CONSTRUCTION STAGE K₀
FROM A MODEL TO EQUILIBRIUM
Each construction stage describes what exists and what acts on it. The solver inherits the ground and structure history, then finds the movement needed to balance the change.
300 six-node triangles describe four soil layers. Beam and bar elements represent the wall and strut.
Add load, install support, remove soil, or lower the prescribed water level.
Iterate displacement and stress until internal forces balance the stage loads.
Pass stresses, plastic strain, structure forces, and total displacement to the next stage.
The model uses quadratic, six-node triangles (T6), three integration points per soil element, and small-strain plane strain: the out-of-plane strain is zero. Young’s modulus E controls elastic stiffness; c′ and φ′ control drained strength.
Mohr–Coulomb is elastic–perfectly plastic. Once the stress reaches the yield surface, plastic strain can develop. ψ = 0° sets zero dilation here. Red points indicate currently yielding integration points, not cracks or accumulated damage.
Water pressure is hydrostatic below the prescribed water level and zero above it. The retained side stays at +17.26 m; the pit is pumped to its floor during the deeper excavation stages.
Stress is tension positive, so compressive pore pressure is negative. The interface uses effective stress; the pressure difference between wall faces loads the wall directly. This model does not solve seepage or consolidation.
Vertical stress comes from the weight of the overlying soil. Subtract pore pressure to obtain effective vertical stress, then prescribe the initial horizontal stress:
This procedure assumes horizontal ground and horizontal layers. Initialization does not introduce gravity settlement. The next stage corrects any initial stresses reported outside the yield surface.
The wall is a three-node Mindlin beam. EA and EI describe axial and bending stiffness per metre out of plane. The strut is a two-node axial bar; displayed strut forces include its 3 m spacing.
Each wall face has a Coulomb interface that can slip or open. Interface elastic stiffness follows the Python API’s virtual-thickness rule and changes with soil E and R_inter. Before wall installation, paired nodes are tied as continuous soil.
Every phase declares all current loads, water, supports, and structures, even when unchanged. Omitting a load unloads it. Soil above the selected floor is deactivated.
History contains soil stress and plastic strain, wall forces, interface tractions and slip/gap, strut forces, and applied load. Total displacement accumulates the phase increments; removed soil is excluded from the displayed extrema. This symmetric half model combines reference phases 1–2 and 3–4.
A phase ramps its force change in increments. Newton iterations solve for equilibrium; difficult structural steps can retry with the initial stiffness and smaller increments.
The requested relative tolerance is 10⁻⁶. Structural fallback may accept up to 10⁻⁴, with those steps marked “relaxed”. An unsuccessful stage retains committed partial results and stops the sequence. A completed solve does not establish mesh convergence or validate the unresolved PLAXIS inputs.
THE SAME MODEL, IN YOUR APPLICATION
The browser runs the C++ solver as WebAssembly. Your application
calls the same solver through awatif_soil. Download a
self-contained example with your current settings and a mesh helper.
Supply nodes and six-node triangle connectivity, define materials, then assign a material to each element. Coordinates use metres; E and c use kPa.
soil = material(E=10_000, nu=0.3, c=1,
phi=30, psi=0, gamma=17, gamma_sat=18)
model = Model(nodes, elements, materials,
material_ids=material_ids)
model.fix(bottom_nodes, dx=0, dy=0)
model.phreatic(17.26, gamma_w=10)Use the same wall and strut declarations in every phase; change their active flags on installation. The geometry must conform to the wall and excavation levels.
model.traction(load_edges, ty=-surcharge)
model.wall(chain, EA=wall_EA, EI=wall_EI,
R_inter=R_inter, active=wall_installed)
model.strut(wall_node, centre_node, EA=strut_EA,
spacing=3, active=strut_installed)
model.deactivate(excavated_elements)
model.phreatic(floor, elements=pit_column)Create the initial stress from a ground-only phase. Each later model repeats everything still active and inherits the previous result’s state.
state = initial_model.k0_state()
for model in construction_models:
model.initial_stress(state)
result = model.solve(initial_load_fraction=0.25,
max_steps=200)
if not result.ok or result.load_factor < 1:
raise RuntimeError(result.message)
state = result.state
displacements is this phase’s increment.
total_displacements includes earlier phases. Wall
forces are per metre; strut() returns force per
strut.
u = result.total_displacements # m, [node, x/y]
M = result.wall(0).M # kNm/m
N = result.strut(0) # kN per strut
contact = result.interface(0, "left")
for step in result.steps:
if step.converged and step.relaxed:
print(step.relative_residual)Install the supplied evaluation wheel matching your platform and Python version, then run the downloaded script. The download includes setup instructions and NumPy-based meshing; Python does not execute inside this page. Annotated snippets above illustrate API usage; the complete download supplies all definitions and stages.
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