## Description

**Fondazioni CA: **

**Soil modeling for piles**

In seismic zones, “analyses for evaluating pile stresses and displacements must take into account the dependence of soil stiffness on the tensional and deformational state” (§ 7.11.5.3.2 NTC). Practical achievement of this directive can be achieved by using an appropriately reduced secant value of the soil elastic modulus or, more properly, by using a nonlinear soil model.

Transverse and axial pile-soil interaction can be modelled either by considering the soil as a continuous, homogeneous elastic medium (Poulos-Randolph), or as a Winkler-like medium with linear or nonlinear springs with a choice of multiple constitutive bonds (p-y curves for transverse pile-soil interaction and t-z transfer curves for axial interaction) to be assigned to layered soils. In particular, the following nonlinear models applicable to both coherent and inconsistent soils are provided:

- Hyperbolic model (Carter)
- Parabolic model (Matlock)
- Elasto-plastic model

For better estimation of axial pile settlements at the SLE, Chin’s nonlinear hyperbolic model has been implemented, which is particularly suitable when performing load-sediment tests on pilot piles.

Also, for better estimation of axial pile settlements (especially in mixed foundations), the (optional) calculation of axial interaction between piles based on the prior determination of interaction factors was also implemented.

**In the case of mixed foundations**, the calculation of the interaction between the plates and the piles is based on the PDR method in order to reduce the Winkler coeff. assigned to the plates in the absence of the piles, arriving at its effective value (usually very small) that takes into account the aforementioned interaction.

Provision is made for approximate kinematic bending moment calculation in two-layer soil (Gazetas 1997). The moment thus calculated is added to that present in the pile both in the section straddling the interface between the two layers and in the section at the attachment with the header.

The structure is solved by automatic discretization of all resisting elements based on a predetermined average mesh size. It is also possible to assign rigid offsets to beam end nodes to account for any eccentricities with respect to the nodes and/or to model beam sections that fall within the abutments.

Optionally, interaction effects can be automatically calculated for piles in groups with reference to transverse loads (the new seismic regulations explicitly require their evaluation).

**The design and verification of reinforcement of beam,** ground slab and pile sections are carried out at ultimate and serviceability limit states according to the new technical standards (DM 17.01.2018).

For plates, slab foundations and continuous beams (including those belonging to ground beams) there is also provision for the design of reinforcement with the possibility of interaction by the user and the creation of files in DXF format to enable the import of program-generated graphs into any CAD program.

**Consecutive beams**

They can be generated as a stand-alone predefined model or as a consecutive series of beams within a ground beam.

Individual spans can be formed either as beams in elevation or as beams on elastic Winkler soil.

The soil is modelled by means of concentrated elastic springs applied at the beam discretization nodes.

The beam supports may also consist of foundation piles (whose geometric and geotechnical characteristics are to be defined in appropriate program modules) that are considered connected to the beam with continuity constraints to translation and rotation.

Each of the beams can be rectangular T-shaped, double T-shaped L-shaped, double T-shaped with unequal wings, circular, and generic (for data). Both the eccentricity of the axis of the beams with respect to the end nodes and the sections of the beams that fall within the ground slab sections can be modelled by automatic or numerical definitions of rigid segments (offsets).

Constant and linearly varying distributed loads are allowed. Any node can be constrained or loaded according to the vertical translator’s direction and the rotary ones around the X and Y axes of the general plan reference.

Load conditions and load combinations and their combination factors should always be defined. The combinations can be either strength (SLU) or serviceability (SLE).

**Foundation piles and micropiles**

Reinforced concrete piles and micropiles made of reinforced concrete or tubular steel can be calculated either in isolation or as a group connected with a continuity or spherical hinge constraint to any predefined rectangular ground beams, ground slab or plinth. The longitudinal axis of individual posts can be inclined at any angle to the vertical. The usually non-negligible thickness of the pile connection header can be automatically modelled by the program by means of a rigid ashlar that connects the attachment section of the pile to the header with the pile reference node usually placed on the extrados of the header.

Starting from the linear elastic behaviour of the pile, the program provides a choice between multiple linear and nonlinear pile-soil interaction models:

- soil modelled as a continuous homogeneous medium with linear elastic behaviour with a solution of the Midlin integrodifferential equation approximated by M.F. Randolph’s parametric study
- soil schematized as linear or nonlinear Winkler springs acting transverse and axial to the pile axis whose reactions are applied to the finite element discretization nodes of the rods into which the pile is divided

The schematization using nonlinear springs allows better capturing of both the distinctly nonlinear behaviour of the interaction (the new seismic standard explicitly requires this type of analysis) and the variability of soil characteristics with depth (stratified soil).

Hyperbolic, parabolic (Matlock) and elastoplastic p-y interaction curves (for transverse deformations) are implemented in the program. For axial deformations, nonlinear t-z type curves valid along the shaft and q-b curves related to the behaviour at the pile tip are provided.

The systematization using nonlinear springs allows better capturing of both the distinctly nonlinear behaviour of the interaction (the new seismic standard explicitly requires this type of analysis) and the variability of soil characteristics with depth (stratified soil).

Hyperbolic, parabolic (Matlock) and elastoplastic p-y interaction curves (for transverse deformations) are implemented in the program. For axial deformations, nonlinear t-z type curves valid along the shaft and q-b curves relate to reinforced concrete piles, and longitudinal and transverse reinforcement is designed and graphically represented based on a special list of options.

The deck in which the pile heads are arranged can be calculated as either being extensionally rigid (case of plates on piles) or extensionally deformable (case of slab foundation on widely spaced piles or with connecting beams that are not sufficiently rigid in the horizontal plane).

The program considers the piles connected with continuity constraint to the beams and fields at the nodes, so, the overall calculation scheme is always that of a three-dimensional one-plane frame with displaceable nodes in which the portions (also inclined with respect to the vertical) are the piles and the horizon by beams and ground slab. As a consequence, the horizontal loads transmitted from the superstructure to the said frame results distributed among the assigned piles both according to their respective stiffnesses at the horizontal translation of the piles and the stiffnesses of the beams and fields connected to the piles.d to the behaviour at the pile tip are provided.

**Ground beams**

They consist of a generic set of beams however arranged in the plane of the deck. Beams can be modelled either as beams in elevation or as beams on Winkler elastic soil. The characteristics of the beam sections and the loads applied to them are as illustrated for continuous beams. Any eccentricity of the axis of the beams with respect to the two end nodes can be modelled by rigid segments (node offsets). The intersection nodes of the beams can be locations of fixed or elastic constraints or concentrated loads (vertical load and torques in the two X,Y directions of the reference).

The calculation also considers both the torsional stiffness of the beam section (possibly reduced by an appropriate efficiency factor of the user’s choice) and that produced by the elastic ground reaction in the direction transverse to the beam axis.

Program outputs include graphs of deformation, stress diagrams (bending, torsion, shear) and calculation of reinforcement in all beam discretization sections.

If continuous beams are defined within the ground beam they are reinforced in bending, shear and torsion in the same manner as set out in the description of continuous beams.

Changes made (via the numerical editor or in the options window) to the longitudinal reinforcement can be rechecked interactively. The reinforcement graph is exportable in DXF format.

**Foundation plates**

The program schematizes foundation plates of generic shape from an appropriate subdivision of its surface into quadrilateral fields which, in the subsequent calculation phase, are automatically discretized into quadrilateral finite elements in whose nodes the ground slab stresses and orthogonal mesh reinforcement assumed to be oriented in the same direction as the general reference axes are evaluated.

The ground is schematized by means of independent vertical springs (Winkler behaviour) applied, automatically, in the nodes of the finite elements.

Fixed and elastic constraints can be inserted at the vertices of the ground slab fields or concentrated loads applied.

Along the sides of the fields fixed constraints, loads and distributed torques with constant or linearly varying intensity can be assigned.

A beam can be inserted in each of the sides of the fields (even belonging to two contiguous fields), which is, in that case, made continuous with the ground slab or plate at the same nodes where the side of the fields in which it is inserted is discretized. This allows the modelling and calculation of ribbed foundation rafts or a ribbed ground slab (cofferdams) in elevation. The program formulates a reinforcement proposal relative to the entire plates by providing zones of refinement at the abutments. It is possible to vary the pitch and diameter of the reinforcement and interactively reverify the new arrangement. The reinforcement graph is exportable in DXF format. In addition to flexural checks, punching checks are also provided at the grounds slabs.

**Surface plinths**

They are planned to be rectangular in plan and have constant, undeformable cross-sections. Interaction with the soil is modelled according to the usual Winkler-style scheme by assigning to each slab foundation type an appropriate subgrade constant. The plinths are to be referred to as the nodes of the generic plan scheme, which, in this case, represent the barycenters of the columns to be characterized by their cross-section and the concentrated loads (vertical load, torques and shear in the two directions X,Y of the reference) they transmit on the extrados of the plinth.

The assigned plinths can be isolated or connected to each other by means of beams (on elastic soil or not) constrained to the same nodes to which the plinths are referenced. In the latter case, the pressures exerted by the plinths on the soil depend not only on the loads directly applied to the plinths but also on the stiffnesses of the other plinths and the assigned connecting beams.

The reinforcements of the plinths in the two directions are calculated on the basis of the bending and shear stresses transmitted by the soil reaction prism; these stresses are evaluated in the plinth sections flush with the columns.

Each of the plinths can, in addition, be assigned a socket to accommodate prefabricated columns with rectangular cross-sections.

**Ground beams on piles**

Pile-supported foundation ground beams differ from superficial ground beams on Winkler-style soil in the circumstance that soil reaction must be excluded for the beams by express regulatory provision (§ 7.2.1 “the concurrent use of pile foundations with superficial foundations must be avoided”) so that all horizontal and vertical loads transmitted to the foundation must be assigned to the piles alone. Piles should be assigned at the beam end nodes. The piles are considered to be always centred at the node they belong to, unlike the beams which can be eccentric to the two end nodes.

Continuous beams within the ground beams are reinforced in bending, shear, and torsion in the same manner as set forth in the description of continuous beams. Changes made (using the numerical editor) to longitudinal reinforcement can be rechecked.

**Plates on piles**

Foundation rafts on piles differ from surface rafts on Winkler soil in the circumstance that for the ground slab fields the soil reaction should be excluded by express normative provision (all horizontal and vertical loads acting on the foundation should be entrusted only to the piles). Piles may be assigned only at the nodes located at the vertices of the ground slab fields; the subdivision of the plates into fields should, therefore, be made on the basis of the desired arrangement of the piles. Stiffening ribs may also be provided along the sides of the fields by assigning normally rectangular beams that are considered congruent with the fields adjacent to the side in which they are inserted. The distribution of horizontal and vertical actions acting on the plates is carried out taking into account the stiffnesses of the piles and the plates. This reduction of stiffnesses is carried out by the method of reductive multipliers of p-y curves (linear and nonlinear) according to the experimental curves proposed by R.L.Mokwa. The case of mixed foundations has been mentioned above.

**Plinths on piles**

For rectangular plinths on 2-, 4-, 5-, 6-, 8-, and 9-piles in current use, there is the automatic generation of a special predefined model that allows both calculation and graphical representation of the geometry and reinforcement designed for the plinth, the piles, and for the reinforced concrete socket, if any, intended to house the precast abutment. The predefined model consists of equivalent elastic ground beams of 12 beams that connect with continuity constraints the abutment to the piles. That is, simplified schematizations of ‘high’ plinths on piles consisting of inclined struts and ties, widely assumed in the literature and in many calculation programs, are not used in the program. Such schemes are acceptable only when the plinth is subjected to a single vertical load transmitted by an abutment centred with respect to the piles: in the presence of strong torques transmitted from the abutment to the plinth (seismic calculation) or in the case of eccentric abutments or with elongated section (septa and shear walls), the ideal resistant trusses would have to be redefined according to schemes that vary according to the direction of the applied torque, the geometry of the abutment and the plinth, making the above-mentioned ground beams calculation schemes uncertain or no longer ‘simplified’.

Therefore, the aforementioned simplified flexural scheme was assumed (for both ‘high’ and less rigid plinths) to take into account, albeit in an approximate manner, the shear and bending deformability of the plinth, the effective dimensions of the abutment, and the continuity constraint with the piles.

4out of 5Stefano(verified owner)–Buon programma. L’ho trovato utile anche x calcolare plinti a bicchiere su monopalo in calcestruzzo armato in opera.

5out of 5goristefano(verified owner)–Ottimo programma