{
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"source": [
"# Connecting D-SheetPiling to the probabilistic library \n",
"\n",
"## Introduction\n",
"\n",
"This tutorial demonstrates how to connect a **D-SheetPiling** model to the **probabilistic library** to perform a **FORM** (First Order Reliability Method) analysis. The connection is made through the [D-GEOLib](https://deltares.github.io/GEOLib/) Python library, which provides a programmatic interface to D-SheetPiling.\n",
"\n",
"The workflow consists of three steps:\n",
"\n",
"1. **Build (or load) a D-SheetPiling model** using D-GEOLib (tested with version 2.8.0)\n",
"2. **Wrap it in a Python function** that the probabilistic library can call as a limit state function\n",
"3. **Parametrize** the stochastic variables.\n",
"4. **Run the FORM analysis** and interpret the results\n",
"5. **Inspect** and post-process the results\n",
"\n",
"### Problem description\n",
"\n",
"We consider a **cantilever sheet pile wall** along a canal in a two-layer soil profile:\n",
"\n",
"- **Sand** (top layer, 0.0 to −5.0 m NAP) — a medium-dense sand whose strength is governed by its friction angle $\\phi$\n",
"- **Clay** (bottom layer, −5.0 m NAP and below) — a soft clay whose strength is governed by its undrained shear strength $S_u$\n",
"\n",
"The wall retains ground on the left side (ground level at 0.0 m NAP) against the canal on the right side (canal bed at −5.0 m NAP, canal water level at −2.0 m NAP). A phreatic surface is present behind the wall on the retained side.\n",
"\n",
"The **limit state function** compares the maximum bending moment computed by D-SheetPiling against the moment capacity of the sheet pile section:\n",
"\n",
"$$g = M_{\\text{capacity}} - |M_{\\text{max,calculated}}|$$\n",
"\n",
"Failure occurs when $g \\leq 0$ (the calculated moment exceeds the section capacity).\n",
"\n",
"### Stochastic variables\n",
"\n",
"| Variable | Description | Unit | Distribution | Mean | CoV |\n",
"|----------|-------------|------|-------------|------|-----|\n",
"| `phi_sand` | Friction angle of the sand layer | ° | Normal | 25 | 0.10 |\n",
"| `su_clay` | Undrained shear strength of the clay layer | kPa | Log-normal | 20 | 0.10 |\n",
"| `phreatic_level` | Phreatic level behind the wall (retained side) | m NAP | Uniform | [−4.0, −2.0] | — |\n",
"\n",
"\n"
]
},
{
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"id": "69d28c15",
"metadata": {},
"source": [
"First, let's import the necessary packages to run this example. You need a Python environment with the GEOLIB library (\n",
"pip install d-geolib) installed to make run the following cells.\n"
]
},
{
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"source": [
"from geolib.models.dsheetpiling import DSheetPilingModel\n",
"from geolib.models.dsheetpiling.constructions import Sheet, SheetPileProperties\n",
"from geolib.models.dsheetpiling.dsheetpiling_model import SheetModelType\n",
"from geolib.models.dsheetpiling.profiles import SoilProfile, SoilLayer\n",
"from geolib.models.dsheetpiling.settings import (\n",
" LateralEarthPressureMethod,\n",
" LateralEarthPressureMethodStage,\n",
" Side,\n",
" PassiveSide,\n",
")\n",
"from geolib.models.dsheetpiling.water_level import WaterLevel\n",
"from geolib.geometry.one import Point\n",
"from geolib.soils import Soil\n",
"from geolib.models.dsheetpiling.surface import Surface\n",
"\n",
"from probabilistic_library import ReliabilityProject, DistributionType, ReliabilityMethod, StandardNormal\n",
"\n",
"import copy\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from pathlib import Path\n",
"import tempfile"
]
},
{
"cell_type": "markdown",
"id": "n1o5pqw9fu8",
"metadata": {},
"source": [
"## Step 1 — Build the D-SheetPiling base model (optional)\n",
"\n",
"We first create a deterministic D-SheetPiling model that represents the **mean** (baseline) configuration. This model will be modified at each iteration of the FORM algorithm, substituting the stochastic parameter values provided by the probabilsitic library.\n",
"\n",
"> **Tip:** If you already have a `.shi` file, you can load it directly with `model.parse(\"path/to/file.shi\")` instead of building it from scratch and fast-forward to step 2."
]
},
{
"cell_type": "markdown",
"id": "mjoivznaejb",
"metadata": {},
"source": [
"### 1.1 — Create the model and set the calculation method"
]
},
{
"cell_type": "code",
"execution_count": 128,
"id": "iadb5v88o4",
"metadata": {
"ExecuteTime": {
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"source": [
"base_model = DSheetPilingModel()\n",
"\n",
"console_path = Path(r\"C:\\Program Files (x86)\\Deltares\\D-Sheet Piling 24.1.1\\DSheetPiling.exe\")\n",
"base_model.set_meta_property(\"dsheetpiling_console_path\", console_path)\n",
"\n",
"# Use the KA-KO-KP earth pressure method for sheet piling\n",
"base_model.set_model(SheetModelType(method=LateralEarthPressureMethod.C_PHI_DELTA))\n",
"base_model.datastructure.input_data.model.check_vertical_balance = False"
]
},
{
"cell_type": "markdown",
"id": "1lqs66volzc",
"metadata": {},
"source": [
"### 1.2 — Define the soils\n",
"\n",
"We define two soil layers:\n",
"- **Sand** — a frictional material (φ = 30°, c = 0)\n",
"- **Clay** — a cohesive material modelled with undrained shear strength (φ = 0°, c = S_u = 25 kPa)\n",
"\n",
"These properties are overwritten at each FORM iteration with the stochastic parameter values defined in the model."
]
},
{
"cell_type": "code",
"execution_count": 129,
"id": "111hi3lxme",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:33:39.606192Z",
"start_time": "2026-03-27T12:33:39.582835Z"
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"outputs": [
{
"data": {
"text/plain": [
"'Clay'"
]
},
"execution_count": 129,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Sand layer (frictional)\n",
"sand = Soil(name=\"Sand\")\n",
"sand.soil_weight_parameters.saturated_weight = 20.0 # saturated unit weight [kN/m³]\n",
"sand.soil_weight_parameters.unsaturated_weight = 17.0 # dry unit weight [kN/m³]\n",
"sand.mohr_coulomb_parameters.friction_angle = 25.0 # friction angle [°] will be overwritten in the limit state function to introduce uncertainty\n",
"sand.mohr_coulomb_parameters.cohesion = 0.0 # cohesion [kPa]\n",
"sand.mohr_coulomb_parameters.friction_angle_interface = 20.0 # wall friction angle [°]\n",
"base_model.add_soil(sand)\n",
"\n",
"# Clay layer (cohesive, undrained)\n",
"clay = Soil(name=\"Clay\")\n",
"clay.soil_weight_parameters.saturated_weight = 18.0 # saturated unit weight [kN/m³]\n",
"clay.soil_weight_parameters.unsaturated_weight = 16.0 # dry unit weight [kN/m³]\n",
"clay.mohr_coulomb_parameters.friction_angle = 0.0 # friction angle [°] (undrained: φ = 0)\n",
"clay.mohr_coulomb_parameters.cohesion = 20.0 # undrained shear strength Su [kPa] will be overwritten in the limit state function to introduce uncertainty\n",
"clay.mohr_coulomb_parameters.friction_angle_interface = 0.0 # wall friction angle [°]\n",
"base_model.add_soil(clay)"
]
},
{
"cell_type": "markdown",
"id": "1164a42foq4g",
"metadata": {},
"source": [
"### 1.3 — Define the sheet pile construction\n",
"\n",
"We place a sheet pile wall with its top at **0.0 m NAP** and a bottom at **−35.0 m NAP**. The section has an elastic stiffness EI = 50 000 kNm²/m and a characteristic elastic moment capacity of **M_capacity = 500 kNm/m**."
]
},
{
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"# Moment capacity of the sheet pile section [kNm/m]\n",
"M_CAPACITY = 500.0\n",
"\n",
"sheet = Sheet(\n",
" name=\"AZ 26\",\n",
" sheet_pile_properties=SheetPileProperties(\n",
" elastic_stiffness_ei=50000, # EI [kNm²/m]\n",
" section_bottom_level=-35.0, # bottom of the sheet pile [m NAP]\n",
" mr_char_el=M_CAPACITY, # characteristic elastic moment capacity [kNm/m]\n",
" ),\n",
")\n",
"base_model.set_construction(top_level=0.0, elements=[sheet])"
]
},
{
"cell_type": "markdown",
"id": "7afva4z47wb",
"metadata": {},
"source": [
"### 1.4 — Define the construction stage\n",
"\n",
"A single construction stage with:\n",
"- **Left (retained) side:** ground level at 0.0 m NAP, Sand from 0.0 to −5.0 m, Clay below −5.0 m. Phreatic level at −1.0 m NAP.\n",
"- **Right (canal) side:** canal bed at −5.0 m NAP, Clay below −5.0 m. Canal water level at −2.0 m NAP."
]
},
{
"cell_type": "code",
"execution_count": 131,
"id": "zginow6n6z",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:33:39.681250Z",
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"outputs": [],
"source": [
"# Add a construction stage\n",
"stage_id = base_model.add_stage(\n",
" name=\"Canal\",\n",
" passive_side=PassiveSide.DSHEETPILING_DETERMINED,\n",
" method_left=LateralEarthPressureMethodStage.C_PHI_DELTA,\n",
" method_right=LateralEarthPressureMethodStage.C_PHI_DELTA,\n",
")\n",
"\n",
"# Add a new surface object at the retained side\n",
"surface_left = Surface(name=\"Surface_left\", points=[Point(x=0.0, z=0.0)])\n",
"base_model.add_surface(surface_left, side=Side.LEFT, stage_id=stage_id)\n",
"\n",
"# Left side (retained): Sand 0.0 to -5.0 m, Clay below -5.0 m\n",
"profile_left = SoilProfile(\n",
" name=\"Left\",\n",
" layers=[\n",
" SoilLayer(top_of_layer=0.0, soil=\"Sand\"),\n",
" SoilLayer(top_of_layer=-5.0, soil=\"Clay\"),\n",
" ],\n",
" coordinate=Point(x=0.0),\n",
")\n",
"base_model.add_profile(profile_left, side=Side.LEFT, stage_id=stage_id)\n",
"\n",
"# Phreatic level behind the wall (retained side) at -1.0 m NAP\n",
"wl_left = WaterLevel(name=\"WL_left\", level=-1.0)\n",
"base_model.add_head_line(wl_left, side=Side.LEFT, stage_id=stage_id)\n",
"\n",
"bottom_depth = -5.0\n",
"\n",
"# Add a new surface object at the canal side\n",
"surface_right = Surface(name=\"Surface_right\", points=[Point(x=0.0, z=bottom_depth)])\n",
"base_model.add_surface(surface_right, side=Side.RIGHT, stage_id=stage_id)\n",
"\n",
"profile_right = SoilProfile(\n",
" name=\"Right\",\n",
" layers=[\n",
" SoilLayer(top_of_layer=bottom_depth, soil=\"Clay\"),\n",
" ],\n",
" coordinate=Point(x=0.0, z=bottom_depth),\n",
")\n",
"base_model.add_profile(profile_right, side=Side.RIGHT, stage_id=stage_id)\n",
"\n",
"# Canal water level\n",
"wl_right = WaterLevel(name=\"WL_right\", level=-2.0)\n",
"base_model.add_head_line(wl_right, side=Side.RIGHT, stage_id=stage_id)"
]
},
{
"cell_type": "markdown",
"id": "5c8d1b1c",
"metadata": {},
"source": [
"### Alternative: Loading an existing `.shi` file\n",
"\n",
"If you already have a D-SheetPiling input file, the setup simplifies to:\n",
"\n",
"```python\n",
"base_model = DSheetPilingModel()\n",
"base_model.parse(Path(\"path/to/your_model.shi\"))\n",
"```\n",
"\n",
"The rest of the workflow (defining the wrapper function, setting up the reliability project, running FORM) remains identical. The only thing that changes is *how* you update the stochastic parameters inside the limit state function — you need to locate the correct soil or water level object in the parsed data structure."
]
},
{
"cell_type": "markdown",
"id": "yfzj6rbuunf",
"metadata": {},
"source": [
"## Step 2 — Define the limit state function\n",
"\n",
"The limit state function is a regular Python function whose **argument names** must match the variable names used in the project object of the probabilistic library. At each FORM iteration the probabilistic library calls this function with a new set of parameter values.\n",
"\n",
"Inside the function we:\n",
"1. **Deep-copy** the base model so the original is not modified\n",
"2. **Update** the stochastic parameters (soil properties, phreatic level)\n",
"3. **Serialize** the model to a `.shi` file and **Execute** D-SheetPiling\n",
"4. **Extract** the maximum bending moment from the output\n",
"5. **Return** $g = M_{\\text{capacity}} - |M_{\\text{max}}|$"
]
},
{
"cell_type": "code",
"execution_count": 132,
"id": "765fcf7d",
"metadata": {},
"outputs": [],
"source": [
"i = 1"
]
},
{
"cell_type": "code",
"execution_count": 133,
"id": "gc7wmap8jys",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:33:39.711230Z",
"start_time": "2026-03-27T12:33:39.692836Z"
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"source": [
"# Working directory for temporary .shi files\n",
"WORK_DIR = Path(tempfile.mkdtemp(prefix=\"dsheet_ptk_\")).resolve()\n",
"\n",
"def lsf_sheetpile(phi_sand, su_clay, phreatic_level):\n",
" \"\"\"\n",
" Limit state function: g = M_capacity - |M_max|\n",
"\n",
" Parameters\n",
" ----------\n",
" phi_sand : float\n",
" Friction angle of the sand layer [°].\n",
" su_clay : float\n",
" Undrained shear strength of the clay layer [kPa].\n",
" phreatic_level : float\n",
" Phreatic level behind the wall (retained side) [m NAP].\n",
" \"\"\"\n",
" global i\n",
" \n",
" # 1. Deep-copy the base model\n",
" model = copy.deepcopy(base_model)\n",
"\n",
" # Add a safeguard against too low strength values, they could make DSheet-piling crash and we consider them as failed anyway.\n",
" if phi_sand <= 5.0 or su_clay <= 5.0:\n",
" return 0\n",
"\n",
" # 2. Update stochastic soil parameters\n",
" # Soil[0] = Sand, Soil[1] = Clay (order follows add_soil calls)\n",
" soils = model.datastructure.input_data.soil_collection.soil\n",
"\n",
" # Sand: update friction angle and wall friction (δ = 2/3 × φ)\n",
" soils[0].soilphi = phi_sand\n",
" soils[0].soildelta = 2 / 3 * phi_sand\n",
"\n",
" # Clay: update undrained shear strength (entered as cohesion with φ = 0)\n",
" soils[1].soilcohesion = su_clay\n",
"\n",
" #. Update the phreatic level on the retained side\n",
" model.datastructure.input_data.waterlevels.levels[0].level = phreatic_level\n",
"\n",
" # 3. Serialize and execute\n",
" shi_path = WORK_DIR / f\"model_{i}.shi\"\n",
" i += 1\n",
"\n",
" model.serialize(shi_path)\n",
" model.execute()\n",
"\n",
" # 4. Extract maximum bending moment from the output\n",
" stage_output = model.output.construction_stage[0]\n",
" mfd = stage_output.moments_forces_displacements.momentsforcesdisplacements\n",
" max_moment = max(abs(row[\"moment\"]) for row in mfd)\n",
"\n",
" # 5. Return the limit state value\n",
" g = M_CAPACITY - max_moment\n",
"\n",
" return g"
]
},
{
"cell_type": "markdown",
"id": "2uwbe8a4cpm",
"metadata": {},
"source": [
"### Key points about the wrapper function\n",
"\n",
"- The function signature `lsf_sheetpile(phi_sand, su_clay, phreatic_level)` defines the **stochastic variables**. The probabilistic library uses introspection on the function arguments to automatically register them.\n",
"- Each call to the function creates a **fresh copy** of the base model (`copy.deepcopy`), updates the relevant parameters, and runs D-SheetPiling. This ensures that each FORM iteration is independent.\n",
"- The soil objects in `model.datastructure.input_data.soil_collection.soil` are indexed in the order they were added: `soil[0]` = Sand, `soil[1]` = Clay.\n",
"- The function must return a **scalar** value: the limit state value $g$. The sign convention is $g > 0$ (safe) and $g \\leq 0$ (failure).\n",
"- D-SheetPiling must be installed on the machine and accessible via the default console path (or set `model.custom_console_path`)."
]
},
{
"cell_type": "markdown",
"id": "gfy60onek47",
"metadata": {},
"source": [
"## Step 3 — Set up the Reliability Project\n",
"\n",
"We create a `ReliabilityProject`, assign the limit state function as the model, and define the stochastic variables with their distributions."
]
},
{
"cell_type": "code",
"execution_count": 134,
"id": "vt55mrbfcpg",
"metadata": {
"ExecuteTime": {
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"start_time": "2026-03-27T12:33:39.721516Z"
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},
"outputs": [],
"source": [
"project = ReliabilityProject()\n",
"project.model = lsf_sheetpile"
]
},
{
"cell_type": "markdown",
"id": "dfmm1ydnts",
"metadata": {},
"source": [
"### Define the stochastic variables\n",
"\n",
"Each argument of `lsf_sheetpile` is automatically available as a variable in `project.variables`. We specify the marginal distribution, mean, and either the coefficient of variation (`variation`) or the standard deviation (`deviation`).\n",
"\n",
"Note that `su_clay` uses a **log-normal** distribution, which is common for undrained shear strength as it is strictly positive and typically right-skewed. The `phreatic_level` uses a **uniform** distribution to represent the range of groundwater levels behind the wall."
]
},
{
"cell_type": "code",
"execution_count": 135,
"id": "cim890a3dl",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:33:39.758890Z",
"start_time": "2026-03-27T12:33:39.747231Z"
}
},
"outputs": [],
"source": [
"# Friction angle of sand: Normal(mean=25°, CoV=0.10)\n",
"project.variables[\"phi_sand\"].distribution = DistributionType.normal\n",
"project.variables[\"phi_sand\"].mean = 25.0\n",
"project.variables[\"phi_sand\"].variation = 0.10\n",
"\n",
"# Undrained shear strength of clay: Log-normal(mean=20 kPa, CoV=0.10)\n",
"project.variables[\"su_clay\"].distribution = DistributionType.log_normal\n",
"project.variables[\"su_clay\"].mean = 20.0\n",
"project.variables[\"su_clay\"].variation = 0.10\n",
"\n",
"# Phreatic level behind the wall: Uniform(lower=-4.0, upper=-2.0)\n",
"project.variables[\"phreatic_level\"].distribution = DistributionType.uniform\n",
"project.variables[\"phreatic_level\"].minimum = -4.0\n",
"project.variables[\"phreatic_level\"].maximum = -2.0"
]
},
{
"cell_type": "markdown",
"id": "v1jfcoqj76f",
"metadata": {},
"source": [
"## Step 4 — Run the FORM analysis\n",
"\n",
"We configure the FORM settings and run the analysis. The `relaxation_factor` controls the step size in the algorithm; a smaller value improves stability for models with a non-smooth response surface but makes convergence slower. The convergence threshold can also be modified the parameter `epsilon_beta`.\n",
"\n",
"For more details about the FORM procedure, please refer to the [scientific documentation](https://github.com/Deltares/ProbabilisticLibrary/releases/download/26.1.1/scientific_background.pdf)."
]
},
{
"cell_type": "code",
"execution_count": 136,
"id": "0jmm6w3lkuy6",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:35:23.673058Z",
"start_time": "2026-03-27T12:33:39.768860Z"
}
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"outputs": [
{
"name": "stderr",
"output_type": "stream",
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"Added 2 lines to run_identification.\n",
"Added 2 lines to run_identification.\n",
"Added 2 lines to run_identification.\n",
"Added 2 lines to run_identification.\n",
"Added 2 lines to run_identification.\n",
"Added 2 lines to run_identification.\n",
"Added 2 lines to run_identification.\n",
"Added 2 lines to run_identification.\n",
"Added 2 lines to run_identification.\n",
"Added 2 lines to run_identification.\n"
]
}
],
"source": [
"project.settings.reliability_method = ReliabilityMethod.form\n",
"\n",
"project.settings.maximum_iterations = 80\n",
"project.settings.relaxation_factor = 0.15 \n",
"project.settings.step_size = 0.05 # Step size for finite difference approximation of the reliability index gradient\n",
"project.settings.epsilon_beta = 0.05 # This is the convergence criterion for the reliability index β (stop if |β_new - β_old| < ε_β)\n",
"\n",
"# Save intermediate results for plotting\n",
"project.settings.save_convergence = True\n",
"project.settings.save_realizations = True\n",
"\n",
"project.run()"
]
},
{
"cell_type": "markdown",
"id": "izq43y92n8",
"metadata": {},
"source": [
"## Step 5 — Read the results\n",
"\n",
"After the FORM analysis converges, the design point contains:\n",
"- **β** — the reliability index\n",
"- **P_f** — the probability of failure\n",
"- **α-factors** — the influence coefficients showing each variable's contribution\n",
"- **Design-point values** — the parameter values at the most likely failure point"
]
},
{
"cell_type": "code",
"execution_count": 137,
"id": "243d2999",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reliability (FORM)\n",
" Reliability index = 1.876\n",
" Probability of failure = 0.0303\n",
" Convergence = 0.04096 (converged)\n",
" Model runs = 80\n",
"Alpha values:\n",
" phi_sand: alpha = 0.2015, x = 24.05\n",
" su_clay: alpha = 0.9114, x = 16.78\n",
" phreatic_level: alpha = -0.3589, x = -2.501\n",
"\n"
]
}
],
"source": [
"project.design_point.print()"
]
},
{
"cell_type": "markdown",
"id": "73788aa0",
"metadata": {},
"source": [
"> **Tip:** The D-Sheetpiling files are saved for every iteration (model_i.shi and model_i.shd) which allows for further control. They can be found in the folder defined as WORK_DIR. It is important to manually check if the values for the stochastic parameters have been correctly written in the file and are physically possible (no negative friction angle for example)."
]
},
{
"cell_type": "markdown",
"id": "6ug2x61deg",
"metadata": {},
"source": [
"## Step 6 — Visualise the results\n",
"\n",
"### 6.1 — FORM convergence\n",
"\n",
"The convergence plot shows the reliability index $\\beta$ and the convergence criterion as a function of the FORM iteration number. A stable, converging $\\beta$ confirms that the algorithm has found a consistent design point."
]
},
{
"cell_type": "code",
"execution_count": 138,
"id": "373431a67e8",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:35:24.801199Z",
"start_time": "2026-03-27T12:35:24.297849Z"
}
},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"iterations = [r.index for r in dp.reliability_results]\n",
"betas = [r.reliability_index for r in dp.reliability_results]\n",
"convergences = [r.convergence for r in dp.reliability_results]\n",
"\n",
"fig, ax1 = plt.subplots(figsize=(8, 4))\n",
"\n",
"color_beta = \"tab:blue\"\n",
"ax1.set_xlabel(\"Iteration [-]\")\n",
"ax1.set_ylabel(\"Reliability index β [-]\", color=color_beta)\n",
"ax1.plot(iterations, betas, \"o-\", color=color_beta, label=\"β\")\n",
"ax1.tick_params(axis=\"y\", labelcolor=color_beta)\n",
"\n",
"ax2 = ax1.twinx()\n",
"color_conv = \"tab:red\"\n",
"ax2.set_ylabel(\"Convergence [-]\", color=color_conv)\n",
"ax2.plot(iterations, convergences, \"s--\", color=color_conv, alpha=0.7, label=\"convergence\")\n",
"ax2.axhline(project.settings.variation_coefficient, color=color_conv, linestyle=\":\", alpha=0.4, label=\"threshold\")\n",
"ax2.tick_params(axis=\"y\", labelcolor=color_conv)\n",
"ax2.set_yscale(\"log\")\n",
"\n",
"fig.suptitle(\"FORM Convergence\", fontweight=\"bold\")\n",
"fig.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "jik8rmyz7te",
"metadata": {},
"source": [
"### 6.2 — Design point in the variable domain\n",
"\n",
"The scatter plot below shows all model evaluations performed during the FORM iterations, projected onto the two most influential variables. The **design point** (black marker) is the most probable failure point. Red points indicate failure ($g \\leq 0$), green points indicate safe evaluations ($g > 0$)."
]
},
{
"cell_type": "code",
"execution_count": 139,
"id": "vipjhpelnnp",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:35:25.092052Z",
"start_time": "2026-03-27T12:35:24.820443Z"
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Identify the two most influential variables\n",
"influence = [alpha.influence_factor for alpha in dp.alphas]\n",
"idx_sorted = np.argsort(influence)\n",
"idx_x, idx_y = int(idx_sorted[-1]), int(idx_sorted[-2])\n",
"\n",
"# Extract realization values\n",
"x_vals = [r.input_values[idx_x] for r in dp.realizations]\n",
"y_vals = [r.input_values[idx_y] for r in dp.realizations]\n",
"z_vals = [r.z for r in dp.realizations]\n",
"colors = [\"red\" if z <= 0 else \"green\" for z in z_vals]\n",
"\n",
"fig, ax = plt.subplots(figsize=(7, 5))\n",
"ax.scatter(x_vals, y_vals, c=colors, alpha=0.5, edgecolors=\"none\", s=30)\n",
"ax.scatter(\n",
" dp.alphas[idx_x].x,\n",
" dp.alphas[idx_y].x,\n",
" marker=\"*\", s=250, c=\"black\", zorder=5, label=\"Design point\",\n",
")\n",
"ax.set_xlabel(dp.alphas[idx_x].identifier)\n",
"ax.set_ylabel(dp.alphas[idx_y].identifier)\n",
"ax.legend()\n",
"ax.set_title(\"FORM Evaluations: Red = Failure, Green = Safe\", fontweight=\"bold\")\n",
"ax.grid(True, alpha=0.3)\n",
"fig.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "c7vjqaje8sj",
"metadata": {},
"source": [
"### 6.3 — Influence factors (pie chart)\n",
"\n",
"The influence factor of each variable equals $\\alpha^2$; all influence factors sum to 1. The pie chart shows at a glance which uncertain parameters dominate the failure probability and where further investigation or risk reduction measures would be most effective."
]
},
{
"cell_type": "code",
"execution_count": 140,
"id": "70sesdzm4ih",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:35:25.282245Z",
"start_time": "2026-03-27T12:35:25.124701Z"
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"project.design_point.plot_alphas()"
]
},
{
"cell_type": "markdown",
"id": "i3s7h15s8f",
"metadata": {},
"source": [
"## Interpretation\n",
"\n",
"The **α-factors** indicate the relative importance of each variable in driving the failure probability:\n",
"\n",
"- A large |α| for `phi_sand` means the sand friction angle dominates the uncertainty — investing in better soil investigation of the sand layer would be the most effective way to reduce uncertainty.\n",
"- A large |α| for `su_clay` indicates that the clay strength is a critical parameter. This is expected for configurations where the sheet pile toe is embedded in clay below the canal bed.\n",
"- A large |α| for `phreatic_level` suggests that the groundwater level behind the wall relative to the canal water level is an important driver. Controlling seepage or drainage on the retained side would reduce uncertainty.\n",
"- The sign of α indicates the direction: a **positive** α means the variable contributes to resistance (increasing it makes the structure safer), while a **negative** α means it contributes to loading.\n",
"\n",
"The **design-point values** $x^*$ represent the most probable combination of parameter values that leads to failure. These can be compared to the characteristic or design values used in semi-probabilistic codes (e.g., Eurocode 7) as a consistency check."
]
},
{
"cell_type": "markdown",
"id": "ee47226d",
"metadata": {},
"source": []
},
{
"cell_type": "markdown",
"id": "6a0e139b",
"metadata": {},
"source": [
"Credits: Thanks to Antonis Mavritsakis (Deltares)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": ".venv (3.12.13)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
![\"\"](\"../tutorials/Dsheetpiling_model.png\")
\n"
]
},
{
"cell_type": "markdown",
"id": "69d28c15",
"metadata": {},
"source": [
"First, let's import the necessary packages to run this example. You need a Python environment with the GEOLIB library (\n",
"pip install d-geolib) installed to make run the following cells.\n"
]
},
{
"cell_type": "code",
"execution_count": 127,
"id": "98g8bo65ojg",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:33:39.544951Z",
"start_time": "2026-03-27T12:33:34.212634Z"
}
},
"outputs": [],
"source": [
"from geolib.models.dsheetpiling import DSheetPilingModel\n",
"from geolib.models.dsheetpiling.constructions import Sheet, SheetPileProperties\n",
"from geolib.models.dsheetpiling.dsheetpiling_model import SheetModelType\n",
"from geolib.models.dsheetpiling.profiles import SoilProfile, SoilLayer\n",
"from geolib.models.dsheetpiling.settings import (\n",
" LateralEarthPressureMethod,\n",
" LateralEarthPressureMethodStage,\n",
" Side,\n",
" PassiveSide,\n",
")\n",
"from geolib.models.dsheetpiling.water_level import WaterLevel\n",
"from geolib.geometry.one import Point\n",
"from geolib.soils import Soil\n",
"from geolib.models.dsheetpiling.surface import Surface\n",
"\n",
"from probabilistic_library import ReliabilityProject, DistributionType, ReliabilityMethod, StandardNormal\n",
"\n",
"import copy\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from pathlib import Path\n",
"import tempfile"
]
},
{
"cell_type": "markdown",
"id": "n1o5pqw9fu8",
"metadata": {},
"source": [
"## Step 1 — Build the D-SheetPiling base model (optional)\n",
"\n",
"We first create a deterministic D-SheetPiling model that represents the **mean** (baseline) configuration. This model will be modified at each iteration of the FORM algorithm, substituting the stochastic parameter values provided by the probabilsitic library.\n",
"\n",
"> **Tip:** If you already have a `.shi` file, you can load it directly with `model.parse(\"path/to/file.shi\")` instead of building it from scratch and fast-forward to step 2."
]
},
{
"cell_type": "markdown",
"id": "mjoivznaejb",
"metadata": {},
"source": [
"### 1.1 — Create the model and set the calculation method"
]
},
{
"cell_type": "code",
"execution_count": 128,
"id": "iadb5v88o4",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:33:39.570500Z",
"start_time": "2026-03-27T12:33:39.558732Z"
}
},
"outputs": [],
"source": [
"base_model = DSheetPilingModel()\n",
"\n",
"console_path = Path(r\"C:\\Program Files (x86)\\Deltares\\D-Sheet Piling 24.1.1\\DSheetPiling.exe\")\n",
"base_model.set_meta_property(\"dsheetpiling_console_path\", console_path)\n",
"\n",
"# Use the KA-KO-KP earth pressure method for sheet piling\n",
"base_model.set_model(SheetModelType(method=LateralEarthPressureMethod.C_PHI_DELTA))\n",
"base_model.datastructure.input_data.model.check_vertical_balance = False"
]
},
{
"cell_type": "markdown",
"id": "1lqs66volzc",
"metadata": {},
"source": [
"### 1.2 — Define the soils\n",
"\n",
"We define two soil layers:\n",
"- **Sand** — a frictional material (φ = 30°, c = 0)\n",
"- **Clay** — a cohesive material modelled with undrained shear strength (φ = 0°, c = S_u = 25 kPa)\n",
"\n",
"These properties are overwritten at each FORM iteration with the stochastic parameter values defined in the model."
]
},
{
"cell_type": "code",
"execution_count": 129,
"id": "111hi3lxme",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:33:39.606192Z",
"start_time": "2026-03-27T12:33:39.582835Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"'Clay'"
]
},
"execution_count": 129,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Sand layer (frictional)\n",
"sand = Soil(name=\"Sand\")\n",
"sand.soil_weight_parameters.saturated_weight = 20.0 # saturated unit weight [kN/m³]\n",
"sand.soil_weight_parameters.unsaturated_weight = 17.0 # dry unit weight [kN/m³]\n",
"sand.mohr_coulomb_parameters.friction_angle = 25.0 # friction angle [°] will be overwritten in the limit state function to introduce uncertainty\n",
"sand.mohr_coulomb_parameters.cohesion = 0.0 # cohesion [kPa]\n",
"sand.mohr_coulomb_parameters.friction_angle_interface = 20.0 # wall friction angle [°]\n",
"base_model.add_soil(sand)\n",
"\n",
"# Clay layer (cohesive, undrained)\n",
"clay = Soil(name=\"Clay\")\n",
"clay.soil_weight_parameters.saturated_weight = 18.0 # saturated unit weight [kN/m³]\n",
"clay.soil_weight_parameters.unsaturated_weight = 16.0 # dry unit weight [kN/m³]\n",
"clay.mohr_coulomb_parameters.friction_angle = 0.0 # friction angle [°] (undrained: φ = 0)\n",
"clay.mohr_coulomb_parameters.cohesion = 20.0 # undrained shear strength Su [kPa] will be overwritten in the limit state function to introduce uncertainty\n",
"clay.mohr_coulomb_parameters.friction_angle_interface = 0.0 # wall friction angle [°]\n",
"base_model.add_soil(clay)"
]
},
{
"cell_type": "markdown",
"id": "1164a42foq4g",
"metadata": {},
"source": [
"### 1.3 — Define the sheet pile construction\n",
"\n",
"We place a sheet pile wall with its top at **0.0 m NAP** and a bottom at **−35.0 m NAP**. The section has an elastic stiffness EI = 50 000 kNm²/m and a characteristic elastic moment capacity of **M_capacity = 500 kNm/m**."
]
},
{
"cell_type": "code",
"execution_count": 130,
"id": "44uxy6zysm",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:33:39.639578Z",
"start_time": "2026-03-27T12:33:39.627574Z"
}
},
"outputs": [],
"source": [
"# Moment capacity of the sheet pile section [kNm/m]\n",
"M_CAPACITY = 500.0\n",
"\n",
"sheet = Sheet(\n",
" name=\"AZ 26\",\n",
" sheet_pile_properties=SheetPileProperties(\n",
" elastic_stiffness_ei=50000, # EI [kNm²/m]\n",
" section_bottom_level=-35.0, # bottom of the sheet pile [m NAP]\n",
" mr_char_el=M_CAPACITY, # characteristic elastic moment capacity [kNm/m]\n",
" ),\n",
")\n",
"base_model.set_construction(top_level=0.0, elements=[sheet])"
]
},
{
"cell_type": "markdown",
"id": "7afva4z47wb",
"metadata": {},
"source": [
"### 1.4 — Define the construction stage\n",
"\n",
"A single construction stage with:\n",
"- **Left (retained) side:** ground level at 0.0 m NAP, Sand from 0.0 to −5.0 m, Clay below −5.0 m. Phreatic level at −1.0 m NAP.\n",
"- **Right (canal) side:** canal bed at −5.0 m NAP, Clay below −5.0 m. Canal water level at −2.0 m NAP."
]
},
{
"cell_type": "code",
"execution_count": 131,
"id": "zginow6n6z",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:33:39.681250Z",
"start_time": "2026-03-27T12:33:39.655926Z"
}
},
"outputs": [],
"source": [
"# Add a construction stage\n",
"stage_id = base_model.add_stage(\n",
" name=\"Canal\",\n",
" passive_side=PassiveSide.DSHEETPILING_DETERMINED,\n",
" method_left=LateralEarthPressureMethodStage.C_PHI_DELTA,\n",
" method_right=LateralEarthPressureMethodStage.C_PHI_DELTA,\n",
")\n",
"\n",
"# Add a new surface object at the retained side\n",
"surface_left = Surface(name=\"Surface_left\", points=[Point(x=0.0, z=0.0)])\n",
"base_model.add_surface(surface_left, side=Side.LEFT, stage_id=stage_id)\n",
"\n",
"# Left side (retained): Sand 0.0 to -5.0 m, Clay below -5.0 m\n",
"profile_left = SoilProfile(\n",
" name=\"Left\",\n",
" layers=[\n",
" SoilLayer(top_of_layer=0.0, soil=\"Sand\"),\n",
" SoilLayer(top_of_layer=-5.0, soil=\"Clay\"),\n",
" ],\n",
" coordinate=Point(x=0.0),\n",
")\n",
"base_model.add_profile(profile_left, side=Side.LEFT, stage_id=stage_id)\n",
"\n",
"# Phreatic level behind the wall (retained side) at -1.0 m NAP\n",
"wl_left = WaterLevel(name=\"WL_left\", level=-1.0)\n",
"base_model.add_head_line(wl_left, side=Side.LEFT, stage_id=stage_id)\n",
"\n",
"bottom_depth = -5.0\n",
"\n",
"# Add a new surface object at the canal side\n",
"surface_right = Surface(name=\"Surface_right\", points=[Point(x=0.0, z=bottom_depth)])\n",
"base_model.add_surface(surface_right, side=Side.RIGHT, stage_id=stage_id)\n",
"\n",
"profile_right = SoilProfile(\n",
" name=\"Right\",\n",
" layers=[\n",
" SoilLayer(top_of_layer=bottom_depth, soil=\"Clay\"),\n",
" ],\n",
" coordinate=Point(x=0.0, z=bottom_depth),\n",
")\n",
"base_model.add_profile(profile_right, side=Side.RIGHT, stage_id=stage_id)\n",
"\n",
"# Canal water level\n",
"wl_right = WaterLevel(name=\"WL_right\", level=-2.0)\n",
"base_model.add_head_line(wl_right, side=Side.RIGHT, stage_id=stage_id)"
]
},
{
"cell_type": "markdown",
"id": "5c8d1b1c",
"metadata": {},
"source": [
"### Alternative: Loading an existing `.shi` file\n",
"\n",
"If you already have a D-SheetPiling input file, the setup simplifies to:\n",
"\n",
"```python\n",
"base_model = DSheetPilingModel()\n",
"base_model.parse(Path(\"path/to/your_model.shi\"))\n",
"```\n",
"\n",
"The rest of the workflow (defining the wrapper function, setting up the reliability project, running FORM) remains identical. The only thing that changes is *how* you update the stochastic parameters inside the limit state function — you need to locate the correct soil or water level object in the parsed data structure."
]
},
{
"cell_type": "markdown",
"id": "yfzj6rbuunf",
"metadata": {},
"source": [
"## Step 2 — Define the limit state function\n",
"\n",
"The limit state function is a regular Python function whose **argument names** must match the variable names used in the project object of the probabilistic library. At each FORM iteration the probabilistic library calls this function with a new set of parameter values.\n",
"\n",
"Inside the function we:\n",
"1. **Deep-copy** the base model so the original is not modified\n",
"2. **Update** the stochastic parameters (soil properties, phreatic level)\n",
"3. **Serialize** the model to a `.shi` file and **Execute** D-SheetPiling\n",
"4. **Extract** the maximum bending moment from the output\n",
"5. **Return** $g = M_{\\text{capacity}} - |M_{\\text{max}}|$"
]
},
{
"cell_type": "code",
"execution_count": 132,
"id": "765fcf7d",
"metadata": {},
"outputs": [],
"source": [
"i = 1"
]
},
{
"cell_type": "code",
"execution_count": 133,
"id": "gc7wmap8jys",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:33:39.711230Z",
"start_time": "2026-03-27T12:33:39.692836Z"
}
},
"outputs": [],
"source": [
"# Working directory for temporary .shi files\n",
"WORK_DIR = Path(tempfile.mkdtemp(prefix=\"dsheet_ptk_\")).resolve()\n",
"\n",
"def lsf_sheetpile(phi_sand, su_clay, phreatic_level):\n",
" \"\"\"\n",
" Limit state function: g = M_capacity - |M_max|\n",
"\n",
" Parameters\n",
" ----------\n",
" phi_sand : float\n",
" Friction angle of the sand layer [°].\n",
" su_clay : float\n",
" Undrained shear strength of the clay layer [kPa].\n",
" phreatic_level : float\n",
" Phreatic level behind the wall (retained side) [m NAP].\n",
" \"\"\"\n",
" global i\n",
" \n",
" # 1. Deep-copy the base model\n",
" model = copy.deepcopy(base_model)\n",
"\n",
" # Add a safeguard against too low strength values, they could make DSheet-piling crash and we consider them as failed anyway.\n",
" if phi_sand <= 5.0 or su_clay <= 5.0:\n",
" return 0\n",
"\n",
" # 2. Update stochastic soil parameters\n",
" # Soil[0] = Sand, Soil[1] = Clay (order follows add_soil calls)\n",
" soils = model.datastructure.input_data.soil_collection.soil\n",
"\n",
" # Sand: update friction angle and wall friction (δ = 2/3 × φ)\n",
" soils[0].soilphi = phi_sand\n",
" soils[0].soildelta = 2 / 3 * phi_sand\n",
"\n",
" # Clay: update undrained shear strength (entered as cohesion with φ = 0)\n",
" soils[1].soilcohesion = su_clay\n",
"\n",
" #. Update the phreatic level on the retained side\n",
" model.datastructure.input_data.waterlevels.levels[0].level = phreatic_level\n",
"\n",
" # 3. Serialize and execute\n",
" shi_path = WORK_DIR / f\"model_{i}.shi\"\n",
" i += 1\n",
"\n",
" model.serialize(shi_path)\n",
" model.execute()\n",
"\n",
" # 4. Extract maximum bending moment from the output\n",
" stage_output = model.output.construction_stage[0]\n",
" mfd = stage_output.moments_forces_displacements.momentsforcesdisplacements\n",
" max_moment = max(abs(row[\"moment\"]) for row in mfd)\n",
"\n",
" # 5. Return the limit state value\n",
" g = M_CAPACITY - max_moment\n",
"\n",
" return g"
]
},
{
"cell_type": "markdown",
"id": "2uwbe8a4cpm",
"metadata": {},
"source": [
"### Key points about the wrapper function\n",
"\n",
"- The function signature `lsf_sheetpile(phi_sand, su_clay, phreatic_level)` defines the **stochastic variables**. The probabilistic library uses introspection on the function arguments to automatically register them.\n",
"- Each call to the function creates a **fresh copy** of the base model (`copy.deepcopy`), updates the relevant parameters, and runs D-SheetPiling. This ensures that each FORM iteration is independent.\n",
"- The soil objects in `model.datastructure.input_data.soil_collection.soil` are indexed in the order they were added: `soil[0]` = Sand, `soil[1]` = Clay.\n",
"- The function must return a **scalar** value: the limit state value $g$. The sign convention is $g > 0$ (safe) and $g \\leq 0$ (failure).\n",
"- D-SheetPiling must be installed on the machine and accessible via the default console path (or set `model.custom_console_path`)."
]
},
{
"cell_type": "markdown",
"id": "gfy60onek47",
"metadata": {},
"source": [
"## Step 3 — Set up the Reliability Project\n",
"\n",
"We create a `ReliabilityProject`, assign the limit state function as the model, and define the stochastic variables with their distributions."
]
},
{
"cell_type": "code",
"execution_count": 134,
"id": "vt55mrbfcpg",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:33:39.735471Z",
"start_time": "2026-03-27T12:33:39.721516Z"
}
},
"outputs": [],
"source": [
"project = ReliabilityProject()\n",
"project.model = lsf_sheetpile"
]
},
{
"cell_type": "markdown",
"id": "dfmm1ydnts",
"metadata": {},
"source": [
"### Define the stochastic variables\n",
"\n",
"Each argument of `lsf_sheetpile` is automatically available as a variable in `project.variables`. We specify the marginal distribution, mean, and either the coefficient of variation (`variation`) or the standard deviation (`deviation`).\n",
"\n",
"Note that `su_clay` uses a **log-normal** distribution, which is common for undrained shear strength as it is strictly positive and typically right-skewed. The `phreatic_level` uses a **uniform** distribution to represent the range of groundwater levels behind the wall."
]
},
{
"cell_type": "code",
"execution_count": 135,
"id": "cim890a3dl",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:33:39.758890Z",
"start_time": "2026-03-27T12:33:39.747231Z"
}
},
"outputs": [],
"source": [
"# Friction angle of sand: Normal(mean=25°, CoV=0.10)\n",
"project.variables[\"phi_sand\"].distribution = DistributionType.normal\n",
"project.variables[\"phi_sand\"].mean = 25.0\n",
"project.variables[\"phi_sand\"].variation = 0.10\n",
"\n",
"# Undrained shear strength of clay: Log-normal(mean=20 kPa, CoV=0.10)\n",
"project.variables[\"su_clay\"].distribution = DistributionType.log_normal\n",
"project.variables[\"su_clay\"].mean = 20.0\n",
"project.variables[\"su_clay\"].variation = 0.10\n",
"\n",
"# Phreatic level behind the wall: Uniform(lower=-4.0, upper=-2.0)\n",
"project.variables[\"phreatic_level\"].distribution = DistributionType.uniform\n",
"project.variables[\"phreatic_level\"].minimum = -4.0\n",
"project.variables[\"phreatic_level\"].maximum = -2.0"
]
},
{
"cell_type": "markdown",
"id": "v1jfcoqj76f",
"metadata": {},
"source": [
"## Step 4 — Run the FORM analysis\n",
"\n",
"We configure the FORM settings and run the analysis. The `relaxation_factor` controls the step size in the algorithm; a smaller value improves stability for models with a non-smooth response surface but makes convergence slower. The convergence threshold can also be modified the parameter `epsilon_beta`.\n",
"\n",
"For more details about the FORM procedure, please refer to the [scientific documentation](https://github.com/Deltares/ProbabilisticLibrary/releases/download/26.1.1/scientific_background.pdf)."
]
},
{
"cell_type": "code",
"execution_count": 136,
"id": "0jmm6w3lkuy6",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:35:23.673058Z",
"start_time": "2026-03-27T12:33:39.768860Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
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],
"source": [
"project.settings.reliability_method = ReliabilityMethod.form\n",
"\n",
"project.settings.maximum_iterations = 80\n",
"project.settings.relaxation_factor = 0.15 \n",
"project.settings.step_size = 0.05 # Step size for finite difference approximation of the reliability index gradient\n",
"project.settings.epsilon_beta = 0.05 # This is the convergence criterion for the reliability index β (stop if |β_new - β_old| < ε_β)\n",
"\n",
"# Save intermediate results for plotting\n",
"project.settings.save_convergence = True\n",
"project.settings.save_realizations = True\n",
"\n",
"project.run()"
]
},
{
"cell_type": "markdown",
"id": "izq43y92n8",
"metadata": {},
"source": [
"## Step 5 — Read the results\n",
"\n",
"After the FORM analysis converges, the design point contains:\n",
"- **β** — the reliability index\n",
"- **P_f** — the probability of failure\n",
"- **α-factors** — the influence coefficients showing each variable's contribution\n",
"- **Design-point values** — the parameter values at the most likely failure point"
]
},
{
"cell_type": "code",
"execution_count": 137,
"id": "243d2999",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Reliability (FORM)\n",
" Reliability index = 1.876\n",
" Probability of failure = 0.0303\n",
" Convergence = 0.04096 (converged)\n",
" Model runs = 80\n",
"Alpha values:\n",
" phi_sand: alpha = 0.2015, x = 24.05\n",
" su_clay: alpha = 0.9114, x = 16.78\n",
" phreatic_level: alpha = -0.3589, x = -2.501\n",
"\n"
]
}
],
"source": [
"project.design_point.print()"
]
},
{
"cell_type": "markdown",
"id": "73788aa0",
"metadata": {},
"source": [
"> **Tip:** The D-Sheetpiling files are saved for every iteration (model_i.shi and model_i.shd) which allows for further control. They can be found in the folder defined as WORK_DIR. It is important to manually check if the values for the stochastic parameters have been correctly written in the file and are physically possible (no negative friction angle for example)."
]
},
{
"cell_type": "markdown",
"id": "6ug2x61deg",
"metadata": {},
"source": [
"## Step 6 — Visualise the results\n",
"\n",
"### 6.1 — FORM convergence\n",
"\n",
"The convergence plot shows the reliability index $\\beta$ and the convergence criterion as a function of the FORM iteration number. A stable, converging $\\beta$ confirms that the algorithm has found a consistent design point."
]
},
{
"cell_type": "code",
"execution_count": 138,
"id": "373431a67e8",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-27T12:35:24.801199Z",
"start_time": "2026-03-27T12:35:24.297849Z"
}
},
"outputs": [
{
"data": {
"image/png": 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",
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