds min allowable FOS for sliding Check overturning and sliding between courses 3 and 4 Wall geometry Horizontal distance to centre of gravity gabion 4;xg4 = w4 / 2 = 0.38 ft Vertical distance to centre of gravity gabion 4;yg4 = h4 / 2 = 0.25 ft Weight of gabion 4;Wg4 = d w4 h4 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 5;xg5 = w5 / 2 + s5 = 0.46 ft Vertical distance to centre of gravity gabion 5;yg5 = h5 / 2 + h4 = 0.75 ft Weight of gabion 5;Wg5 = d w5 h5 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 6;xg6 = w6 / 2 + s5 + s6 = 0.54 ft Vertical distance to centre of gravity gabion 6;yg6 = h6 / 2 + h4 + h5 = 1.25 ft Weight of gabion 6;Wg6 = d w6 h6 = 0.06 kips/ft Weight of entire gabion;Wg = Wg4 + Wg5 + Wg6 = 0.17 kips/ft Horiz distance to centre of gravity entire gabion;xg = ((Wg4 xg4) + (Wg5 xg5) + (Wg6 xg6)) / Wg = 0.46 ft Vert distance to centre of gravity entire gabion;yg = ((Wg4 yg4) + (Wg5 yg5) + (Wg6 yg6)) / Wg = 0.75 ft Correcting for wall inclination horiz dist;Xg = xg cos() + yg sin() = 0.47 ft Vertical change in height due to wall inclination;Hf = yg6 + h6/2 - ((yg6 + h6/2) cos() - (xg6 + w6/2) sin()) = 0.02 ft Design dimensions Effective angle of rear plane of wall; = Atan((w4 - (xg6 + (w6 / 2))) / (yg6 + h6 / 2)) + 90 deg + = 84.7 deg Effective face angle; = Atan((yg6 + (h6 / 2)) / ((xg6 - (w6 / 2)))) - = 82.7 deg Effective height of wall;H = (yg6 + h6 / 2) + (w4 sin()) - Hf + (cos(90 - ) sin( + ) w6) / sin (180 - ( + )) = 1.51 ft Height of wall from toe to front edge of top gabion;Hincl = ((yg6 + h6 / 2) cos() - (xg6 - (w6 / 2)) sin()) = 1.50 ft Active pressure using Coulomb theory;Ka = sin( + ')2 / (sin()2 sin( - ) [1 + [sin(' + ) sin(' - ) / (sin( - ) sin( + ))]]2) = 0.285 Active thrust due to soil;Pa,soil = 0.5 Ka s H2 = 0.0 kips/ft Horizontal forces Retained soil;Fsoil_h = Pa,soil cos(90 - + ) = 0.0 kips/ft Height of soil thrust resolved vertically;dh,soil = H / 3 - w4 sin() = 0.49 ft Vertical forces Gabion weight;Fgabion_v = Wg = 0.2 kips/ft Retained soil;Fsoil_v = Pa,soil sin(90 - + ) = 0.0 kips/ft Horizontal dist to where soil thrust acts;bv,soil = w4 cos() - (H / 3) / tan() = 0.70 ft 8 of 11 mlUm Damucene Stnlctul'III Englneertng 7812 Vassar Ave, Canoga Park, CA 91304 I I I I Phone: +1(661) 803-7837 Project 4615 Telescope Ave,Carlsbad, CA 92008 Job Ref. 2023-84 Section Sheet no./rev. 8 Calc. by B.J. Date 5/5/2023 Chk'd by Date App'd by M.M. Date 5/5/2023 Overturning stability - take moments about the toe Overturning moment;Mo = Fsoil_h dh,soil = 0.0 kips_ft/ft Restoring moment;MR = Fgabion_v Xg + Fsoil_v bv,soil = 0.1 kips_ft/ft Factor of safety;FoSM = MR / Mo = 5.502 Allowable factor of safety;FoSM_allow = 1.500 PASS - Design FOS for overturning exceeds min allowable FOS for overturning Sliding stability - ignore any passive pressure in front of the structure Total horizontal force;T = Fsoil_h = 0.0 kips/ft Total vertical force;N = Fgabion_v + Fsoil_v = 0.2 kips/ft Sliding force;Ff = T cos() - N sin() = 0.0 kips/ft Sliding resistance;FR = (T sin() + N cos()) tan(bg) = 0.1 kips/ft Factor of safety;FoSS = FR / Ff = 4.291 Allowable factor of safety;FoSS_allow = 1.500 PASS - Design FOS for sliding exceeds min allowable FOS for sliding Check overturning and sliding between courses 4 and 5 Wall geometry Horizontal distance to centre of gravity gabion 5;xg5 = w5 / 2 = 0.38 ft Vertical distance to centre of gravity gabion 5;yg5 = h5 / 2 = 0.25 ft Weight of gabion 5;Wg5 = d w5 h5 = 0.06 kips/ft Horizontal distance to centre of gravity gabion 6;xg6 = w6 / 2 + s6 = 0.46 ft Vertical distance to centre of gravity gabion 6;yg6 = h6 / 2 + h5 = 0.75 ft Weight of gabion 6;Wg6 = d w6 h6 = 0.06 kips/ft Weight of entire gabion;Wg = Wg5 + Wg6 = 0.11 kips/ft Horiz distance to centre of gravity entire gabion;xg = ((Wg5 xg5) + (Wg6 xg6)) / Wg = 0.42 ft Vert distance to centre of gravity entire gabion;yg = ((Wg5 yg5) + (Wg6 yg6)) / Wg = 0.50 ft Correcting for wall inclination horiz dist;Xg = xg cos() + yg sin() = 0.43 ft Vertical change in height due to wall inclination;Hf = yg6 + h6/2 - ((yg6 + h6/2) cos() - (xg6 + w6/2) sin()) = 0.01 ft Design dimensions Effective angle of rear plane of wall; = Atan((w5 - (xg6 + (w6 / 2))) / (yg6 + h6 / 2)) + 90 deg + = 86.2 deg Effective face angle; = Atan((yg6 + (h6 / 2)) / ((xg6 - (w6 / 2)))) - = 84.2 deg Effective height of wall;H = (yg6 + h6 / 2) + (w5 sin()) - Hf + (cos(90 - ) sin( + ) w6) / sin (180 - ( + )) = 1.01 ft Height of wall from toe to front edge of top gabion;Hincl = ((yg6 + h6 / 2) cos() - (xg6 - (w6 / 2)) sin()) = 1.00 ft Active pressure using Coulomb theory;Ka = sin( + ')2 / (sin()2 sin( - ) [1 + [sin(' + ) sin(' - ) / (sin( - ) sin( + ))]]2) = 0.273 Active thrust due to soil;Pa,soil = 0.5 Ka s H2 = 0.0 kips/ft Horizontal forces Retained soil;Fsoil_h = Pa,soil cos(90 - + ) = 0.0 kips/ft Height of soil thrust resolved vertically;dh,soil = H / 3 - w5 sin() = 0.32 ft Vertical forces Gabion weight;Fgabion_v = Wg = 0.1 kips/ft Retained soil;Fsoil_v = Pa,soil sin(90 - + ) = 0.0 kips/ft 9 of 11 mlUm Damucene Stnlctul'III Englneertng 7812 Vassar Ave, Canoga Park, CA 91304 I I I I Phone: +1(661) 803-7837 Project 4615 Telescope Ave,Carlsbad, CA 92008 Job Ref. 2023-84 Section Sheet no./rev. 9 Calc. by B.J. Date 5/5/2023 Chk'd by Date App'd by M.M. Date 5/5/2023 Horizontal dist to where soil thrust acts;bv,soil = w5 cos() - (H / 3) / tan() = 0.73 ft Overturning stability - take moments about the toe Overturning moment;Mo = Fsoil_h dh,soil = 0.0 kips_ft/ft Restoring moment;MR = Fgabion_v Xg + Fsoil_v bv,soil = 0.1 kips_ft/ft Factor of safety;FoSM = MR / Mo = 11.131 Allowable factor of safety;FoSM_allow = 1.500 PASS - Design FOS for overturning exceeds min allowable FOS for overturning Sliding stability - ignore any passive pressure in front of the structure Total horizontal force;T = Fsoil_h = 0.0 kips/ft Total vertical force;N = Fgabion_v + Fsoil_v = 0.1 kips/ft Sliding force;Ff = T cos() - N sin() = 0.0 kips/ft Sliding resistance;FR = (T sin() + N cos()) tan(bg) = 0.1 kips/ft Factor of safety;FoSS = FR / Ff = 6.726 Allowable factor of safety;FoSS_allow = 1.500 PASS - Design FOS for sliding exceeds min allowable FOS for sliding Check overturning and sliding between courses 5 and 6 Wall geometry Horizontal distance to centre of gravity gabion 6;xg6 = w6 / 2 = 0.38 ft Vertical distance to centre of gravity gabion 6;yg6 = h6 / 2 = 0.25 ft Weight of gabion 6;Wg6 = d w6 h6 = 0.06 kips/ft Weight of entire gabion;Wg = Wg6 = 0.06 kips/ft Horiz distance to centre of gravity entire gabion;xg = ((Wg6 xg6)) / Wg = 0.38 ft Vert distance to centre of gravity entire gabion;yg = ((Wg6 yg6)) / Wg = 0.25 ft Correcting for wall inclination horiz dist;Xg = xg cos() + yg sin() = 0.38 ft Vertical change in height due to wall inclination;Hf = yg6 + h6/2 - ((yg6 + h6/2) cos() - (xg6 + w6/2) sin()) = 0.01 ft Design dimensions Effective angle of rear plane of wall; = 90 deg + = 91.0 deg Effective face angle; = 90deg - = 89.0 deg Effective height of wall;H = (yg6 + h6 / 2) + (w6 sin()) - Hf + (cos(90 - ) sin( + ) w6) / sin (180 - ( + )) = 0.51 ft Height of wall from toe to front edge of top gabion;Hincl = ((yg6 + h6 / 2) cos() - (xg6 - (w6 / 2)) sin()) = 0.50 ft Active pressure using Coulomb theory;Ka = sin( + ')2 / (sin()2 sin( - ) [1 + [sin(' + ) sin(' - ) / (sin( - ) sin( + ))]]2) = 0.240 Active thrust due to soil;Pa,soil = 0.5 Ka s H2 = 0.0 kips/ft Horizontal forces Retained soil;Fsoil_h = Pa,soil cos(90 - + ) = 0.0 kips/ft Height of soil thrust resolved vertically;dh,soil = H / 3 - w6 sin() = 0.16 ft Vertical forces Gabion weight;Fgabion_v = Wg = 0.1 kips/ft Retained soil;Fsoil_v = Pa,soil sin(90 - + ) = 0.0 kips/ft Horizontal dist to where soil thrust acts;bv,soil = w6 cos() - (H / 3) / tan() = 0.75 ft 10 of 11 mlUm Damucene Stnlctul'III Englneertng 7812 Vassar Ave, Canoga Park, CA 91304 I I I I Phone: +1(661) 803-7837 Project 4615 Telescope Ave,Carlsbad, CA 92008 Job Ref. 2023-84 Section Sheet no./rev. 10 Calc. by B.J. Date 5/5/2023 Chk'd by Date App'd by M.M. Date 5/5/2023 Overturning stability - take moments about the toe Overturning moment;Mo = Fsoil_h dh,soil = 0.0 kips_ft/ft Restoring moment;MR = Fgabion_v Xg + Fsoil_v bv,soil = 0.0 kips_ft/ft Factor of safety;FoSM = MR / Mo = 41.882 Allowable factor of safety;FoSM_allow = 1.500 PASS - Design FOS for overturning exceeds min allowable FOS for overturning Sliding stability - ignore any passive pressure in front of the structure Total horizontal force;T = Fsoil_h = 0.0 kips/ft Total vertical force;N = Fgabion_v + Fsoil_v = 0.1 kips/ft Sliding force;Ff = T cos() - N sin() = 0.0 kips/ft Sliding resistance;FR = (T sin() + N cos()) tan(bg) = 0.0 kips/ft Factor of safety;FoSS = FR / Ff = 17.163 Allowable factor of safety;FoSS_allow = 1.500 PASS - Design FOS for sliding exceeds min allowable FOS for sliding 11 of 11 mlUm Damucene Stnlctul'III Englneertng 7812 Vassar Ave, Canoga Park, CA 91304 I I I I Phone: +1(661) 803-7837