St. Louis County Masterplan

Transcript

1 St. Louis County Masterplan Stockman Stoneworks, LLC 398 Stockman Lane Jefferson City, MO 6509 (573) Stockmanstoneworks.com

2 Modular Retaining Wall Design VAN DEURZEN AND ASSOCIAES, P.A. December, 04 ii

3 ABLE OF CONENS Page Mayt Rx Retaining Wall Specification... Mayt Rx Modular Retaining Wall Block Properties...5 Raugrid /3-30 Geogrid echnical Information...7 Mayt Rx Retaining Wall Construction Details...9 Preparation for leveling pad...0 Placement of leveling pad and backfill... Placement of first course of modular blocks... Placement of geogrid reinforcement and backfill...3 Mayt Rx Retaining Wall Design Sections...4 Gravity wall...5 Reinforced soil wall...6 iered wall...7 Mayt Rx Retaining Wall -6 all Design Calculations...8 Mayt Rx Retaining Wall -0 all Design Calculations... Mayt Rx Retaining Wall 3-0 all Design Calculations...30 Mayt Rx Retaining Wall 4-0 all Design Calculations...38 Mayt Rx Retaining Wall 5-0 all Design Calculations...46 Mayt Rx Retaining Wall 6-0 all Design Calculations...54 Mayt Rx iered Retaining Wall 3-0 all Design Calculations...6 Mayt Rx iered Retaining Wall 4-0 all Design Calculations...70 iii

4 LIS OF FIGURES Figure Page CS Mayt Rx Modular Block Properties...6 CS Leveling pad preparation...8 CS3 Leveling pad and backfill placement...9 CS4 Placement of first course of modular blocks...0 CS5 Placement of reinforcement and backfill... RW Gravity retaining wall design...3 RW Reinforced soil wall design...4 RW3 iered retaining wall design...5 iv

5 MAY RX REAINING WALL SPECIFICAION

6 MAY RX REAINING WALL SPECIFICAION.0 LIMIAIONS. his specification applies only to: a) "small residential retaining walls" as defined by the St. Louis County, Department of Public Works, b) retaining walls constructed above the water table, c) walls with back slopes less than vertical to 5 horizontal ( degrees from the horizontal), and d) the materials and methods described below.. his specification is appropriate for walls no greater than 6 feet in height and to tiered retaining walls consisting of two walls no greater than 4 feet in height each, for a total of 8 feet measured from the bottom of the lower wall..3 he soil parameters used in the design assume the soils on site are competent materials typically used in foundation construction. Peats, very soft clays, loose fills and other poor materials that cannot be compacted are not acceptable for the foundation soil or backfill..0 MAERIALS. Facing Units are concrete blocks stacked without mortar that form the front of the retaining wall. For walls constructed to heights less than -6 feet, the blocks or facing units, support the soil behind them. For taller walls, geogrid is required in addition to the facing units in order to support the soil. a) he facing units applicable to this design are units having a minimum width of -3/8 inches, a height of 6 inches, and a length of6 inches. b) he facing units shall be: Mayt Rx Retaining Wall Units. Geogrid is a woven polyester grid that is placed in horizontal layers behind the facing units. Sufficient layers of geogrid unify the surrounding backfill to create a stable body. he geogrid shall be Raugrid 3X3N as manufactured by Lückenhaus North America, Inc..3 Backfill is the material placed behind the facing units and over the geogrid. Backfill generally consists of granular material or stiff clay found on site that is free of debris and large rocks ( / inches +). his soil is placed in layers not thicker than 4 inches and compacted by hand tamper or plate compactor..4 Drainage Fill consists of crushed rock or gravel. he drainage fill is placed directly behind the facing units to ensure water does not accumulate behind the facing units..5 he Leveling Pad consists of crushed rock or gravel. he leveling pad is constructed to provide a firm, level surface on which to place the first course of facing units..6 he combination of the facing units, drainage fill, geogrid, and compacted backfill form a rigid body referred to as a gravity retaining wall.

7 3.0 REAINING WALL YPES 3. Cut Wall refers to a retaining wall that is constructed to support an excavation into an existing embankment. 3. Fill Wall refers to a retaining wall that is constructed at the existed ground level and additional soil is filled in behind the wall to form a level surface. 3.3 iered Wall refers to the combination of two retaining walls that provide the required grade separation. wo retaining walls horizontally spaced more than twice the lower wall height apart are considered two independent walls. his specification assumes that the bottom of the upper tier is at the same elevation as the top of the lower tier. 3.4 Gravity Retaining Wall refers to a wall shorter than feet in height and not having any geogrid reinforcement attached. 4.0 CONSRUCION REQUIREMENS 4. Preparation of Ground Surface for Retaining Wall Construction a) he ground surface covering the area of construction shall be prepared prior to construction. b) A minimum excavation 6 inches deep shall be made for the entire length of the wall to remove topsoil, shrubs, trees, or other obstructions. c) If the wall is a cut wall, the excavation depth shall be 6 inches below the bottom of the wall. Caution is required if working in excavations or near vertical embankments greater than 3-0 in height. If the excavation or embankment is unstable it shall be cut back to a 45 degree slope. d) he width of the excavation shall be equal to the width of the facing unit plus inches. If geogrid is required, this excavation must extend behind the wall to the length of the geogrid. e) All debris, such as shrub roots, tree stumps, or construction waste, uncovered during excavation shall be removed. f) Soft, spongy, or organic soil uncovered during excavation shall be cut out and replaced with gravel or crushed rock. 4. Leveling Pad Construction a) he leveling pad shall extend for the entire length of the wall and consist of crushed rock or gravel. b) he width of the leveling pad shall be 6 inches greater than the facing unit width. c) he leveling pad shall have a minimum thickness of 4 inches. d) he material shall be compacted so as to provide a hard and level surface on which to place the first course of facing units. 4.3 Facing Unit Placement a) A string line shall be stretched the length of the wall to assist wall alignment. b) he first course of wall units shall be placed side by side on the leveling pad and shall be checked for level and for full contact with the leveling pad. c) Excess drainage fill shall be swept from top of units before installation of the next course. d) Subsequent courses shall be placed ¾ back from the face of the lower units. e) Place pins through the forward outside holes of the upper course and slide the pin down into the slots of the units below. Each pin should attach to a separate unit below 3

8 the upper course and should be recessed approximately below the top of the upper unit. 4.4 Placement of Drainage Fill a) Drainage fill shall be placed behind the facing units to a minimum width of inches. 4.5 Backfill Placement a) Backfill shall be placed in layers not thicker than 4 inches. b) Compaction of backfill shall be completed by hand tamper, or plate compactor. Only hand operated equipment shall be used within 3 feet of the facing units. 4.6 Geogrid Placement a) Sections of geogrid shall be unrolled and cut to the required length. b) Each geogrid section shall be laid horizontally on the compacted backfill, and laid over the top of the current course of facing units. c) he next course of facing units shall be placed. d) he geogrid shall be pulled taut to eliminate loose folds and the end of the geogrid farthest from the face of the wall shall be staked to keep the geogrid in place during the placement of the next backfill layer. f) he next layer of backfill shall be placed, spread, and compacted in such a manner that minimizes the development of slack or loss of tension of the geogrid. Backfill shall be placed from the face of the wall to the back of the geogrid to insure that the geogrid remains taut. 4

9 MAY RX MODULAR REAINING WALL BLOCK PROPERIES 5

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11 RAUGRID 3X3N GEOGRID ECHNICAL INFORMAION 7

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13 MAY RX REAINING WALL CONSRUCION DEAILS 9

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18 MAY RX REAINING WALL DESIGN SECIONS 4

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22 MAY RX REAINING WALL -6 ALL DESIGN CALCULAIONS 8

23 Gravity Retaining Wall Design Wall Height H.5ft Surcharge q 0psf Block Properties Unit Height Unit Width Unit density Centroid Batter Base Angle H u 6in.375 in γ u 3pcf G u in ω 7.5 deg i b 0deg Connection strength Excess footing length each side a u 50plf λ u 35deg t 4in Soil Properties friction angle unit weight friction angle for foundation soil(leveling pad) ϕ 6deg γ 0pcf ϕ d 40deg cohesion Interface friction angle c 0psf δ i 3 ϕ δ i 7.33 deg backfill inclination masonry friction (NCMA) combined wall inclination β.3deg μ b.7 Ψ ω i b Ψ 7.3deg External Analysis Coulomb Active Earth Pressure Coefficient cos( ϕ Ψ) K a cos( Ψ) cos Ψ δ i sin( ϕ β) cos Ψ β sin ϕ δ i cos Ψ δ i ( ) K a 0.35 Hinge Height G u.5 tani b cos i b H h tanω i b H h 8.5ft H h if H h H H H h H h.5ft Effective Height of Wall H e H cosi b H H u tan( ω) sin i b H e.5ft

24 Horizontal Earth Pressure self weight surcharge P s K aγh e cosδ i Ψ P q qk a H e cosδ i Ψ P s 46.9plf P q 0plf distance from toe distance from toe H e H e Y s sini b Y s 0.5 ft Y q sini b Y q 0.75 ft 3 Resultants P a P s P q P a 46.9plf Weight of Segmental Units W b W b Sliding H h γ u 90.7plf W w W b W w 90.3 plf Resistance from block to soil interaction R s W w cosi b tanϕ d cw u μ b R s.76plf Resistance from soil to soil interaction R s W w cos i b tan( ϕ) cw u cosi b R s 9.8plf Factor Safety for Sliding =.5 R s FS sl FS cosδ i ω sl.38 P a cosδ i Ψ R s FS sl FS sl.98 P a Overturning Overturning Moment M o P s Y s P q Y q M o 3.45 lbf resisting moment arm W w sini b X b G u H h H u tan( ω) H h tani b cos i b X b 0.58 ft

25 resisting moment M r W b X b M r 0lbf Factor of Safety for Overturing =.0 M r FS o FS o 4.69 M o Base Eccentricity block eccentricity cos i b M r M o e e 0.06 ft W w e if( e 0 0 e) e 0.06 ft Effective footing width B f cos i b t e B f.58 ft Applied Bearing Stress W w Q a Q a 0.7 psf B f

26 MAY RX REAINING WALL -0 ALL DESIGN CALCULAIONS

27 Segmental Retaining Wall Design Calculations per NCMA Wall Geometry Height Backslope Dead Load Live Load Distance to Slope Wall below grade at toe H.0 ft β.3 deg q d 0psf q l 0psf Z.0 ft H emb.5ft Soil Properties Reinforced Soil Retained Soil Drainage Fill Foundation Soil Pullout Direct Sliding γ i ϕ i 0 pcf γ r 0 pcf γ d 0 pcf γ f 0 pcf C i.7 C ds.8 6 deg ϕ r 6 deg ϕ d 3 deg ϕ f 6 deg c f 0psf Segmental Unit Properties Height Length Width Setback Center of Gravity Batter Shear Capacity H u 3 6in L u 6 in.375in Δ u 4 in G u 6.875in ω atan Δ u a u 500 lbf λ u 35 deg ft H u Infilled Unit Weight γ u Hinge Height 3 pcf H h G u H h 8.5ft tan( ω) Internal Interface Friction Angle δ i 3 ϕ i δ i 7.333deg Internal Active Earth Pressure ω 7.5 deg V umax 640 plf External Interface Friction Angle δ e if ϕ i ϕ r ϕ r ϕ i δ e 6 deg External Active Earth Pressure cos ϕ i ω cos ϕ r ω Ka i Ka e ( cos ( ω) ) sinϕ cosω δ i i δ i sinϕ i β cos ( ω) sin ϕ cos ω δ e r cos ω ( ) cos ω δ i cos ω β Ka i Ka e δ e sinϕ r β δ e cos ( ω β α i α e Orientation of Critical Internal Failure Surface tanϕ i β cotϕ i ω cotϕ i ω tanϕ i β cotϕ i ω tan ϕ i β tan ϕ i β tan δ i ω atan ϕ i α i 47.83deg tan δ i ω Orientation of Critical External Failure Surface tanϕ r β cotϕ r ω cotϕ r ω tanϕ r β cotϕ r ω tan ϕ r β tan ϕ r β tan δ e ω atan ϕ r α e 45.9deg tan δ e ω

28 Sliding Given External Stability Analysis.5 = min C ds L Ztan( β) tan( ω) C ds q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) L Ztan( β) tan( ω) C ds q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) L Ztan( β) tan( ω) c f L q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) cosδ e ω tan( β) tan( ω) L W q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω tanϕ i tanϕ d tanϕ f L sliding Overturning Given Find( L) L sliding ft.0 = L γ i H ( L Htan( ω) ) γ il ZL q d L L Ztan( β) tan( ω) tan( β) tan( ω) L Ztan( β) tan( ω) tan( β) tan( ω) Z L Z tan( β) Htan( ω) L Ztan( β) tan( ω) tan( β) tan( ω) 3 Z L Htan( ω) Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) tan( ω) tan( β) cosδ e ω 3 H L W L Zta u tan( β) L W q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω H L W L u tan L t L overturning Find( L) L overturning 0.74 L sliding L max L ft L overturning Based on Overturning and Sliding L 4.00ft ft

29 Eccentricity L' L L'.969ft L Ztan( β) tan( ω) L'' L'' 0.05 ft tan( β) tan( ω) L β L L Ztan( β) tan( ω) tan( β) tan( ω) Z L β.09 ft L Z h tan( β) tan( ω) L Z tan( β) tan( ω) tan( β) h ft W r Lγ i H W r 960plf X r ( L Htan( ω) ) X r.5 ft W β γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) W β 47.66plf X β Htan( ω) 3 L β Z X β 3.67 ft Surcharge is applied over Z L β X q Htan( ω) L Ztan( β) tan( ω) L 3.09 ft tan( β) tan( ω) X q.79 ft P s Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) tan( ω) β) cosδ e ω P s 3.95plf Y s 3 H L W L Ztan( β) tan( ω) u Z tan( β) tan( β) tan( ω) Y s 0.80 ft L W P q q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω P q 0plf Y q H L W L Ztan( β) tan( ω) u Z tan( β) tan( ω) tan( β) Y q.0 ft e L P s Y s P q Y q W r X r W L β X β L Ztan( β) tan( ω) L q d L X q tan( β) tan( ω) L Ztan( β) tan( ω) W r W β q d L tan( β) tan( ω) B L e e 0.05 ft B 4. ft L W W r W β q d q l u Ztan( β) tan( ω) L tan( β) tan( ω) q q 39.97psf B

30 Bearing Capacity N q ϕ f tan 45deg exp πtan ϕ f N q.854 N c if ϕ f = 05.4N q cotϕ f N c.54 N γ N q tan ϕ f N γ.539 q u c f N c γ fbn γ γ f H emb N q q u psf FS bearing q u FS bearing 6. q Internal Stability Reinforcement Properties Ultimate Strength Uncertainties Durability Installation Creep Connection Strength ult 055plf FS unc.55 RF d.08 RF id.5 RF cr.67 a cs 500plf λ cs 5deg a ult Allowable Strength a plf V csmax 000plf RF d RF id RF cr FS unc Required Number of reinforcement layers P a Ka iγ i H cosδ i ω q l q d Ka i Hcosδ i ω P a plf N min P a ceil N min a ension in Geogrid Enter Geogrid Elevations from top down E F g.0ft H F g γ i D q l q d Ka i cosδ i ω a dd FS ten F 0ft g plf FS ten Pullout Capacity Anchorage Length La L ( H E) tan 90deg α i ( H E) tan( ω) La.67 ft

31 Average Depth of overburden d E ( H E) tan 90deg d.64 ft Anchorage Capacity AC La AC FS po C i plf dγ i q d α i tanϕ i AC FS po.48 F g La Z Htan( ω) Δ u tan β ( ) Internal Sliding Failure Reduced reinforcement length ΔL 0ft L' s L ΔL L' s.969 ft Length of sloping ground L' s tan( β) tan( ω) L sβ L' s Z L sβ.08 ft tan( β) tan( ω) Height of slope above crest of wall h' L sβ tan( β) h' ft Weight of reduced reinforced area W' r L' s E γ i Weight of wedge beyond reinforced soil zone W' r 356.5plf W' β L sβ h' γ i W' β 48.84plf Friction developed by weight R' s C ds q d L sβ Z W' r W' β tanϕ i R' s 58.06plf Shear capacity of facing elements V u if V umax a u if E H h V u plf Driving Forces H h From retained soil E γ u tanλ u V umax a u if E H h H h From surcharge E γ u tanλ u P s Ka eγ r ( E h' ) cosδ e ω P q q d q l Ka e ( E h' ) cosδ e ω

32 Factor of safety against internal sliding R' s V u FS sl FS sl 9.6 P s P q Local Stability of Facing Units Facing Connection Strength conn if V csmax a cs if E H h H h E γ u tanλ cs V csmax a cs if E H h H h E γ u tanλ cs conn plf FS conn conn FS conn F g Resistance to Bulging Shear capacity at each geogrid layer V u if V umax a u if E H h H h E γ u tanλ u V umax a u if E H h H h E γ u tanλ u V u 589plf Driving Force at each geogrid layer P a Ka iγ i ( E) cosδ i ω P a plf q d q l Ka i ( E) cosδ i ω Sum of tension in reinforcement layers above layer being considered FS sc V u P a FS sc 8.45 Maximum unreinforced height of SRnits Moment equilibrium Driving Moments P' s Ka iγ i ( E) cosδ i ω P' s 0.847plf P' q q d q l Ka i ( E) cosδ i ω P' q 0plf P' a P' s P' q P' a 0.847plf Y' s 3 E Y' s ft Y' q E Y' q 0.5 ft M' o P' s Y' s P' q Y' q M' o 6.949lbf Resisting Moments W' w Eγ u W' w 6.844plf

33 X' w G u ( E) tan( ω) X' w ft M' r W' w X' w M' r ftplf FS ot M' r FS ot M' o Factor of Safety against Shear failure V' u a u W' w tan λ u V' u plf FS sh V' u FS sh 8.45 P' a Wall Height H ft Summary Unreinforced Stability FS ot FS sh 8.45 FS bearing 6. Upper Layer Stability Grid Elevation E ft ensile Force F g plf Anch. Capacity FS Pullout (.5) FS Conn (.5) AC FS po.48 FS conn plf Geogrid Length Anch. Length FS Grid ension (.0) FS Int Sliding (.5) FS Bulging (.5) L 4ft La.67 ft FS ten FS sl 9.6 FS sc 8.45

34 MAY RX REAINING WALL 3-0 ALL DESIGN CALCULAIONS 30

35 Segmental Retaining Wall Design Calculations per NCMA Wall Geometry Height Backslope Dead Load Live Load Distance to Slope Wall below grade at toe H 3.0 ft β.3 deg q d 0psf q l 0psf Z.0 ft H emb.5ft Soil Properties Reinforced Soil Retained Soil Drainage Fill Foundation Soil Pullout Direct Sliding γ i ϕ i 0 pcf γ r 0 pcf γ d 0 pcf γ f 0 pcf C i.7 C ds.8 6 deg ϕ r 6 deg ϕ d 3 deg ϕ f 6 deg c f 0psf Segmental Unit Properties Height Length Width Setback Center of Gravity Batter Shear Capacity H u 3 6in L u 6 in.375in Δ u 4 in G u 6.875in ω atan Δ u a u 500 lbf λ u 35 deg ft H u Infilled Unit Weight γ u Hinge Height 3 pcf H h G u H h 8.5ft tan( ω) Internal Interface Friction Angle δ i 3 ϕ i δ i 7.333deg Internal Active Earth Pressure ω 7.5 deg V umax 640 plf External Interface Friction Angle δ e if ϕ i ϕ r ϕ r ϕ i δ e 6 deg External Active Earth Pressure cos ϕ i ω cos ϕ r ω Ka i Ka e ( cos ( ω) ) sinϕ cosω δ i i δ i sinϕ i β cos ( ω) sin ϕ cos ω δ e r cos ω ( ) cos ω δ i cos ω β Ka i Ka e δ e sinϕ r β δ e cos ( ω β α i α e Orientation of Critical Internal Failure Surface tanϕ i β cotϕ i ω cotϕ i ω tanϕ i β cotϕ i ω tan ϕ i β tan ϕ i β tan δ i ω atan ϕ i α i 47.83deg tan δ i ω Orientation of Critical External Failure Surface tanϕ r β cotϕ r ω cotϕ r ω tanϕ r β cotϕ r ω tan ϕ r β tan ϕ r β tan δ e ω atan ϕ r α e 45.9deg tan δ e ω

36 Sliding Given External Stability Analysis.5 = min C ds L Ztan( β) tan( ω) C ds q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) L Ztan( β) tan( ω) C ds q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) L Ztan( β) tan( ω) c f L q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) cosδ e ω tan( β) tan( ω) L W q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω tanϕ i tanϕ d tanϕ f L sliding Overturning Given Find( L) L sliding.847 ft.0 = L γ i H ( L Htan( ω) ) γ il ZL q d L L Ztan( β) tan( ω) tan( β) tan( ω) L Ztan( β) tan( ω) tan( β) tan( ω) Z L Z tan( β) Htan( ω) L Ztan( β) tan( ω) tan( β) tan( ω) 3 Z L Htan( ω) Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) tan( ω) tan( β) cosδ e ω 3 H L W L Zta u tan( β) L W q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω H L W L u tan L t L overturning Find( L) L overturning.046 ft L sliding L max L.847 ft L overturning Based on Overturning and Sliding L 4.00ft

37 Eccentricity L' L L'.969ft L Ztan( β) tan( ω) L'' L'' 0.05 ft tan( β) tan( ω) L β L L Ztan( β) tan( ω) tan( β) tan( ω) Z L β.09 ft L Z h tan( β) tan( ω) L Z tan( β) tan( ω) tan( β) h ft W r Lγ i H W r 440plf X r ( L Htan( ω) ) X r.88 ft W β γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) W β 47.66plf X β Htan( ω) 3 L β Z X β 3.75 ft Surcharge is applied over Z L β X q Htan( ω) L Ztan( β) tan( ω) L 3.09 ft tan( β) tan( ω) X q.96 ft P s Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) tan( ω) β) cosδ e ω P s 8.5plf Y s 3 H L W L Ztan( β) tan( ω) u Z tan( β) tan( β) tan( ω) Y s.34 ft L W P q q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω P q 0plf Y q H L W L Ztan( β) tan( ω) u Z tan( β) tan( ω) tan( β) Y q.70 ft e L P s Y s P q Y q W r X r W L β X β L Ztan( β) tan( ω) L q d L X q tan( β) tan( ω) L Ztan( β) tan( ω) W r W β q d L tan( β) tan( ω) B L e e ft B 4.7 ft L W W r W β q d q l u Ztan( β) tan( ω) L tan( β) tan( ω) q q psf B

38 Bearing Capacity N q ϕ f tan 45deg exp πtan ϕ f N q.854 N c if ϕ f = 05.4N q cotϕ f N c.54 N γ N q tan ϕ f N γ.539 q u c f N c γ fbn γ γ f H emb N q q u psf FS bearing q u FS bearing q Internal Stability Reinforcement Properties Ultimate Strength Uncertainties Durability Installation Creep Connection Strength ult 055plf FS unc.55 RF d.08 RF id.5 RF cr.67 a cs 500plf λ cs 5deg a ult Allowable Strength a plf V csmax 000plf RF d RF id RF cr FS unc Required Number of reinforcement layers P a Ka iγ i H cosδ i ω q l q d Ka i Hcosδ i ω P a 87.69plf N min P a ceil N min a ension in Geogrid Enter Geogrid Elevations from top down E F g.0ft H F g γ i D q l q d Ka i cosδ i ω a dd FS ten F 0ft g 87.69plf FS ten Pullout Capacity Anchorage Length La L ( H E) tan 90deg α i ( H E) tan( ω) La.67 ft

39 Average Depth of overburden d E ( H E) tan 90deg d.39 ft Anchorage Capacity AC La AC FS po C i plf dγ i q d α i tanϕ i AC FS po.05 F g La Z Htan( ω) Δ u tan β ( ) Internal Sliding Failure Reduced reinforcement length ΔL 0ft L' s L ΔL L' s.969 ft Length of sloping ground L' s tan( β) tan( ω) L sβ L' s Z L sβ.08 ft tan( β) tan( ω) Height of slope above crest of wall h' L sβ tan( β) h' ft Weight of reduced reinforced area W' r L' s E γ i Weight of wedge beyond reinforced soil zone W' r 7.5plf W' β L sβ h' γ i W' β 48.84plf Friction developed by weight R' s C ds q d L sβ Z W' r W' β tanϕ i R' s plf Shear capacity of facing elements V u if V umax a u if E H h V u plf Driving Forces H h From retained soil E γ u tanλ u V umax a u if E H h H h From surcharge E γ u tanλ u P s Ka eγ r ( E h' ) cosδ e ω P q q d q l Ka e ( E h' ) cosδ e ω

40 Factor of safety against internal sliding R' s V u FS sl FS sl P s P q Local Stability of Facing Units Facing Connection Strength conn if V csmax a cs if E H h H h E γ u tanλ cs V csmax a cs if E H h H h E γ u tanλ cs conn plf FS conn conn FS conn 3.07 F g Resistance to Bulging Shear capacity at each geogrid layer V u if V umax a u if E H h H h E γ u tanλ u V umax a u if E H h H h E γ u tanλ u V u 678plf Driving Force at each geogrid layer P a Ka iγ i ( E) cosδ i ω P a 83plf q d q l Ka i ( E) cosδ i ω Sum of tension in reinforcement layers above layer being considered FS sc V u P a FS sc 8.6 Maximum unreinforced height of SRnits Moment equilibrium Driving Moments P' s Ka iγ i ( E) cosδ i ω P' s plf P' q q d q l Ka i ( E) cosδ i ω P' q 0plf P' a P' s P' q P' a plf Y' s 3 E Y' s ft Y' q E Y' q ft M' o P' s Y' s P' q Y' q M' o 55.59lbf Resisting Moments W' w Eγ u W' w plf

41 X' w G u ( E) tan( ω) X' w 0.64 ft M' r W' w X' w M' r 6.59 ftplf FS ot M' r FS ot.93 M' o Factor of Safety against Shear failure V' u a u W' w tan λ u V' u plf FS sh V' u FS sh 8.6 P' a Wall Height H 3ft Summary Unreinforced Stability FS ot.93 FS sh 8.6 FS bearing Upper Layer Stability Grid Elevation E ft ensile Force F g plf Anch. Capacity FS Pullout (.5) FS Conn (.5) AC FS po.05 FS conn 3.07 plf Geogrid Length Anch. Length FS Grid ension (.0) FS Int Sliding (.5) FS Bulging (.5) L 4ft La.67 ft FS ten FS sl FS sc 8.6

42 MAY RX REAINING WALL 4-0 ALL DESIGN CALCULAIONS 38

43 Segmental Retaining Wall Design Calculations per NCMA Wall Geometry Height Backslope Dead Load Live Load Distance to Slope Wall below grade at toe H 4.0 ft β.3 deg q d 0psf q l 0psf Z.0 ft H emb.5ft Soil Properties Reinforced Soil Retained Soil Drainage Fill Foundation Soil Pullout Direct Sliding γ i ϕ i 0 pcf γ r 0 pcf γ d 0 pcf γ f 0 pcf C i.7 C ds.8 6 deg ϕ r 6 deg ϕ d 3 deg ϕ f 6 deg c f 0psf Segmental Unit Properties Height Length Width Setback Center of Gravity Batter Shear Capacity H u 3 6in L u 6 in.375in Δ u 4 in G u 6.875in ω atan Δ u a u 500 lbf λ u 35 deg ft H u Infilled Unit Weight γ u Hinge Height 3 pcf H h G u H h 8.5ft tan( ω) Internal Interface Friction Angle δ i 3 ϕ i δ i 7.333deg Internal Active Earth Pressure ω 7.5 deg V umax 640 plf External Interface Friction Angle δ e if ϕ i ϕ r ϕ r ϕ i δ e 6 deg External Active Earth Pressure cos ϕ i ω cos ϕ r ω Ka i Ka e ( cos ( ω) ) sinϕ i δ i sinϕ i β cosω δ i cos ( ω) sin ϕ r cos ω δ e cos ω ( ) cos ω δ i cos ω β Ka i Ka e δ e sinϕ r β δ e cos ( ω β α i α e Orientation of Critical Internal Failure Surface tanϕ i β cotϕ i ω cotϕ i ω tanϕ i β cotϕ i ω tan ϕ i β tan ϕ i β tan δ i ω atan ϕ i α i 47.83deg tan δ i ω Orientation of Critical External Failure Surface tanϕ r β cotϕ r ω cotϕ r ω tanϕ r β cotϕ r ω tan ϕ r β tan ϕ r β tan δ e ω atan ϕ r α e 45.9deg tan δ e ω

44 Sliding Given External Stability Analysis.5 = min C ds L Ztan( β) tan( ω) C ds q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) L Ztan( β) tan( ω) C ds q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) L Ztan( β) tan( ω) c f L q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) cosδ e ω tan( β) tan( ω) L W q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω tanϕ i tanϕ d tanϕ f L sliding Overturning Given Find( L) L sliding.69 ft.0 = L γ i H ( L Htan( ω) ) γ il ZL q d L L Ztan( β) tan( ω) tan( β) tan( ω) L Ztan( β) tan( ω) tan( β) tan( ω) Z L Z tan( β) Htan( ω) L Ztan( β) tan( ω) tan( β) tan( ω) 3 Z L Htan( ω) Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) tan( ω) tan( β) cosδ e ω 3 H L W L Zta u tan( β) L W q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω H L W L u tan L t L overturning Find( L) L overturning.567 ft L sliding L max L.69 ft L overturning Based on Overturning and Sliding L 4.5ft

45 Eccentricity L' L L' 3.469ft L Ztan( β) tan( ω) L'' L'' ft tan( β) tan( ω) L β L L Ztan( β) tan( ω) tan( β) tan( ω) Z L β.53 ft L Z h tan( β) tan( ω) L Z tan( β) tan( ω) tan( β) h ft W r Lγ i H W r 60plf X r ( L Htan( ω) ) X r.5 ft W β γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) W β plf X β Htan( ω) 3 L β Z X β 4.9 ft Surcharge is applied over Z L β X q Htan( ω) L Ztan( β) tan( ω) L 3.53 ft tan( β) tan( ω) 3.97 ft X q P s Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) tan( ω) β) cosδ e ω P s 400.5plf Y s 3 H L W L Ztan( β) tan( ω) u Z tan( β) tan( β) tan( ω) Y s.50 ft L W P q q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω P q 0plf Y q H L W L Ztan( β) tan( ω) u Z tan( β) tan( ω) tan( β) Y q.53 ft e L P s Y s P q Y q W r X r W L β X β L Ztan( β) tan( ω) L q d L X q tan( β) tan( ω) L Ztan( β) tan( ω) W r W β q d L tan( β) tan( ω) B L e e ft B ft L W W r W β q d q l u Ztan( β) tan( ω) L tan( β) tan( ω) q q psf B

46 Bearing Capacity N q ϕ f tan 45deg exp πtan ϕ f N q.854 N c if ϕ f = 05.4N q cotϕ f N c.54 N γ N q tan ϕ f N γ.539 q u c f N c γ fbn γ γ f H emb N q q u psf FS bearing q u FS bearing q Internal Stability Reinforcement Properties Ultimate Strength Uncertainties Durability Installation Creep Connection Strength ult 055plf FS unc.55 RF d.08 RF id.5 RF cr.67 a cs 500plf λ cs 5deg a ult Allowable Strength a plf V csmax 000plf RF d RF id RF cr FS unc Required Number of reinforcement layers P a Ka iγ i H cosδ i ω q l q d Ka i Hcosδ i ω P a plf N min P a ceil N min a ension in Geogrid Enter Geogrid Elevations from top down.0 E 3.5 top length E p top top grids length( E) n 0 top l 0 grids E E p p D D 0ft D H p 0 grids EL L E F gn D n γ i D q l q d Ka i cosδ i ω a dd FS tenn D n F gn D ( )ft F g ( ) plf

47 FS ten ( ) Pullout Capacity Anchorage Length La L W n n u H E n tan90 deg α i H E n tan( ω) La ( )ft Increase in La L L 0 0 Anchorage Length La L W n n u H E n tan90 deg α i H E n tan( ω) La ( )ft Average Depth of overburden d E H E tan 90 deg α n n n i d ( )ft Anchorage Capacity AC La C n n i d γ n i q d AC ( ) plf F g ( ) plf tanϕ i La n Z Htan( ω) Δ u tan β ( ) FS po AC F g Internal Sliding Failure FS po Reduced reinforcement length ( ) ΔL E E l l l tan( ω) tanα e ΔL ( 0.65 )ft L' sn L W n u ΔL n L' s ( )ft Length of sloping ground L' sn tan( β) tan( ω) L sβn L' sn Z tan( β) tan( ω) L sβ ( )ft Height of slope above crest of wall h' L n sβn tan( β) h' ( )ft Weight of reduced reinforced area W' rn L' sn E n γ i W' r ( ) plf

48 Weight of wedge beyond reinforced soil zone W' βn L sβn h' n γ i Friction developed by weight R' sn C ds q d L sβn Z W' rn W' βn tanϕ i W' β R' s ( ) plf ( ) plf Shear capacity of facing elements V un if V umax a u if E H n h H h E n γ u tan λ u V u ( ) plf Driving Forces From retained soil V umax a u if E H n h H h From surcharge E n γ u tan λ u P sn Ka eγ r E h' cos δ n n e ω P qn q d q l Ka e E h' cos δ n n e ω Factor of safety against internal sliding P s ( ) plf R' sn V un FS sln P sn P qn FS sl ( ) Facing Connection Strength Local Stability of Facing Units connn if V csmax a cs if E H n h H h E n γ u tan λ csv csmax a cs if E H n h H h E n γ u tan λ cs conn ( ) plf FS connn connn F gn FS conn ( ) Resistance to Bulging Shear capacity at each geogrid layer V un if V umax a u if E H n h H h E n γ u tan λ u V u ( ) plf V umax a u if E H n h H h E n γ u tan λ u Driving Force at each geogrid layer P an Ka iγ i E n cosδ i ω P a ( ) plf q d q l Ka i E cos δ n i ω

49 Sum of tension in reinforcement layers above layer being considered n F n i 0 F gi F ( ) plf FS scn P an V un F n FS sc ( ) Maximum unreinforced height of SRnits Moment equilibrium Driving Moments P' s Ka iγ i E cos δ 0 i ω P' s plf P' q q d q l Ka i E cos δ 0 i ω P' q 0plf P' a P' s P' q P' a plf Y' s 3 E Y' 0 s ft Y' q E Y' 0 q ft M' o P' s Y' s P' q Y' q M' o 55.59lbf Resisting Moments W' w E γ 0 u W' w plf X' w G u E tan( ω) X' 0 w 0.64 ft M' r W' w X' w M' r 6.59 ftplf FS ot M' r FS ot.93 M' o Factor of Safety against Shear failure V' u a u W' w tan λ u V' u plf FS sh V' u FS sh 8.6 P' a Wall Height H 4ft Summary Unreinforced Stability FS ot.93 FS sh 8.6 FS bearing Grid Elevation E n ft 3.5 Geogrid Length L n 4.5 ft 4.5 ensile Force F gn plf Anch. Length La n Anch. Capacity AC n plf ft FS Grid ension (.0) FS tenn FS Pullout (.5) FS pon FS Int Sliding (.5) FS sln FS Conn (.5) FS connn FS Bulging (.5) FS scn

50 MAY RX REAINING WALL 5-0 ALL DESIGN CALCULAIONS 46

51 Segmental Retaining Wall Design Calculations per NCMA Wall Geometry Height Backslope Dead Load Live Load Distance to Slope Wall below grade at toe H 5.0 ft β.3 deg q d 0psf q l 0psf Z.0 ft H emb.5ft Soil Properties Reinforced Soil Retained Soil Drainage Fill Foundation Soil Pullout Direct Sliding γ i ϕ i 0 pcf γ r 0 pcf γ d 0 pcf γ f 0 pcf C i.7 C ds.8 6 deg ϕ r 6 deg ϕ d 3 deg ϕ f 6 deg c f 0psf Segmental Unit Properties Height Length Width Setback Center of Gravity Batter Shear Capacity H u 3 6in L u 6 in.375in Δ u 4 in G u 6.875in ω atan Δ u a u 500 lbf λ u 35 deg ft H u Infilled Unit Weight γ u Hinge Height 3 pcf H h G u H h 8.5ft tan( ω) Internal Interface Friction Angle δ i 3 ϕ i δ i 7.333deg Internal Active Earth Pressure ω 7.5 deg V umax 640 plf External Interface Friction Angle δ e if ϕ i ϕ r ϕ r ϕ i δ e 6 deg External Active Earth Pressure cos ϕ i ω cos ϕ r ω Ka i Ka e ( cos ( ω) ) sinϕ i δ i sinϕ i β cosω δ i cos ( ω) sin ϕ r cos ω δ e cos ω ( ) cos ω δ i cos ω β Ka i Ka e δ e sinϕ r β δ e cos ( ω β α i α e Orientation of Critical Internal Failure Surface tanϕ i β cotϕ i ω cotϕ i ω tanϕ i β cotϕ i ω tan ϕ i β tan ϕ i β tan δ i ω atan ϕ i α i 47.83deg tan δ i ω Orientation of Critical External Failure Surface tanϕ r β cotϕ r ω cotϕ r ω tanϕ r β cotϕ r ω tan ϕ r β tan ϕ r β tan δ e ω atan ϕ r α e 45.9deg tan δ e ω

52 Sliding Given External Stability Analysis.5 = min C ds L Ztan( β) tan( ω) C ds q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) L Ztan( β) tan( ω) C ds q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) L Ztan( β) tan( ω) c f L q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) cosδ e ω tan( β) tan( ω) L W q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω tanϕ i tanϕ d tanϕ f L sliding Overturning Given Find( L) L sliding ft.0 = L γ i H ( L Htan( ω) ) γ il ZL q d L L Ztan( β) tan( ω) tan( β) tan( ω) L Ztan( β) tan( ω) tan( β) tan( ω) Z L Z tan( β) Htan( ω) L Ztan( β) tan( ω) tan( β) tan( ω) 3 Z L Htan( ω) Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) tan( ω) tan( β) cosδ e ω 3 H L W L Zta u tan( β) L W q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω H L W L u tan L t L overturning Find( L) L overturning.05 ft L sliding L max L ft L overturning Based on Overturning and Sliding L 5.0ft

53 Eccentricity L' L L' 3.969ft L Ztan( β) tan( ω) L'' L'' ft tan( β) tan( ω) L β L L Ztan( β) tan( ω) tan( β) tan( ω) Z L β ft L Z h tan( β) tan( ω) L Z tan( β) tan( ω) tan( β) h ft W r Lγ i H W r 3000plf X r ( L Htan( ω) ) X r.83 ft W β γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) W β plf X β Htan( ω) 3 L β Z X β ft Surcharge is applied over Z L β X q Htan( ω) L Ztan( β) tan( ω) L ft tan( β) tan( ω) ft X q P s Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) tan( ω) β) cosδ e ω P s 60.47plf Y s 3 H L W L Ztan( β) tan( ω) u Z tan( β) tan( β) tan( ω) Y s.869 ft L W P q q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω P q 0plf Y q H L W L Ztan( β) tan( ω) u Z tan( β) tan( ω) tan( β) Y q.804 ft e L P s Y s P q Y q W r X r W L β X β L Ztan( β) tan( ω) L q d L X q tan( β) tan( ω) L Ztan( β) tan( ω) W r W β q d L tan( β) tan( ω) B L e e ft B ft L W W r W β q d q l u Ztan( β) tan( ω) L tan( β) tan( ω) q q 60.5psf B

54 Bearing Capacity N q ϕ f tan 45deg exp πtan ϕ f N q.854 N c if ϕ f = 05.4N q cotϕ f N c.54 N γ N q tan ϕ f N γ.539 q u c f N c γ fbn γ γ f H emb N q q u psf FS bearing q u FS bearing 7. q Internal Stability Reinforcement Properties Ultimate Strength Uncertainties Durability Installation Creep Connection Strength ult 055plf FS unc.55 RF d.08 RF id.5 RF cr.67 a cs 500plf λ cs 5deg a ult Allowable Strength a plf V csmax 000plf RF d RF id RF cr FS unc Required Number of reinforcement layers P a Ka iγ i H cosδ i ω q l q d Ka i Hcosδ i ω P a 5.64plf N min P a ceil N min a ension in Geogrid Enter Geogrid Elevations from top down.0 E 3.5 ft top length( E) p top top 4.5 grids length( E) n 0 top l 0 grids E E p p D D 0ft D H p 0 grids EL L E F gn D n γ i D q l q d Ka i cosδ i ω a dd FS tenn D n F gn D ( )ft F g ( ) plf

55 FS ten ( ) Pullout Capacity Anchorage Length La L W n n u H E n tan90 deg α i H E n tan( ω) La ( )ft Increase in La L L 0 0 Anchorage Length La L W n n u H E n tan90 deg α i H E n tan( ω) La ( )ft Average Depth of overburden d E H E tan 90 deg α n n n i d ( )ft Anchorage Capacity AC La C n n i d γ n i q d tanϕ i AC ( ) plf F g ( ) plf La n Z Htan( ω) Δ u tan β ( ) FS po AC F g Internal Sliding Failure FS po Reduced reinforcement length ( ) ΔL E E l l l tan( ω) tanα e ΔL ( )ft L' sn L W n u ΔL n L' s ( )ft Length of sloping ground L' sn tan( β) tan( ω) L sβn L' sn Z tan( β) tan( ω) L sβ ( )ft Height of slope above crest of wall h' L n sβn tan( β) h' ( )ft Weight of reduced reinforced area W' rn L' sn E n γ i W' r ( ) plf

56 Weight of wedge beyond reinforced soil zone W' βn L sβn h' n γ i Friction developed by weight R' sn C ds q d L sβn Z W' rn W' βn tanϕ i W' β R' s ( ) plf ( ) plf Shear capacity of facing elements V un if V umax a u if E H n h H h E n γ u tan λ u V u ( ) plf Driving Forces From retained soil V umax a u if E H n h H h From surcharge E n γ u tan λ u P sn Ka eγ r E h' cos δ n n e ω P qn q d q l Ka e E h' cos δ n n e ω Factor of safety against internal sliding P s ( ) plf R' sn V un FS sln P sn P qn FS sl ( ) Facing Connection Strength Local Stability of Facing Units connn if V csmax a cs if E H n h H h E n γ u tan λ csv csmax a cs if E H n h H h E n γ u tan λ cs conn ( ) plf FS connn connn F gn FS conn ( ) Resistance to Bulging Shear capacity at each geogrid layer V un if V umax a u if E H n h H h E n γ u tan λ u V u ( ) plf V umax a u if E H n h H h E n γ u tan λ u Driving Force at each geogrid layer P an Ka iγ i E n cosδ i ω P a ( ) plf q d q l Ka i E cos δ n i ω

57 Sum of tension in reinforcement layers above layer being considered n F n i 0 F gi F ( ) plf FS scn P an V un F n FS sc ( ) Maximum unreinforced height of SRnits Moment equilibrium Driving Moments P' s Ka iγ i E cos δ 0 i ω P' s plf P' q q d q l Ka i E cos δ 0 i ω P' q 0plf P' a P' s P' q P' a plf Y' s 3 E Y' 0 s ft Y' q E Y' 0 q ft M' o P' s Y' s P' q Y' q M' o 55.59lbf Resisting Moments W' w E γ 0 u W' w plf X' w G u E tan( ω) X' 0 w 0.64 ft M' r W' w X' w M' r 6.59 ftplf FS ot M' r FS ot.93 M' o Factor of Safety against Shear failure V' u a u W' w tan λ u V' u plf FS sh V' u FS sh 8.6 P' a Wall Height H 5ft Summary Unreinforced Stability FS ot.93 FS sh 8.6 FS bearing 7. Grid Elevation E n ft Geogrid Length L n 5 ft 5 5 ensile Force F gn plf Anch. Length La n Anch. Capacity AC n plf ft FS Grid ension (.0) FS tenn FS Pullout (.5) FS pon FS Int Sliding (.5) FS sln FS Conn (.5) FS connn FS Bulging (.5) FS scn

58 MAY RX REAINING WALL 6-0 ALL DESIGN CALCULAIONS 54

59 Segmental Retaining Wall Design Calculations per NCMA Wall Geometry Height Backslope Dead Load Live Load Distance to Slope Wall below grade at toe H 6.0 ft β.3 deg q d 0psf q l 0psf Z.0 ft H emb.5ft Soil Properties Reinforced Soil Retained Soil Drainage Fill Foundation Soil Pullout Direct Sliding γ i ϕ i 0 pcf γ r 0 pcf γ d 0 pcf γ f 0 pcf C i.7 C ds.8 6 deg ϕ r 6 deg ϕ d 3 deg ϕ f 6 deg c f 0psf Segmental Unit Properties Height Length Width Setback Center of Gravity Batter Shear Capacity H u 3 6in L u 6 in.375in Δ u 4 in G u 6.875in ω atan Δ u a u 500 lbf λ u 35 deg ft H u Infilled Unit Weight γ u Hinge Height 3 pcf H h G u H h 8.5ft tan( ω) Internal Interface Friction Angle δ i 3 ϕ i δ i 7.333deg Internal Active Earth Pressure ω 7.5 deg V umax 640 plf External Interface Friction Angle δ e if ϕ i ϕ r ϕ r ϕ i δ e 6 deg External Active Earth Pressure cos ϕ i ω cos ϕ r ω Ka i Ka e ( cos ( ω) ) sinϕ i δ i sinϕ i β cosω δ i cos ( ω) sin ϕ r cos ω δ e cos ω ( ) cos ω δ i cos ω β Ka i Ka e δ e sinϕ r β δ e cos ( ω β α i α e Orientation of Critical Internal Failure Surface tanϕ i β cotϕ i ω cotϕ i ω tanϕ i β cotϕ i ω tan ϕ i β tan ϕ i β tan δ i ω atan ϕ i α i 47.83deg tan δ i ω Orientation of Critical External Failure Surface tanϕ r β cotϕ r ω cotϕ r ω tanϕ r β cotϕ r ω tan ϕ r β tan ϕ r β tan δ e ω atan ϕ r α e 45.9deg tan δ e ω

60 Sliding Given External Stability Analysis.5 = min C ds L Ztan( β) tan( ω) C ds q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) L Ztan( β) tan( ω) C ds q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) L Ztan( β) tan( ω) c f L q d L Lγ i H tan( β) tan( ω) γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) cosδ e ω tan( β) tan( ω) L W q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω tanϕ i tanϕ d tanϕ f L sliding Overturning Given Find( L) L sliding 4.38 ft.0 = L γ i H ( L Htan( ω) ) γ il ZL q d L L Ztan( β) tan( ω) tan( β) tan( ω) L Ztan( β) tan( ω) tan( β) tan( ω) Z L Z tan( β) Htan( ω) L Ztan( β) tan( ω) tan( β) tan( ω) 3 Z L Htan( ω) Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) tan( ω) tan( β) cosδ e ω 3 H L W L Zta u tan( β) L W q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω H L W L u tan L t L overturning Find( L) L overturning.55 ft L sliding L max L 4.38 ft L overturning Based on Overturning and Sliding L 5.75ft

61 Eccentricity L' L L' 4.79ft L Ztan( β) tan( ω) L'' L'' ft tan( β) tan( ω) L β L L Ztan( β) tan( ω) tan( β) tan( ω) Z L β 3.84 ft L Z h tan( β) tan( ω) L Z tan( β) tan( ω) tan( β) h 0.76 ft W r Lγ i H W r 440plf X r ( L Htan( ω) ) X r 3.5 ft W β γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) W β plf X β Htan( ω) 3 L β Z X β 5.34 ft Surcharge is applied over Z L β X q Htan( ω) L Ztan( β) tan( ω) L 4.84 ft tan( β) tan( ω) 4.88 ft X q P s Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) tan( ω) β) cosδ e ω P s 90.00plf Y s 3 H L W L Ztan( β) tan( ω) u Z tan( β) tan( β) tan( ω) Y s.54 ft L W P q q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω P q 0plf Y q H L W L Ztan( β) tan( ω) u Z tan( β) tan( ω) tan( β) Y q 3.38 ft e L P s Y s P q Y q W r X r W L β X β L Ztan( β) tan( ω) L q d L X q tan( β) tan( ω) L Ztan( β) tan( ω) W r W β q d L tan( β) tan( ω) B L e e 0.05 ft B 5.7 ft L W W r W β q d q l u Ztan( β) tan( ω) L tan( β) tan( ω) q q psf B

62 Bearing Capacity N q ϕ f tan 45deg exp πtan ϕ f N q.854 N c if ϕ f = 05.4N q cotϕ f N c.54 N γ N q tan ϕ f N γ.539 q u c f N c γ fbn γ γ f H emb N q q u psf FS bearing q u FS bearing q Internal Stability Reinforcement Properties Ultimate Strength Uncertainties Durability Installation Creep Connection Strength ult 055plf FS unc.55 RF d.08 RF id.5 RF cr.67 a cs 500plf λ cs 5deg a ult Allowable Strength a plf V csmax 000plf RF d RF id RF cr FS unc Required Number of reinforcement layers P a Ka iγ i H cosδ i ω q l q d Ka i Hcosδ i ω P a plf N min P a ceil N min a ension in Geogrid Enter Geogrid Elevations from top down.0 E 4.0 ft top length( E) p top top 5.5 grids length( E) n 0 top l 0 grids E E p p D D 0ft D H p 0 grids EL L E F gn D n γ i D q l q d Ka i cosδ i ω a dd FS tenn D n F gn D ( )ft F g ( ) plf

63 FS ten ( ) Pullout Capacity Anchorage Length La L W n n u H E n tan90 deg α i H E n tan( ω) La ( )ft Increase in La L L 0 0 Anchorage Length La L W n n u H E n tan90 deg α i H E n tan( ω) La ( )ft Average Depth of overburden d E H E tan 90 deg α n n n i d ( )ft Anchorage Capacity AC La C n n i d γ n i q d tanϕ i AC ( ) plf F g ( ) plf La n Z Htan( ω) Δ u tan β ( ) FS po AC F g Internal Sliding Failure FS po Reduced reinforcement length ( ) ΔL E E l l l tan( ω) tanα e ΔL ( )ft L' sn L W n u ΔL n L' s ( )ft Length of sloping ground L' sn tan( β) tan( ω) L sβn L' sn Z tan( β) tan( ω) L sβ ( )ft Height of slope above crest of wall h' L n sβn tan( β) h' ( )ft Weight of reduced reinforced area W' rn L' sn E n γ i W' r ( ) plf

64 Weight of wedge beyond reinforced soil zone W' βn L sβn h' n γ i Friction developed by weight R' sn C ds q d L sβn Z W' rn W' βn tanϕ i W' β R' s ( ) plf ( ) plf Shear capacity of facing elements V un if V umax a u if E H n h H h E n γ u tan λ u V u ( ) plf Driving Forces From retained soil V umax a u if E H n h H h From surcharge E n γ u tan λ u P sn Ka eγ r E h' cos δ n n e ω P qn q d q l Ka e E h' cos δ n n e ω Factor of safety against internal sliding P s ( ) plf R' sn V un FS sln P sn P qn FS sl ( ) Facing Connection Strength Local Stability of Facing Units connn if V csmax a cs if E H n h H h E n γ u tan λ csv csmax a cs if E H n h H h E n γ u tan λ cs conn ( ) plf FS connn connn F gn FS conn ( ) Resistance to Bulging Shear capacity at each geogrid layer V un if V umax a u if E H n h H h E n γ u tan λ u V u ( ) plf V umax a u if E H n h H h E n γ u tan λ u Driving Force at each geogrid layer P an Ka iγ i E n cosδ i ω P a ( ) plf q d q l Ka i E cos δ n i ω

65 Sum of tension in reinforcement layers above layer being considered n F n i 0 F gi F ( ) plf FS scn P an V un F n FS sc ( ) Maximum unreinforced height of SRnits Moment equilibrium Driving Moments P' s Ka iγ i E cos δ 0 i ω P' s plf P' q q d q l Ka i E cos δ 0 i ω P' q 0plf P' a P' s P' q P' a plf Y' s 3 E Y' 0 s ft Y' q E Y' 0 q ft M' o P' s Y' s P' q Y' q M' o 55.59lbf Resisting Moments W' w E γ 0 u W' w plf X' w G u E tan( ω) X' 0 w 0.64 ft M' r W' w X' w M' r 6.59 ftplf FS ot M' r FS ot.93 M' o Factor of Safety against Shear failure V' u a u W' w tan λ u V' u plf FS sh V' u FS sh 8.6 P' a Wall Height H 6ft Summary Unreinforced Stability FS ot.93 FS sh 8.6 FS bearing Grid Elevation E n ft Geogrid Length L n 5.75 ft ensile Force F gn plf Anch. Length La n Anch. Capacity AC n plf ft FS Grid ension (.0) FS tenn FS Pullout (.5) FS pon FS Int Sliding (.5) FS sln FS Conn (.5) FS connn FS Bulging (.5) FS scn

66 MAY RX IERED REAINING WALL 3-0 ALL DESIGN CALCULAIONS 6

67 Segmental Retaining Wall Design Calculations per NCMA Wall Geometry Height Backslope Dead Load Live Load Distance to Slope Wall below grade at toe H 3.0 ft β 0.0 deg q d 0psf q l 0psf Z 0ft H emb.5ft Soil Properties Reinforced Soil Retained Soil Drainage Fill Foundation Soil Pullout Direct Sliding γ i ϕ i 0 pcf γ r 0 pcf γ d 0 pcf γ f 0 pcf C i.7 C ds.8 6 deg ϕ r 6 deg ϕ d 3 deg ϕ f 6 deg c f 0psf Segmental Unit Properties Height Length Width Setback Center of Gravity Batter Shear Capacity H u 3 6in L u 6 in.375in Δ u 4 in G u 6.875in ω atan Δ u a u 500 lbf λ u 7 deg ft H u Infilled Unit Weight γ u Hinge Height 3 pcf H h G u H h 8.5ft tan( ω) Internal Interface Friction Angle δ i 3 ϕ i δ i 7.333deg Internal Active Earth Pressure ω 7.5 deg V umax 640 plf External Interface Friction Angle δ e if ϕ i ϕ r ϕ r ϕ i δ e 6 deg External Active Earth Pressure cos ϕ i ω cos ϕ r ω Ka i Ka e ( cos ( ω) ) sinϕ cosω δ i i δ i sinϕ i β cos ( ω) sin ϕ cos ω δ e r cos ω ( ) cos ω δ i cos ω β Ka i 0.99 Ka e 0.9 δ e sinϕ r β δ e cos ( ω β α i α e Orientation of Critical Internal Failure Surface tanϕ i β cotϕ i ω cotϕ i ω tanϕ i β cotϕ i ω tan ϕ i β tan ϕ i β tan δ i ω atan ϕ i α i 50.97deg tan δ i ω Orientation of Critical External Failure Surface tanϕ r β cotϕ r ω cotϕ r ω tanϕ r β cotϕ r ω tan ϕ r β tan ϕ r β tan δ e ω atan ϕ r α e 49.57deg tan δ e ω

68 Sliding Given External Stability Analysis eir Properties ier Height Overlap Distance between tiers 4.0ft L t.0ft X 5.0ft H t H s H t H H s 7ft γ i HL H t L t tan ϕ f γ rh s Ka e cosδ e ω =.5 L sliding Find( L) L sliding 5.598ft Overturning Given L γ i H γ i H t L t L L t 6 γ 3 rh s Ka e cosδ e ω =.5 L overturning Find( L) L overturning 3.03ft Eccentricity Given L L γ i H γ i H t L t L L t 6 γ 3 rh s Ka e cosδ e ω γ i HL H t L t = L 6 L eccentricity Find( L) L eccentricity 3.865ft L sliding L overturning L max L 5.598ft L eccentricity Based on Overturning and Sliding L 6.0ft

69 Eccentricity L' L L' 4.969ft L Ztan( β) tan( ω) L'' L'' 0 ft tan( β) tan( ω) L β L L Ztan( β) tan( ω) tan( β) tan( ω) Z L Z h tan( β) tan( ω) L Z tan( β) tan( ω) tan( β) h 0ft L β ft W r Lγ i H W r 60plf X r ( L Htan( ω) ) X r 3.88 ft W β γ L W il Z u Ztan( β) tan( ω) L Z tan( β) tan( β) tan( ω) W β 0plf X β Htan( ω) 3 L β Z X β 4.79 ft Surcharge is applied over Z L β X q Htan( ω) L Ztan( β) tan( ω) L ft tan( β) tan( ω) 3.89 ft X q P s Ka L Ztan( β) tan( ω) eγ r H L Z tan( β) tan( ω) β) cosδ e ω P s plf Y s 3 H L W L Ztan( β) tan( ω) u Z tan( β) tan( β) tan( ω) Y s ft L W P q q d q l u Ztan( β) tan( ω) Ka e H L Z tan( β) tan( ω) tan( β) cosδ e ω P q 0plf Y q H L W L Ztan( β) tan( ω) u Z tan( β) tan( ω) tan( β) Y q.5 ft e L P s Y s P q Y q W r X r W L β X β L Ztan( β) tan( ω) L q d L X q tan( β) tan( ω) L Ztan( β) tan( ω) W r W β q d L tan( β) tan( ω) B L e e 0.9 ft B 6.37 ft L W W r W β q d q l u Ztan( β) tan( ω) L tan( β) tan( ω) q q 346.3psf B

70 Bearing Capacity N q ϕ f tan 45deg exp πtan ϕ f N q.854 N c if ϕ f = 05.4N q cotϕ f N c.54 N γ N q tan ϕ f N γ.539 q u c f N c γ fbn γ γ f H emb N q q u psf FS bearing q u FS bearing q Internal Stability Internal ier Surcharge Distance Between tiers X 5ft Length of grid L 6ft.3L.8 ft Maximum surcharge γ i H t 480psf Surcharge from top tier [[ L ( X) ]] q d if X.3Lγ i H t if ( X) L0 psf L γ i H t Reinforcement Properties Ultimate Strength Uncertainties Durability Installation Creep Connection Strength ult 055plf FS unc.55 RF d.08 RF id.5 RF cr.67 a cs 500plf λ cs 5deg a ult Allowable Strength a plf V csmax 000plf RF d RF id RF cr FS unc Required Number of reinforcement layers P a Ka iγ i H cosδ i ω q l q d Ka i Hcosδ i ω P a 9.777plf P a a ension in Geogrid N min ceil N min Enter Geogrid Elevations from top down E.0ft H F g γ i D q l q d Ka i cosδ i ω a dd FS ten F 0ft g

71 F g 9.777plf FS ten.78 Pullout Capacity Anchorage Length La L ( H E) tan 90deg α i ( H E) tan( ω) La 4.8 ft Average Depth of overburden d E ( H E) tan 90deg d ft Anchorage Capacity AC La AC FS po C i plf dγ i q d α i tanϕ i AC FS po 4.07 F g La Z Htan( ω) Δ u tan β ( ) Internal Sliding Failure Reduced reinforcement length ΔL 0ft L' s L ΔL L' s ft Length of sloping ground L' s tan( β) tan( ω) L sβ L' s Z L sβ ft tan( β) tan( ω) Height of slope above crest of wall h' L sβ tan( β) h' 0 ft Weight of reduced reinforced area W' r L' s E γ i Weight of wedge beyond reinforced soil zone W' r 9.5plf W' β L sβ h' γ i W' β 0plf Friction developed by weight R' s C ds q d L sβ Z W' r W' β tanϕ i R' s plf