gravity wall calculator ta.xls
TRANSCRIPT
1415 N 32nd, Fort Smith, AR 72904Ph: 800-736-9089 Fax:479-785-0633
To: Engineers:
Thank you very much for your interest in our products and solutions. The purpose of this calculator is toshow the simplicity and ease of designing Terra Aqua Gabions gravity retaining walls. We are using thefamiliar Excel environment to illustrate each step of the calculations used in the gabion gravity retainingwalls design analysis for verification.
Additional calculations may have to be performed including and not limiting to global stabilityanalysis (by Geotechnical Engineer), seismic forces (by Seismic Engineer) and hydraulic forces
drained uniformed retained and foundation soil properties. The calculations should be reviewed, checkedand certified by a Professional Engineer. To the best of our knowledge, the calculator and informationwas prepared accurately. Terra Aqua is not responsible for the reliability and validity of the geotechnicalparameters assumed in the calculations. The calculator is intended to provide design assistance to theengineer for the purpose of designing with Terra Aqua products.
Please do not hesitate to contact us if you have any questions or if you are in need of any assistance.We will assist you in anyway we can.
Colin Glass
Terra Aqua Gabions
5/30/2007
(by Hydraulic Engineer). Please check local, State and Federal requirements. The calculator assumes
TERRA AQUA GABIONS GRAVITY RETAINING WALL CALCULATIONS(STRAIGHT LINE BACK)PROJECT NAME: PROJECT #:
LOCATION: SECTION:
GEOTECHNICAL ENGINEER: REPORT #:
NOTES: DRAWING #:
DATE:
Descriptions symbols Input Units NotesValues
Backfill slope angle above wall β 18.440 ºAngle of internal friction Φ 28.000 ºWall friction reduction by geotextile 20.000 % Back of wall Angle of wall friction δ 22.400 ºInclination angle to vertical plane ω 6.000 º for wall with straight back (no offsets)Back of wall angle to horizontal α 96.000 ºCohesion c 0 psf Ignore cohesionSurcharge q 150.000 psfSoil density 125.000 pcfRock density 138.000 pcfVoid in gabion v 30.000 %Gabion density 96.600 pcfActual height of wall H 11.934 ftEmbedment d 3.000 ft 0 ft to ignore passive thrustWidth of base B 7.5 ftAllowable soil bearing capacity 2000.000 psf determined by Geotechnical Engineer
< Ф
frΦ(100-fr)/100
90+ω
γsγr
γg γr(100-v)/100(hCosω) Corrected for inclination
qa
X Y
Row # Width Height offset Area X Moment Y Moment(ft) (ft) (ft) (ft)
15 0.000 0.000 0.000 0.000 0.00014 0.000 0.000 0.000 0.000 0.00013 0.000 0.000 0.000 0.000 0.00012 0.000 0.000 0.000 0.000 0.00011 0.000 0.000 0.000 0.000 0.00010 0.000 0.000 0.000 0.000 0.0009 0.000 0.000 0.000 0.000 0.0008 0.000 0.000 0.000 0.000 0.0007 0.000 0.000 0.000 0.000 0.0006 0.000 0.000 0.000 0.000 0.0005 0.000 0.000 0.000 0.000 0.0004 3.0 3.0 4.50 9.000 6.000 54.000 10.500 94.5003 4.5 3.0 3.00 13.500 5.250 70.875 7.500 101.2502 6.0 3.0 1.50 18.000 4.500 81.000 4.500 81.0001 7.5 3.0 0.00 22.500 3.750 84.375 1.500 33.750
h= 12.0 63.000 4.607 290.250 4.929 310.500
(from toe) (ft) (ft²) (ft³) (ft³)
-3 0 3 6 9 12 15 18 21 24 27 30 33 36-6
-3
0
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45 GABION RETAINING WALLROW 1
ROW 2
ROW 3
ROW 4
ROW 5
ROW 6
ROW 7
ROW 8
ROW 9
ROW 10
ROW 11
ROW 12
ROW 13
ROW 14
ROW 15
EMBEDMT
BACKFILL
X
Y
1 COULOMB'S THEORY
BACK
Active earth pressure =coefficient ²
0.6870.989 0.959 0.771 0.166 ²
0.959 0.910
0.6871.814
0.379
Active soil thrust =
= 3372.263 lb/ft
Active surcharge thrust =
= 0.995 678.1680.910
= 740.835 lb/ft
Horizontal active soil thrust =
= 3235.059 lb/ft
Horizontal active surcharge =thrust
= 710.693 lb/ft
Vertical active soil thrust =
= 952.130 lb/ft
Vertical active surcharge =thrust
= 209.168 lb/ft
FRONT
Inclination angle to vertical = 0.000Front face angle to horizontal =
= 90.000Backfill slope = 0.000Angle of wall friction = 0.000
Passive earth pressure =
Ka Sin²(α+Φ)Sin² α Sin(α-δ) 1+ Sin(Φ+δ) Sin(Φ-β)
Sin(α-δ) Sin(α+β)
1+
Ps 0.5Kaγs H²
Pq Sinα KaqH Sin(α+β)
Phs PsCos(δ- ω)
Phq PqCos(δ- ω)
Pvs PsSin(δ- ω)
Pvq PqSin(δ- ω)
ωp
αp 90-ωp
βpδp
Kp Sin²(α-Φ)
coefficient ²
0.7801.000 1.000 0.469 0.469 ²
1.000 1.000
0.7800.281
2.770
Passive soil thrust =
= 1558.027 lb/ft
2 Check Overturning:
=
= 3.194 ft
=
= 5.183 ft
Overturning moment =
= 14016.823 ft-lb / ft
Weight of Gabion =
= 6085.800 lb / ft
=
= 5.097 ft
=
7.877
=
8.086
= d/3
= 1.000
Resisting moment =
= 41769.145 ft-lb / ft
Overturning factor of safety =
Sin² α Sin(α+δ) 1- Sin(Φ+δ) Sin(Φ+β)Sin(α+δ) Sin(α+β)
1-
Pp 0.5Kpγs d²
Vertical distance to Phs Yhs H/3-BSinω
Vertical distance to Phq Yhq H/2-BSinω
∑Mo YhsPhs + YhqPhq
Wg ∑A γg
Horizontal distance to Wg Xg Ysinω + XCosω
Horizontal distance to Pvs Xvs B/Cosω + (H/3-BSinω)Tanω
Horizontal distance to Pvq Xvq B/Cosω + (H/2-BSinω)Tanω
Vertical distance to Pp YPp
∑Mr Wg Xg + Pvs Xvs + Pvq Xvq + PpYPp
SFo ∑Mr
2.980 ≥ 2.000 O.K
3 Check Sliding
Total Normal forces ∑W =
= 7456.983 lb/ft
Frictional force = ∑W
= 7456.983 0.532
= 3964.948
Total Resisting Forces =
= 5514.440
Total Driving Forces at base =
3166.609
Siding factor of safety =
1.741 ≥ 1.500 O.K
4 Check the Eccentricity of Resultant Force(Resultant is in middle one third)
Eccentricity e = - -∑W
= 3.750 - 3.722
= ≤ e ≤
-1.250 ≤ 0.028 ≤ 1.250O.K O.K
5 Check Bearing
Applied bearing pressure P = ∑WB
= 994.264 0.023 )
Left = 1016.810 psf ≤ 2000.000 O.K
Right = 971.719 psf ≤ 2000.000 O.K
Additional calculations may have to be performed including and not limiting to global stability analysis (by (Geotechnical Engineer), seismic forces (by Seismic Engineer) and hydraulic forces (by Hydraulic Engineer).Please check local, State and Federal requirements. The calculator assumes drained uniformed retained and foundation
∑Mo
WgCosω + PsSinδ + PqSinδ - PpSinω
Ff TanΦ
∑Fr Ff + CosωPp
∑Fd PsCosδ + PqCosδ - WgSinω
SFs ∑Fr∑Fd
0.5 B ( ∑Mr Mo)
-B/6 +B/6
(1± 6e/B)
(1±
soil properties. The calculations should be reviewed, checked and certified by a Professional Engineer. To the best of ourknowledge, the calculator and information was prepared accurately. Terra Aqua is not responsible for the reliability and validity of the geotechnical parameters assumed in the calculations. The calculator is intended to provided designdesign assistance to the engineer for the purpose of designing with Terra Aqua products.
2/3*φ
Angle of inclination of wall,α= 90+
30 Degc 0
20 kN/m3
LL surcharge,q 20 kN/m2
0.5
Allowable soil bearing capacity 200 kN/m2
Angle of surcharge,β=
Backfill soil parameter,φ=
Unit wt of soil,γ
Friction coefficient,μ