Gravity Wall Calculator TA

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 ft

< Ф

frΦ(100-fr)/100

90+ω

γs

γr

γg γr(100-v)/100(hCosω) Corrected for inclination

Allowable soil bearing capacity 2000.000 psf determined by Geotechnical Engineer

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 7.500 101.250

qa

(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

45GABION RETAINING WALL

ROW 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

2 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

1 COULOMB'S THEORY

BACK

Active earth pressure =coefficient ²

0.687

0.989 0.959 0.771 0.166 ²0.959 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 = 0.000

Front face angle to horizontal == 90.000

Backfill slope = 0.000

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

βp

Angle of wall friction = 0.000

Passive earth pressure =coefficient ²

0.780

1.000 1.000 0.469 0.469 ²1.000 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 =

δp

Kp Sin²(α-Φ)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

= 41769.145 ft-lb / ft

Overturning factor of safety =

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

SFo ∑Mr

∑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±

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 foundationsoil 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.