CHAPTER 8. EXCAVATION WITH SHEET-PILE WALL - TUTORIAL … · 8.3.3 Existence function definition for seepage elements 214 8.3.4 Material hydraulic properties 214 8.3.5 Analysis 215

Getting started with ZSOIL.PC

Chapter 8. Excavation with sheet-pile wall - tutorial Page 180

CHAPTER 8. EXCAVATION WITH SHEET-PILE WALL -

TUTORIAL

Contents

8.1 Problem Description 181

8.2 Deformation analysis 182

8.2.1 Project creation 182

8.2.2 Pre-processing 183

8.2.3 Analysis and drivers definition 200

8.2.4 Solving algorithm 201

8.2.5 Material definition 202

8.2.6 Existence function definition 203

8.2.7 Loading function definition 205

8.2.8 Calculation 207

8.2.9 Post-processing 208

8.3 Deformation + flow analysis 211

8.3.1 Project creation 211

8.3.2 Pre-processing 211

8.3.3 Existence function definition for seepage elements 214

8.3.4 Material hydraulic properties 214

8.3.5 Analysis 215

8.3.6 Post-processing 216



The goal of this chapter is to get the ZSOIL user more and more familiar with the main

features of the program in the context of another realistic case study.

8.1 Problem Description

The objective of this exercise is to perform a numerical analysis of an anchored retaining

wall using ZSOIL. We will analyze two cases; in the first one a deformation problem and

in the second one a coupled hydro-mechanical problem for the geometry given in the

Fig. 8.1. The retaining wall has a total height of 12 m and the pre-stressed anchor a

length of 10 m.

Fig. 8.1 Anchored wall geometry

The geometry of the model will evolve in time (staggered construction). The sequence of

steps are: an initial state in equilibrium (t=0) with the retaining wall already constructed,

a first excavation stage of 4 m, the installation of a pre-stressed anchor and finally a

second excavation stage of an additional 4 m. The sequence is depicted in Fig. 8.2 with

the corresponding times of occurrence t:

t=0 t=1 t=1.6 t=2

Fig. 8.2 Construction sequence

This analysis will provide information on stresses and displacements in the soil as well as

in the retaining structures. In the flow analysis we will in addition obtain fluid velocities,

and water pressures.



8.2 Deformation analysis

8.2.1 Project creation

Open ZSOIL program. Click “Continue” on the screen below.

Fig. 8.3 ZSOIL welcome screen

Set the Preferences window with Version type: Basic, Analysis type: Plane strain,

Problem type: Deformation, Unit system: Standard. The Preferences window can be

recalled at any time from the menu Control/Project preselection.

Fig. 8.4 Preferences



Save the project with File/Save As... and name the project

Ex_8_1_retainingWall.inp. Click Save. Remember to save regularly the project with

Ctrl+S.

8.2.2 Pre-processing

8.2.2.1 Geometry definition

From the main window of the software launch the pre-processor

Assembly/Preprocessing. Type A if you want construction to lines disappear. Then

use the Minus zoom and the Hand tools (see red arrows in Fig. 8.5) in order to cover

the span x = -10 m to x = 30 m (horizontally) and y = 0 to y = -20 m (vertically).

Fig. 8.5 Pre-processing screen



In the right tool bar, choose Macro Model/Point/Create/Point. Click then on the grid

in the graph pane to create 12 points with the following coordinates: (-10;0) (-10;-4)

(-10;-8) (-10;-12) (-10;-20) (0;0) (0;-4) (0;-8) (0;-12) (0;-20) (30;0) (30;-20).

Fig. 8.6 Points

x

y



In the right tool bar, choose Macro Model/Objects/Create/Line. Uncheck the

Continue option in the dialog box and start creating lines between points as indicated

below. Each segment between two points is a Line object. You can erase lines by

selecting them and clicking on Delete or with the Delete/Delete command appearing

in the right box.

Fig. 8.7 Lines



In the right tool bar, choose Update/Split and split the three lines indicated below in Fig.

8.8. This will create three new points.

Fig. 8.8 Split lines

Update the coordinate of point situated at (30;-10) to (30;-8). For this, in the right tool

bar, choose Macro Model/Point/Update/Set Point’s position and click on the point

situated at (30;-10). Then click at the new position, i.e. (30;-8).



Create two new lines to split the big rectangle in four. For that, in the right tool bar,

choose Macro Model/Objects/Create/Line, and create the two lines indicated below.

When prompted if you want to make automatic intersection, say Yes.

Fig. 8.9 Line’s intersection



Create the last four Lines used for defining the excavation zone, as indicated below. For

that, in the right tool bar, choose Macro Model/Objects/Create/Line.

Fig. 8.10 Excavated part geometry



8.2.2.2 Create continuum

Subdomains have to be created inside the drawn contours. On the right menu select

Macro Model/Subdomain/Create/2D continuum inside contour and click inside

the 8 subdivisions of the domain as indicated below.

Fig. 8.11 Subdomains

We are going to assign the existence and loading functions for subdomains 1 and 2, in

order to be able later to define our excavation sequence. The existence function controls

the existence or inexistence for a given component and loading function allows defining a

temporal variability for a value, for example to simulate unloading conditions after an

excavation. For that, use option Macro Model/Subdomain/Update/Parameters, click inside

of subdomain 1, and specify existence function = 1 and load function = 1. Repeat the

same for subdomain 2, with existence function = 2 and load function = 2.

Fig. 8.12 Subdomains parameters

5

1

2

3

4 6 8

7



In order to check if the correct attributes have been attached to the subdomains, we can

visualize the existence function distribution by choosing Exist Function in the list

situated just below the right tool bar, as indicated below. You should now see subdomain

1 in light pink (existence function = 1), subdomain 2 in pink (existence function = 2),

and the remaining subdomains in dark grey (existence function = 0, meaning these

subdomains will always exist).

Fig. 8.13 Subdomains existence functions



8.2.2.3 Mesh Generation

Now we will create virtual meshes for all subdomains. Click on Macro

Model/Subdomain/Mesh/Create virtual mesh in the right tool bar, and click inside

the subdomain 1. There are three possibilities of creating the virtual mesh: structured,

unstructured, or through morphing. For subdomain 1, we will choose the structured

method, and 10x4 split of the subdomain. Each subdomain is defined by the control

points which appear in red on the screen below. Enter Edge 1-2 = 10, Edge 1-4 = 4, and

click Create virtual mesh. In case the control points are not automatically identified

(case of subdomain contour having more than 4 points), the control points have to be

added manually using the Pick button in the Meshing parameters window and

selecting the subdomain corners.

Fig. 8.14 Virtual meshing

Repeat the same operation for subdomains 2 (split 10x4), 3 (split 10x4) and 4 (split

10x8), in order to have a regular mesh in these subdomains. Finally click the “Create

virtual mesh” button.



For subdomain 5, we select the Unstructured radio button and check the Approximate

element size on boundary radio button. Define a value of 1 m, and click on Create

virtual mesh. Repeat the same operation for subdomains 6, 7 and 8, selecting them

and creating an unstructured mesh with an approximate element size on boundary of

respectively 1 m (subdomain 6) and 2 m (subdomains 7 and 8). Note that compatibility

between subdomains is guaranteed as long as the Adjust split to existing meshed

Subdomains checkbox is checked. You should get the image as shown below. You may

then close the Meshing parameters dialog box.

Fig. 8.15 Unstructured virtual meshing



The created virtual mesh has to be converted in a real mesh. Select the Macro

Model/Subdomain/Mesh/Virtual -> Real mesh tool in the right tool bar and apply it

to all 8 subdomains by clicking on them. This will create the finite element mesh. The

newly created elements will inherit their properties (material, existence and load

functions) from their subdomains. You may then hide the macro model with Ctrl-M and

the grid with G and you’ll get the image as shown below.

Fig. 8.16 Real mesh



8.2.2.4 Boundary Conditions definition

Once the mesh has been created, kinematical boundary conditions have to be applied.

Select the FE model/Boundary conditions/Solid BC/BC on box in the right tool bar.

This will automatically create box-type displacement boundary conditions on the mesh,

as shown below (restrained degrees of freedom are indicated with a red line). Nodes

situated on both sides of the mesh have a ux = 0 condition (no horizontal displacement),

but their vertical displacement remains free. All nodes situated at the bottom of the

mesh (lowest y-coordinate) receive a fixed boundary condition in both directions, ux = 0

and uy = 0.

Fig. 8.17 Boundary conditions



8.2.2.5 Wall definition

To define the retaining wall, select the select one edge tool indicated in Fig. 8.18 (red

arrow), and select the 12 edges situated between coordinates (0;0) and (0;-12). Be sure

to select edges belonging to the grey elements, as shown below. If you select a wrong

edge, you can unselect it by clicking once more at the same place.

Fig. 8.18 Selection of edges



Select the FE model/Beam/Create/On edge(s) tool in the right tool bar. Click Yes

when prompted if you want to create beams on selected edges, and set initial material of

the beams to 2 (default). Leave all other parameters equal to zero and click OK. 12 new

beam elements will be created, as shown below.

Fig. 8.19 Beam elements



You can keep the 12 edges which have been selected before as highlighted. We will now

use them in order to create interface elements at the rear of the wall. This will

introduce a frictional contact between the wall and the soil, allowing sticking, sliding or

separation. For this, select the FE model/Interface/On edge(s) tool in the right tool

bar. Click Yes when prompted if you want to create interface on selected edges, and set

material of the interface elements to 3 (default, see Fig. 8.20). Click OK, and unselect

the edges with the Menu option Selections/Unselect all. You should get the image

depicted in Fig. 8.21.

Fig. 8.20 Interface elements dialog box



Fig. 8.21 Interface elements

8.2.2.6 Anchor definition

To define the anchor, select the FE model/Anchor/Create/Point+Vector+Length

tool in the right tool bar. Click on the node situated on the wall at (0;-3), and introduce a

directional vector of (1;-0.15) and a distance of 10 m. Initial material is equal to 4 and

its existence function is equal to 4 (Fig. 8.22).

Fig. 8.22 Anchor dialog box

In order to define an initial pre-stress, click on Prestress and set the pre-stress value

to 1e6 kN/m2 = 1’000 N/mm2 and the existence function to 3. Then click OK.



Fig. 8.23 Anchor prestress

To create the sealing zone for the anchor, select again the FE

model/Anchor/Create/Point+Vector+Length tool in the right tool bar. Click on the

right end of the newly created anchor, and introduce a directional vector of (1;-0.15)

and a distance of 7 m. As before, Initial material is equal to 4 and existence function =

4. Click OK.

Then select the FE model/Anchor/Update/Split tool. Click on the 7 m anchor and

split it in 10. Then, using the FE model/Anchor/[Un]Outline/In zoom box tool,

select the newly created 10 anchors. Finally, using the FE

model/Anchor/Update/Link to continuum tool, answering Yes and OK when

prompted, we link the nodes of the 10 anchors in the sealing zone with their background

soil elements.



Fig. 8.24 Anchor elements

Click on File/Exit and say Yes when prompted if you want to save changes.

8.2.3 Analysis and drivers definition

The analysis sequence consists in an initial state analysis, and two excavation stages.

The initial state computes an undeformed initial stress state in equilibrium with the

applied boundary conditions at time 0. Then, the excavation stages can take place at

(fictitious) times 1 and 2. We will define two drivers, one representing the initial state

and the other representing the whole time dependent process from t = 0 to t = 3.

Select Control/Analysis & Drivers. For the initial state driver, enter 1 for Ini. Load

fac., Fin. Load and Increment. Then click on Modify. To define a time dependent

process, under Driver, choose Time dependent and leave Driven Load for the Type.

Set Time start = 0, Time end = 3, Time incr. = 1 and Multiplier = 1. Click on Add,

you should get the image as shown in Fig. 8.25.



Fig. 8.25 Analysis & drivers screen

Check that the type of analysis is defined as (2D) plane strain, and the problem is

chosen as Deformation (we will study the case of Deformation + Flow later). Now,

click OK.

8.2.4 Solving algorithm

To change the solver, select Control/Control and change the algorithm to BFGS. BFGS

is often preferable to Newton-Raphson, because more robust, in problems which include

interface elements. Leave everything else as it is defined, and click on OK.



Fig. 8.26 Control screen

8.2.5 Material definition

To define the material parameters select Assembly/Materials from the main window. A

dialog box will appear. In this case we will define 4 different materials:

Soil: For the first material click on Modify, name it: Soil, and choose Material

formulation = Mohr-Coulomb. Then click OK. In the Open dialog box next to Elastic,

enter E = 30’000 kN/m2, leave Poisson ratio = 0.3, click OK. In the Open dialog

box next to Unit weight, enter Weight / unit volume = 20 and click OK. Uncheck the

Flow check box and then move to the Open dialog box next to Non linear. Enter

cohesion c = 1 kPa and friction angle = 38°, then OK. Your first material is defined.

Wall: For the second material, click on the second line in the list and on Modify. Name

it to: Wall, and click OK. In the Open dialog box next to Elastic, enter E = 2e7

kN/m2, and Poisson ratio = 0.2. We will also define a load function which will multiply

the value of the wall’s Young modulus and evolve between time = 0 (E wall = E soil) and

time = 1 (E wall = E concrete). The loading function avoids the disturbances that might

appear due the presence of a rigid beam (wall) embedded in the soil (presence of

spurious stresses). For defining the load function, click on Data mode and select Load

function, and associate load function = 3 to E. Then, click “OK” (the definition of load

function 3 will come afterwards).

In the Open dialog box next to Unit weight, enter Weight / unit volume = 25 and

click OK. In the Open dialog box next to Geometry, set b = 1 m (as we are in plane

strain) and h = 0.6 m (wall’s thickness), then click OK.

Interface: For the third material, click on the third line in the list and then on Modify.

Name it to: Interface and then click OK. Uncheck the Flow check box and then move



to the Open dialog box next to Non linear. Enter cohesion c = 1 kPa and friction

angle = 20°, then click OK.

Anchor: For the fourth material, click on the fourth line in the list and then click on

Modify. Name it to: Anchor and then click OK. In the Open dialog box next to Elastic,

enter Young modulus = 2e8 kN/m2 and click OK. In the Open dialog box next to

Geometry, set Area = 0.0001 m2 (this is an area per unit meter, as we leave Interval

between anchors = 1 m). In the preprocessor we set the pre-stress value of the

anchor to 1e6 kN/m2. This means that we will have a pre-stress force of P0 = 1e6

kN/m2 * 0.0001 m2/m’ = 100 kN/m’). Click OK. The material definition window should

look as shown in Fig. 8.27. Click on OK to leave it.

Fig. 8.27 Material screen

8.2.6 Existence function definition

Existence functions define at which analysis step the model components (excavated soil,

wall, anchors) will appear or disappear according to the construction process. From the

main window select Assembly/Existence functions. In the box we will define 4



different existence functions:

First excavation stage: For function number 1, which was associated with subdomain

1, set its name to exc1. For Active period 1, set t1 = 0 and t2 = 1. In this way, all

elements associated with subdomain 1 will disappear just after t = 1.

Second excavation stage: For function number 2, which was associated with

subdomain 2, click on the second line in the list and set its name to exc2. For Active

period 1, set t1 = 0 and t2 = 2. In this way, all elements associated with subdomain 2

will disappear just after t = 2.

Anchor: function number 4 was associated with the anchor. So click on the fourth line

in the list and set its name to anchor. For Active period 1, set t1 = 1.6 and set t2 =

INF (means “Infinity”). In this way, the anchor will appear just after t = 1.6, in the time

span [1; 2] when we excavate the elements associated with subdomain 1. In order to

model the soil unloading during the process of anchoring, we have to define unloading

function 1 (see next section), which will go from 1 to 0 in the time span [1; 2]. This way,

the creation of the anchor happens after 60% of unloading of the elements associated

with subdomain 1 has taken place.

Anchor pre-stress: existence function 3 was associated with the anchor’s initial

prestress in the prepro. So click on the third line in the list and set its name to

prestress. For Active period 1, set t1 = 1.6 and t2 = 2. This way, the initial prestress

will appear at the same time as the anchor, and then, from T = 2, the prestress inside

the anchor will be able to evolve with respect to the anchor’s displacement. The dialog

box should now look as shown in Fig. 8.28. If this is the case, click “OK”.



Fig. 8.28 Existence function screen

8.2.7 Loading function definition

The definition of the loading functions lets us choose the values of applied loads and

their evolution with time. The values defined in the load function are multiplied with the

values defined in the pre-processor to obtain the final values (varying with time). In

order to define the loading functions, select Assembly/Load functions from the main

window menu.

Unloading due to 1st excavation: Function number 1 is associated with subdomain 1.

Set its name to lf1 and click on Modify. In the table’s first line, set Time = 0, Value = 1,

then in the second line Time = 1, Value = 1, then in the third line Time = 2, Value = 0.

This way, unloading function 1 goes from 1 to 0 in the time span [1;2] and drives the

unloading forces associated with subdomain 1.



Figure 8.29. Load function number 1

Unloading due to 2nd excavation: Function number 2 is associated with subdomain 2.

Select it in the listbox next to Function, set its name to lf2 and click on Modify. In the

table’s first line, set Time = 0, Value = 1, then in the second line Time = 2, Value = 1,

then in the third line Time = 3, Value = 0. This way, unloading function 2 goes from 1 to

0 in the time span [2;3] and drives the unloading forces associated with subdomain 2.

Wall stiffness evolution: We need to define a third loading function, which will multiply

the value of the wall’s Young modulus during the time analysis. Set Number = 3, Name

= E wall and click Add. In the table’s first line set Time = 0, Value = 1e-3, then in the

second line set Time = 1, Value = 1. Then, click OK.



8.2.8 Calculation

When the data input phase is completed, launch the calculation selecting Analysis/Run

analysis. This will run the analysis for the initial state, followed by analysis times 1, 1.6,

2, and 3. The calculation module window will appear and the calculation progress can be

followed.

Fig. 8.29 Analysis screen



8.2.9 Post-processing

When the calculation is finished, launch the post-processor from the main window menu

Results/Postprocessing. The following window will appear:

Fig. 8.30 Post-processor

The post-processor offers several tools to visualize and export data. From the menu

Time/Select current time it is possible to select any time step.

Check first the deformed mesh and the displacement vectors under Graph

option/Deformed mesh and Graph options/Displacement vectors.



Fig. 8.31 Displacement vectors at time = 3

Remark:

- As is well known, Mohr-Coulomb model has limited capability to simulate both

loading and unloading behavior. In ZSOIL it is recommended to use Hardening

Small Strain constitutive model for a proper simulation of deformations.

To visualize color maps, first select Graph option/Maps and then choose the type of

result to display with Settings/graph contents. In the window we can select Nodal

quantities to visualize displacements or Continuum to visualize stresses. Graphical

settings can be adjusted here. Once a variable has been selected it is possible to switch

among the calculation steps using “+” and “-” to see the evolution with time in the

overall domain. For example in the next continuum plot the value of the total YY-stress is

represented (Fig. 8.32).

Fig. 8.32 Total vertical stresses at time = 3



It is also possible to visualize the evolution of displacements with time for specified

points, selecting Graph option/Nodal time history and selecting the points of interest

on the upper right window and clicking Add. With Settings/Graph contents is possible

to choose the variables displayed in the plot and also the scale. For example in the

following graphic we can view the displacement at the crown of the retaining wall, which

attains a maximal absolute value of 2 cm.

Fig. 8.34 Nodal time history

For visualizing the efforts on the structure we can select Graph options/MNT for

beams/anchors/rings and then Settings/Graph contents from the menu bar to

select the quantities to visualize, for instance bending moments Mz. The corresponding

Labels can be added through Labels...Automatic option (Fig. 8.35).

Fig. 8.35 Bending moments in wall



8.3 Deformation + flow analysis

8.3.1 Project creation

For simplicity we will keep the same geometry created in the previous example. We can

reopen the project used in Case 1 Ex_8_1_retainingWall.inp and save it under

another name, i.e. Ex_8_2_retainingWallwater.inp.

To take into account flow processes we have to change the Preferences settings of the

project. Select Control/Project preselection from the main window and in the box

choose Problem type = Deformation + Flow.

Fig. 8.36 Preferences

8.3.2 Pre-processing

8.3.2.1 Seepage elements

Seepage elements have to be created in order to apply properly the hydraulic boundary

conditions; these elements allow simulating water run-off when a flux is imposed and the

saturation ratio becomes equal to 1. Select the icon Select edge (circled in red in Fig.

8.37) and highlight the subdomain edges indicated with the green arrow in Fig. 8.37,

making sure that the selected edges appear under the first excavation line. You can use

the zoom tool to check that the seepage elements are correct. On the right menu select

FE Model/Seepage/Create/On edge(s), and answer Yes.



Fig. 8.37 Seepage elements creation

In the Set parameters windows introduce Material = 5 and Existence function = 5.

Fig. 8.38 Seepage parameters

Unselect all edges (Selections/Unselect all) and repeat the same procedure for the

second excavation. In the Set parameters windows introduce Material = 5 and

Existence function = 6.

Seepage elements have to be defined as well on the right hand-side boundary. In this

Material will still be = 5 as well but there is no need to define an existence function as

the seepage elements will be present during the whole simulation.

8.3.2.2 Hydraulic Boundary Conditions

Additionally to the mechanical boundary conditions, we define now a hydraulic boundary

condition. A fixed piezometric head equivalent to a hydrostatic condition with the water

table situated 2 m under the terrain surface has to be defined on the right side of the

model. Move to FE Model/Node/Outline/In zoom box and create a box around the

node elements belonging to the right-hand side boundary. Move to FE



Model/Boundary Conditions/Pressure BC/Create/Fluid head on selected nodes

and enter Fluid head = -2 m in the box. Then press OK.

Fig. 8.39 Fluid head definition

Seepage elements have to be defined as well on this boundary. Unselect all edges

(Selections/Unselect all) and repeat the procedure seen above for all edges belonging

to the right-hand side boundary. In the Set parameters windows introduce Material = 5

and Existence function = 0.

The pressure condition will appear as a blue triangle in the right boundary of the model

as well as the seepage elements in blue. At the end of this procedure you will have

defined the following water boundary conditions: 3 seepage regions (on edges) and one

constant water table (on nodes), see Fig. 8.40.

Click on File/Exit and say Yes when prompted if you want to save changes.

Fig. 8.40 Water boundary conditions

SEEPAGE 1 EF=5

SEEPAGE 2 EF=6 SEEPAGE 3

WATER TABLE



8.3.3 Existence function definition for seepage elements

We have to define two new existence functions for seepage elements created in the

previous section. From the main window select Assembly/Existence functions.

For the first excavation stage, click on the fifth line, name it Seepage1. For Active

period 1, set t1 = 1 and t2 = 2.

For the final excavation stage, click on the sixth line, you can rename it with Seepage2

and for Active period 1, set t1 = 2 and t2 = INF.

8.3.4 Material hydraulic properties

To account for water flow we have to define the hydraulic properties of the materials.

Select from the main menu Assembly/Materials. Select Soil material and check Flow

box. Then click on the Open button located next to Flow. We have to define the

Permeability coefficients for soil, we will set Kx=Ky= 1e-5 m/s and click on “OK”.

Fig. 8.41 Soil permeabilities

Then click on the Open button next to Unit Weights. For deformation+flow analyses

the weight per unit volume will be computed as: γ = γD + n · S · γW, where n = e / (1+ e) and

S is the saturation ratio. We have to specify the values of the dry density γD and the

initial void ratio e0. Enter Weight/unit volume = 17 kN/m3 and Initial void ratio =

0.3 and click on OK.



Fig. 8.42 Unit weight input screen

The retention wall is considered impermeable. The condition has to be applied to the

interface elements. Click on Interface material and make sure that the Flow box is

unchecked.

Material 5 has also been created, click on it and rename it to Seepage and click on

Modify.

Click on OK to end up with the material’s properties definition.

8.3.5 Analysis

At this stage, save the project under File/Save and launch the calculation with

Analysis/Run Analysis.

When the calculation is finished, select Results/Postprocessing in order to visualize

the results.



8.3.6 Post-processing

Select Graph Options/Fluid velocities to observe the direction and the magnitude of

the water flow.

Fig. 8.43 Fluid velocities

Select Graph Options/Maps and then Settings/Graph contents to visualize effective

stresses in the soil, fluid velocities as a map, saturation ratio, water pore pressures...

Documents

CHAPTER 8. EXCAVATION WITH SHEET-PILE WALL - TUTORIAL … · 8.3.3 Existence function definition for seepage elements 214 8.3.4 Material hydraulic properties 214 8.3.5 Analysis 215