`*Embedded region, interaction-surface`

*Embedded region, interaction-surface [, type=constant | type=mohr-coulomb]
                                      [, section=circular]
                                      [, tension=no | tension=yes]
                                      [, sigma=interface | sigma=soil]
                                      [, recovery=idw | recovery=gaussian]
                                      [, lrec=<real>] [, pmax=<real>]
                                      [, baselaw=elastic-plastic | baselaw=hyperbolic]
                                      [, bfac=<real>] [, bexp=<real>]
                                      [, ghost=yes | ghost=shaft | ghost=no]
                                      [, np=<integer>] [, nb=<integer>]

Upcoming release

The *Embedded region, interaction feature will be available with the upcoming release

The synopsis is wrapped for readability; the keyword and all selected options are written on one input line.

This keyword couples three-dimensional beam elements to a three-dimensional continuum through an implicit cylindrical shaft surface and, optionally, a base disk. The guest beam retains its translational and rotational degrees of freedom. The shaft and base tractions are integrated over analytically generated coupling points; no surface finite elements are created.

See the Theory Manual for the kinematics, constitutive response, stress recovery, base cubature and ghost-zone treatment.

Keyword options

Option	Values	Default	Availability and effect
`Type`	`constant`, `Mohr-Coulomb`	`constant`	Tangential shaft capacity. The selected type also determines the in-plane base cap when separation is active.
`Section`	`Circular`	`Circular`	Only circular interaction surfaces are currently supported.
`Tension`	`no`, `yes`	`no`	`no` activates separation at shaft and base points. `yes` restores the bilateral legacy response; see Contact behaviour.
`sigma`	`Interface`, `Soil`	`Interface`	Pressure source for `Type=Mohr-Coulomb`.
`Recovery`	`IDW`, `Gaussian`	`IDW`	Host-stress recovery for `Type=Mohr-Coulomb, sigma=Soil`.
`Lrec`	positive real	`1.0`	Gaussian support factor in \(\ell=L_{\mathrm{rec}}\max(R,h)\). Requires `Recovery=Gaussian`.
`pmax`	positive real	none	Upper bound on the pressure entering the shaft Mohr–Coulomb capacity. It does not cap mechanical normal traction or base resistance.
`Baselaw`	`Elastic-Plastic`, `Hyperbolic`	`Elastic-Plastic`	Axial base mobilisation. Requires a base node set when specified explicitly.
`Bfac`	real \(\ge1\)	`1.0`	Hyperbolic asymptote factor \(f\). Requires `Baselaw=Hyperbolic`.
`Bexp`	positive real	`1.0`	Hyperbolic mobilisation exponent \(m\). Requires `Baselaw=Hyperbolic`.
`ghost`	`yes`, `shaft`, `no`	`yes`	`yes`: shaft cylinder and toe half-sphere; `shaft`: cylinder only; `no`: no elastic ghost response.
`np`	integer \(\ge3\)	`8`	Circumferential shaft points at every beam integration station.
`nb`	`1` or integer \(\ge4\)	`9`	Number of base-disk points. `nb=1` has no moment arm; larger rules use one centre point and a moment-preserving ring.

sigma, Recovery, Lrec and pmax are valid only with the combinations stated above. Unknown, duplicated or incompatible options are rejected.

Data lines

One or more region definitions may follow the keyword line.

Constant shaft capacity

<guest elset>, <host elset>, <base nset | none>, D, k_t, k_n, k_b, t_ult, sigma_lim [, E_ghost, nu_ghost]

Mohr–Coulomb shaft capacity

<guest elset>, <host elset>, <base nset | none>, D, k_t, k_n, k_b, c, phi, sigma_lim [, E_ghost, nu_ghost]

The ghost parameters are present if and only if ghost=yes or ghost=shaft.

Data item	Unit	Requirement and meaning
`guest elset`	--	Set of `u2-beam-3D` or `u3-beam-3D` elements. Every guest node must provide `U1`–`U3` and `R1`–`R3`.
`host elset`	--	Three-dimensional continuum host region searched for shaft and base points.
`base nset`	--	Toe-node set. Every member must be an end node of a coupled guest beam. Use `none` to omit the base disk.
`D`	L	Interaction-surface diameter; \(D>0\).
`k_t`	F/L³	Tangential shaft stiffness per unit area; \(k_t>0\). The same value is used axially and circumferentially.
`k_n`	F/L³	Normal shaft stiffness per unit area; \(k_n\ge0\).
`k_b`	F/L³	Initial axial base tangent and closed-state in-plane base stiffness per unit area. It must be positive when a base is present.
`t_ult`	F/L²	`Type=constant`: shaft capacity. A non-positive value leaves the shaft tangential response elastic. With `Tension=no`, the same positive value caps in-plane base traction.
`c`	F/L²	`Type=Mohr-Coulomb`: interface cohesion; \(c\ge0\).
`phi`	degree	`Type=Mohr-Coulomb`: friction angle; \(0\le\varphi<90^\circ\). `c` and `phi` must not both be zero.
`sigma_lim`	F/L²	Compressive axial base capacity. For `Elastic-Plastic`, a non-positive value leaves the axial response elastic. `Hyperbolic` requires a positive value.
`E_ghost`	F/L²	Young's modulus of the elastic ghost response; positive.
`nu_ghost`	--	Ghost Poisson ratio; \(0\le\nu_{\mathrm{ghost}}<0.5\).

Contact behaviour

`Tension=no` — default

A shaft point with negative normal relative displacement is open. Its normal, axial and circumferential tractions and its complete contact tangent are zero. The tangential slip reference follows the open motion so that recontact starts without a spurious traction jump.

A base point opens when its axial constitutive traction becomes tensile. The complete base traction and tangent are then zero. While closed, the in-plane base response is elastic–perfectly plastic:

Type=constant: positive t_ult is the in-plane cap; a non-positive value gives an elastic in-plane response;
Type=Mohr-Coulomb: \(t_{\mathrm{cap,b}}=c+q_{\mathrm b}\tan\varphi\), where \(q_{\mathrm b}\) is the current compressive axial base traction.

`Tension=yes` — bilateral legacy response

The shaft normal spring transmits unlimited tension and compression. The axial base relation is bilateral, and the in-plane base response is the uncapped linear spring \(k_b\). This option is intended mainly for regression and comparison with the earlier response.

Capacity-pressure source

For Type=Mohr-Coulomb,

\[ t_{\mathrm{cap}}=\max(c+p_{\mathrm{cap}}\tan\varphi,0). \]

sigma=Interface: the source is a lagged interface-pressure state seeded from the geostatic host stress and updated by the normal spring. The initial pressure is recovered with the internally generated inverse-distance map; Recovery and Lrec are not available for this source. Consequently, k_n affects both compatibility and shaft capacity.
sigma=Soil: the source is the compressive normal stress recovered from the committed host stress field. k_n then acts primarily as a normal-compatibility penalty.
pmax, when present, limits only \(p_{\mathrm{cap}}\).

Both sources use committed values during the current increment. Their trial states are committed only after convergence.

Base mobilisation

For Baselaw=Elastic-Plastic, the monotonic compressive envelope is

\[ q_{\mathrm b}=\min(k_b s,\sigma_{\lim}) \]

when \(\sigma_{\lim}>0\).

For Baselaw=Hyperbolic,

\[ q_{\mathrm b}=\min\left[ \frac{k_b s}{\left(1+\left[\dfrac{k_b s}{f\sigma_{\lim}}\right]^m\right)^{1/m}}, \sigma_{\lim} \right]. \]

Bfac is \(f\) and Bexp is \(m\). Bexp=1 gives the Kondner hyperbola. For \(f>1\), the cap is reached at

\[ s^*=\frac{f\sigma_{\lim}}{k_b}(f^m-1)^{-1/m}. \]

Unloading and reloading are linear with slope \(k_b\) from the largest converged compressive displacement.

Geometry, host mapping and state

Two axial Gauss stations are generated per two-node beam and three per three-node beam.
np points are distributed uniformly around every station, offset by half a circumferential segment.
Shaft areas sum to the cylindrical area when all points are active.
The default nb=9 disk consists of one centre point and eight points at \(0.75R\).
A point outside the host set is inactive and its tributary area is not redistributed.
Host element identities and natural coordinates are determined in the reference configuration and remain fixed.
Guest beam nodes and host continuum nodes must be topologically distinct, even when their coordinates coincide.
Plastic slips, interface-pressure state and base history are committed only after a converged increment.
Explicit dynamic steps are not supported.

Ghost zone

ghost=yes and ghost=shaft replace the mechanical constitutive update at supported host integration points inside the selected virtual pile volume by linear elasticity with E_ghost and nu_ghost. Original material state variables remain frozen. For coupled displacement–pressure elements, hydraulic terms remain active.

Membership is evaluated at host integration points. The represented ghost volume therefore depends on the host mesh, quadrature and pile position. This dependence is particularly pronounced for one-point reduced-integration solids and must be checked in mesh studies.

Examples

Mohr–Coulomb shaft, Gaussian recovery and capped hyperbolic base

*Embedded region, interaction-surface, type=mohr-coulomb, sigma=soil, recovery=gaussian, lrec=1.0, tension=no, ghost=shaft, np=8, nb=9, baselaw=hyperbolic, bfac=18.5, bexp=0.255
pile-shaft, soil, pile-toe, 0.8, 43760., 481357., 264413., 0.75, 25.11, 1691., 75000., 0.30

Constant-capacity shaft without a base or ghost zone

*Embedded region, interaction-surface, type=constant, tension=no, ghost=no, np=8
anchor-grout, soil, none, 0.20, 20000., 50000., 0.0, 100.0, -1.0

With none, k_b and sigma_lim are read but no base contribution is generated.

Theory manual

The theory behind it

*Embedded region, interaction-surface