A ground anchor has two forms of capacity, a geotechnical and a structural resistance. The structural resistance of the tendons is defined by EC steel standards while the bonded zone has to be examined for its pull-out capacity (geotechnical check). The new software includes a number of ground anchor (tieback) sections. Hence, a ground anchor section can be reused over and over in many different support levels and in many different design sections (the same approach is also utilized for steel struts, rakers (inclined struts), and concrete slabs). The tieback capacities (ultimate and permissible) can be calculated using the following equations:
Ultimate geotechnical capacity used for the geotechnical yielding is:
RULT.GEO = LFIX x π x DFIX x qULT/(γ R)
2. The design geotechnical capacity (for stress check ratios) is calculated as:
RDES.GEO = LFIX x π x DFIX x qULT/ γ R x γ SU xFS Geo)
Where:
qULT = Ultimate Skin friction (options available)
LFIX = Fixed body length
DFIX = Fixed body diameter (0.09m to 0.15m typically)
FS Geo = 1.0 to 2.0 user specified safety factor.
FS Geo = 1.0 in M2 design approach methods.
γ R = 1 to 1.2 Resistance factor geotechnical capacity
γSU = 1 to 1.4 (Shear strength, used for bond values)
Note that γ R and γ SU are by default 1, but take Eurocode or DM08 specified values when a design approach is used.
3. The ultimate and design Structural capacity can be calculated as:
PULT.STR = φULT.CODE x (Area of Tendons) x Fy
φ ULT.CODE = Material strength reduction factor typically 0.9
PDES.STR = φDES x (Area of Tendons) x Fy
φ DES = Material strength reduction factor 0.6 to 0.9
The ultimate capacity is used to determine the structural yielding of the element while the permissible is used for the stress checks. φULT.CODE is always picked up from the structural code that is used. φDES can be specified by the user or can be set automatically when the some code settings are specified. When Eurocodes are used φALL should be the same as φULT.CODE.
Note that φ= 1/ γ M
In the default setting during a Nonlinear analysis, the new software models a tieback automatically as a yielding element (Wire with yielding properties) with its yielding force determined as the minimum STR or GEO capacity. A ground anchor can also be modeled as a non-yielding wire element by selecting the appropriate option in the Advanced Tab of the Tieback dialog. However, it is felt that due to legal reasons it is better to include a tieback as yielding element by default.
The Figure below shows the main tieback section dialog. The main parameters of interest are the steel material, the cross sectional area of the steel tendons, and the fixed body diameter (Dfix).
Figure: Main tieback section dialog (Elastic-Wire command in Red)
The geotechnical capacity represents the capacity of the soil to resist the tensile forces transferred by the steel strands to the grouted body. The new software subdivides the fixed body into a number of elements were soil resistance is computed. As previously mentioned, the geotechnical tieback capacity is evaluated for every stage. Within the current Nonlinear engine, it is currently possible to change the yield limit of an ELPL spring from stage to stage. Initially, in the Nonlinear mode the software uses the capacity at the stage of installation. The capacity is adjusted at each stage and the final support check is performed for the actual capacity for each stage. A number of options exist for defining the geotechnical capacity of a tieback:
Soil resistance is computed from frictional and cohesive components. For the frictional component, DeepEX uses the average of the vertical and lateral at-rest stress times the tangent of the friction angle. For the cohesive component, adhesion factors can be applied. Furthermore, individual densification factors can be applied separately to the frictional and cohesive components to simulate the effect of pressure grouting. End bearing at the start of the grouted body is ignored. These calculations should be considered as a first order estimate. Hence, in this case the ultimate skin friction can be defined as:
t ULT =F1 x 0.5 x (σ’V+ σ’H-Ko) x tan (φ) + F2 x α x (c’ or SU)
In an undrained analysis the software will use SU and φ=0. For a drained analysis the program will use φ and c’.
Where
F1 = Frictional densification factor (default 1)
F2 = Cohesional densification factor (default 1)
α = Adhesion factor (default =1), but program also offers a dynamic tri-linear approach for defining this parameter based on c’ or Su. In this approach:
α = Value 1 = 0.8 if c’ or Su <= Climit1
α = Value 2 = 0.5 if c’ or Su >= Climit2
α = Linear interpolation for c’ or Su between Clim1 and Clim2.
User-defined geotechnical capacity (and structural) defined from the advanced tieback tab.
Figure: Advanced tieback dialog tab
Ultimate specific bond resistance for tieback section.
t ULT = qULT in Geotechnical tab of tieback section
Figure: Geotechnical tieback dialog tab (Wire command in Red)
Ultimate bond resistance determined from integrating soil ultimate skin friction resistances over the fixed length.
t ULT = qULT from Soil type (Bond Tab)
In this case, the skin friction can be determined from the Bustamante design charts when pressuremeter test data are available.
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When a Eurocode design approach is applied ultimate pull out resistance is calculated from bond values by applying the same safety factor (in combination with all other safety factors) as for the undrained shear strength Su. However, in certain cases like the M2 the program does not apply the User Specified FS_geo in order to produce consistent capacity results. Thus, when Eurocode 7 or NTC settings are applied, the user specified FS_Geo is only used in cases where M1 factors are applied.
When the pullout resistance is calculated from soil cohesion and friction, then the skin friction is calculated directly from the adjusted friction angle and shear strength/cohesion values according the M safety factors.
Figure: Estimation of bond resistance for tiebacks from TA-95 according to Bustamante.
Figure: Estimation of bond resistance for tiebacks from Pressuremeter tests FHWA and French recommendations.
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