Lythos Wall — examples
Every output is from a real run. The starter project: a 6 m cantilever wall.
| Input | Value |
|---|---|
| Geometry | H = 6.0 m, B = 4.8 m (toe 1.2 m, heel 3.0 m), stem 0.30–0.60 m, footing 0.70 m, 0.5 m of soil over the toe |
| Backfill | γ = 18 kN/m³, φ′ = 32°, c′ = 0; live surcharge 10 kPa |
| Foundation soil | γ = 19 kN/m³, φ′ = 30°, c′ = 5 kPa; no water |
| Earth pressure | Rankine on the virtual back; base friction and adhesion 0.67 |
| Earthquake | TBDY 2018, site class ZC, Ss = 0.8, S1 = 0.22 (off in example 1) |
| Concrete | C30 / B420C, covers 50 / 60 mm |
1. The starter wall
lythos-wall example -o project.lwall
lythos-wall run project.lwallCANTILEVER RETAINING WALL — RESULTS
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Wall: H = 6.00 m, B = 4.80 m (toe 1.20 m, heel 3.00 m), stem 0.30–0.60 m, footing 0.70 m, soil over the toe 0.50 m, β = 0.0°
Earth pressure: Rankine, K = 0.3073 at ω = 0.0° on the virtual back, h = 6.00 m
ΣV = 455.5 kN/m, ΣH = 118.0 kN/m, M_R = 1262.7 kNm/m, M_O = 254.4 kNm/m, e = 0.187 m
STABILITY
FS · static required
Sliding 1.55 1.50 OK
Overturning 4.96 2.00 OK
Eccentricity 0.187 0.800 OK
Bearing capacity 7.40 3.00 OK
Global stability (Bishop) 1.74 1.50 OK
Global stability (Fellenius) 1.40 1.50 for comparison
Sliding resistance: friction 166.7 + adhesion 16.1 + passive 0.0 = 182.8 kN/m
Base pressure: toe 117.5 kPa, heel 86.1 kPa, in contact over 4.80 m
B' = 4.553 m, σv = 107.3 kPa, q_ult = 794.2 kPa (Vesić (1973))
BEARING CAPACITY BY METHOD
Method Nc Nq Nγ q_ult kPa q_ult / FS kPa FS
Vesić (1973) 30.14 18.40 22.40 794.2 264.7 7.40
Meyerhof (1963) 30.14 18.40 15.67 614.3 204.8 5.73
Brinch Hansen (1970) 30.14 18.40 15.07 589.9 196.6 5.50
Terzaghi (1943) 37.16 22.46 20.12 1,568.0 522.7 14.61
EN 1997-1 Annex D 30.14 18.40 20.09 747.4 249.1 6.97
EARTH PRESSURE BY METHOD (virtual back)
Method K ω ° Kh P kN/m Ph kN/m Pv kN/m
Rankine 0.3073 0.0 0.3073 118.0 118.0 0.0
Coulomb 0.2750 21.4 0.2560 105.6 98.3 38.6
At rest (K0) 0.4701 0.0 0.4701 180.5 180.5 0.0
Trial wedge 0.2750 21.4 0.2560 105.6 98.3 38.6
Rankine passive (Kp) 3.000
Coulomb passive (Kp) 4.977
REINFORCED CONCRETE DESIGN (TS 500)
C30 / B420C: fcd = 20.00 MPa, fctd = 1.278 MPa, fyd = 365.2 MPa, ρmax = 0.0200
SECTIONS
Section h mm d mm Md kNm Vd kN As req. mm² As min mm² Bars As prov. mm² Mr/Md Vcr/Vd Comb. Status
Stem, base (back face) 600 543 288.6 123.5 1,500 1,200 Ø14/100 1,539 1.03 3.65 C1 OK
Footing, bottom (toe) 700 631 96.7 76.2 423 1,400 Ø18/175 1,454 3.38 6.88 C1 OK
Footing, top (heel) 700 631 246.9 128.8 1,092 1,400 Ø18/175 1,454 1.32 4.07 C2 OK
Stem, front face (minimum) 600 600 Ø14/250 616 OK
Stem, horizontal (each face) 450 337 Ø12/300 377 OK
Footing, along the wall (each face) 700 525 Ø12/200 565 OK
The stem bars run the full height.
BAR BENDING SCHEDULE (per metre of wall)
Pos. Bar Ø mm s mm Length m Number /m Total m kg/m Mass kg
1 Stem, back face, full height 14 100 6.05 10.00 60.54 1.208 73.2
2 Stem, front face 14 250 6.05 4.00 24.18 1.208 29.2
3 Stem, horizontal 12 300 1.00 36 36.00 0.888 32.0
4 Footing, bottom 18 175 5.16 5.71 29.50 1.998 58.9
5 Footing, top 18 175 5.16 5.71 29.50 1.998 58.9
6 Footing, along the wall 12 200 1.00 48 48.00 0.888 42.6
Steel per metre of wall 294.8
Concrete 5.745 m³/m, steel 294.8 kg/m (51 kg/m³)
The stability checks need a heel of 2.87 m; the wall has 3.00 m.Reading the output. Sliding is the tightest check (1.55 against 1.50); the stability checks need a 2.87 m heel and the wall has 3.00 m. Coulomb gives a smaller thrust than Rankine because the thrust leans on the virtual back; the trial wedge reproduces Coulomb. The five bearing methods span 590 to 1 568 kPa — Terzaghi's factors stand apart. At the stem base Mr/Md = 1.03: Ø14/100 is just enough. Fellenius is shown for comparison only; it is known to be conservative.
2. An earthquake by TBDY 2018
Turning the earthquake on ("seismic": {"enabled": true, ...} in the project file):
lythos-wall run seis.lwallSTABILITY
FS · static required FS · seismic required
Sliding 1.55 1.50 OK 0.74 1.10 NOT OK
Overturning 4.96 2.00 OK 1.87 1.50 OK
Eccentricity 0.187 0.800 OK 0.978 1.600 OK
Bearing capacity 7.40 3.00 OK 1.47 1.40 OK
Global stability (Bishop) 1.74 1.50 OK 1.20 1.10 OK
Global stability (Fellenius) 1.40 1.50 for comparison 0.97 1.10 for comparison
Sliding resistance: friction 166.7 + adhesion 16.1 + passive 0.0 = 182.8 kN/m
Base pressure: toe 117.5 kPa, heel 86.1 kPa, in contact over 4.80 m
B' = 4.553 m, σv = 107.3 kPa, q_ult = 794.2 kPa (Vesić (1973))
EARTHQUAKE (TBDY 2018)
Parameter Value
Local site class ZC
Ss / S1 0.800 / 0.220
Fs / F1 1.200 / 1.500
SDS / SD1 0.960 / 0.330
TA / TB / TL 0.069 / 0.344 / 6.0 s
Displacement factor βr 0.50
kh / kv 0.192 / 0.096
Dynamic thrust Mononobe–Okabe
KAE 0.4509
Dynamic increment ΔPAE 34.3 kN/m @ 3.00 m
Inertia of wall and soil kh·W 85.3 kN/m
Governing kv kv upwardReading the output. SDS = 0.8 × 1.2 = 0.96 and, for a wall free to move (βr = 0.5), kh = 0.5·0.4·0.96 = 0.192. The dynamic increment (34 kN/m) is smaller than the inertia of the wall and the soil on its heel (85 kN/m) — the inertia is the larger part of the seismic load that brings sliding down to 0.74. The heel also carries more moment in the seismic combination C3−, and its top steel goes from Ø18/175 to Ø18/150.
3. A shear key and a longer heel
The wall of example 2 slides. A shear key with the passive resistance in front of it counted, then a deeper key, then a slightly longer heel:
from lythoswall import forms
from lythoswall.web.session import Session
session = Session(lang="en")
base = forms.defaults() # H = 6 m, B = 4.8 m, heel 3.0 m
base["seismic_enabled"] = True # TBDY 2018, ZC, Ss = 0.8, S1 = 0.22
cases = {
"as drawn": {},
"shear key": dict(key_enabled=True, key_depth=0.6, passive=True),
"shear key 1.0 m": dict(key_enabled=True, key_depth=1.0, passive=True),
"+ heel 3.40 m": dict(key_enabled=True, key_depth=1.0, passive=True, heel=3.4),
}
for name, change in cases.items():
r = session.analyse({**base, **change})
sliding = r["stability"]["rows"][0]["cells"]
print(f"{name:16s} sliding FS static {sliding[1]} seismic {sliding[4]}"
f" heel needed {r['required_heel']:.2f} m")as drawn sliding FS static 1.55 seismic 0.74 heel needed 7.75 m
shear key sliding FS static 2.08 seismic 0.98 heel needed 4.57 m
shear key 1.0 m sliding FS static 2.28 seismic 1.07 heel needed 3.39 m
+ heel 3.40 m sliding FS static 2.43 seismic 1.10 heel needed 3.39 mWith no key the heel would have to be 7.75 m. A 1.0 m key brings the heel it needs down to 3.39 m, and with a 3.40 m heel every check holds, static and seismic. The key's moment and shear are designed like the rest of the wall.
4. The drawing and the DXF
lythos-wall run project.lwall -o report.pdf --dxf wall.dxfThe report carries every table above with the figures, the warnings and the method notes. wall.dxf is an AutoCAD R12 drawing in millimetres, with the layers CONCRETE, REBAR, REBAR_DIST, DIMENSION, TEXT, GROUND and LEADER; the bar positions match the bar bending schedule.