landfilldesign.com - Concrete Anchor Calculator

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Concrete Anchor - Design Calculator

Anchorage is designed to prevent wind and water from moving under the geomembrane; it is not designed to allow geomembranes to be tensioned. Concrete anchors have been used as an anchorage block, but seldom is the tension justified. This is directly reflected in the anchorage ratio:

AR	Anchorage Ratio
T_{GM allow}	Allowable geomembrane tension from ASTM D3886
T_{AT allow}	Allowable concrete anchor tension from analytic model

Anchorage Ratio > 1	Geomembrane pull-out mode controls
Anchorage Ratio = 1	Balanced Design
Anchorage Ratio < 1	Geomembrane tension rupture mode controls

Note that the factor of safety is placed on the geomembrane force T, which is used as an allowable value.

σ_allow	The allowable geomembrane stress
t	The geomembrane thickness
σ_ult	The ultimate geomembrane stress, e.g., yield or break
T_ATallow	Allowable anchor trench tension
γ	Soil unit weight
γ_con	Concrete unit weight
d	Thickness of the cover soil
L	Embedment length
d_AT	Depth of the concrete anchor trench
δ_L	FML / soil friction angle (below geomembrane)
δ_U	Cover soil / geomembrane friction angle (above geomembrane)
Φ	Soil internal friction angle
β	Side slope angle
K_P	Coefficient of passive earth pressure = tan²(45^o+ Φ/2)
K_A	Coefficient of active earth pressure = tan²(45^o- Φ/2)
FS	The factor of safety for geomembrane against tension response
F_U_σ	Shear force above geomembrane due to cover soil (for thin cover soils tensile cracking will occur and this value will then be negligible)
F_L_σ	Shear force below the geomembrane due to cover soil
F_LT	Shear force below geomembrane due to vertical component of T_allow
σ_n	Applied normal stress from the cover soil

Figure 1- Cross section of concrete anchor section and related stresses and forces involved

Input Values

Geometry
Side slope angle (β)		degrees
Thickness of the cover soil (d)		mm
Embedment length (L)		m
Depth of the concrete trench (d_AT)		mm
Soil Properties
FML / soil friction angle (δ_L)		degrees
Cover soil / FML friction angle (δ_U)		degrees
Soil friction angle (Φ)		degrees
Soil unit weight (γ)		kN/m³
Concrete unit weight (γ_con)		kN/m³
Geomembrane Properties
Thickness geomembrane (t)		mm
Allowable stress in geomembrane (σ_allow)		kPa

References

"Designing with Geosynthetics". R.M. Koerner, Prentice Hall Publishing Co., Englewood Cliffs, NJ, 1998.

"Geosynthetic Design Guidance for Hazardous Waste Landfill Cells and Surface Impoundments", G. N. Richardson and R. M. Koerner, 1987.