Example A - Modeling a complex high-rise building

Franck DUBOIS - Structures Engineering
Thierry RICHARD - Structures Engineering

Part A: Presentation of the example

Purpose of the example

This example focuses on the calculation of the general forces of a high-rise building using finite element global modeling.

This calculation takes place at the beginning of the execution studies, its objective is firstly to determine the reinforcement of the foundations (diaphragm walls and drilled shafts) of the base in order to start the drilling of the diaphragm walls and drilled shafts.

Then, in a second step, the modeling will be used to calculate the general forces in the walls and floors necessary to calculate the reinforcement of the different elements (walls, columns, floors).

This example studies in particular the sensitive points of the modeling of this building:

soil-structure interaction;
seismic calculations;
non-linear calculations;
as well as phased calculations.

Particular attention is paid to the management of the modeling, detailing its preparation, its integration in the general study, its organization and its validation.

Presentation of the project

This building is located in Monaco on a major urban site, in the middle of sloped soils. It is made up of 2 major areas:

a base buried in its rear area on 13 levels consisting of rear parking lots and dwellings including a school on the sea side;
a 25-storey tower sitting on part of the base.

Figure 2: general view of the model (3D view).

Part B: Preparation and organization of the modeling

This is a very important step, because it will be very difficult to modify the model later on when it is advanced, so it is essential to have clarified all the characteristics of the calculation model before starting it.

A.1 Particularities and constraints of the project

They allow to identify the sensitive points of the modeling:

The large excavation area, the school area and the tower form a single monolithic block, there are no expansion joints.
The excavation is integrated in sloped terrains, its dimensions are significant (109m x 169m on 13 levels), its support consists of a peripheral diaphragm wall reinforced by buttresses and inner drilled shafts.
It is moreover asymmetrical with strong active earth pressure on the upstream zone and no passive earth pressure on the downstream zone.

Diaphragm wall panels rest on buttresses (no embedding)
The project is on an urban site in the middle of existing structures which are very close to the site
Presence of the high-rise building on part of the base
Taking into account a second tower (possibly built in the future) for the dimensioning of the base
Very tight work schedule

A.2 PRO file studies
The study of the calculation notes of the PRO file allows to quantify a rough estimate of the forces, and to identify the sensitive points.

In our case, it clearly appears that the foundations are dimensioned by the earthquake cumulated to the earth pressure, in fact the foundations’ notes show very important shear rates in the diaphragm wall (5 Mpa) with reinforcement rates exceeding the usual uses.

A resizing of the foundations will certainly be necessary.

A.3 Main modeling features

The first findings for the modeling are:

The size of the model will be very important because there is no expansion joint.
Taking into account the active earth pressure as well as seismic calculations are the key elements of the modeling.
The precision on deformations required due to the proximity of existing structures cannot be obtained through conventional structural modeling.

It is therefore necessary to carry out simultaneously a "3D Geotechnical” finite element modeling which will be used solely to calculate the deformations. It will take into account on the one hand all the soils around the project and on the other hand the structure of the project itself.

The active earth pressure applied to modeling will be derived from the "3D Geotechnical” model.

Asymmetric active earth pressures and their high intensities require consideration of passive earth pressure zones, and modeling of horizontal wall friction on the ground where possible.
The up and down excavation construction method without the use of tie rods, associated with active earth pressure asymmetry, has very important consequences on modeling. Indeed, during construction, the active earth pressures are taken up on the one hand by the peripheral diaphragm wall (which is classic), but also by the inner drilled shafts, which make the classical 2D calculations obsolete. It is therefore necessary to integrate the construction phases in the determination of the forces.

A.4 Input data:

It is necessary to list and validate all the input data that form the basis of the calculation:

The PRO architectural file
The PRO structural work file carried out by the project management (plans and calculation notes)
The overview of the reservations which appear in the PRO files and which unfortunately will evolve throughout the studies
The "2D" active earth pressure calculated by BET FONDATION in a first step, which will be used to develop the modeling
The "3D" active earth pressure that results from the 3D geotechnical modeling that takes place in parallel with the structural modeling. They will make it possible to correct the classic "2D" active earth pressure caused by the geometry of both the soils and structure (vault effects in particular)
Seismic active earth pressures that will be added to inertial seismic effects
Ground stiffness and friction in statics
Ground stiffness and friction in dynamics
Construction phases
Construction site methods

A.5 Output Data

They are quite simple as they are relative to the definition of the reinforcement of the diaphragm walls and drilled shafts, which are to be transmitted to BET Fondation so that it can carry out the reinforcement plans.

A.6 Interfaces between participants

The complexity of the input data and the ties between participants requires an interface flowchart to ensure consistency between the modeling and all other stakeholders. (see next page).

A.7 Assumptions Note and Modeling Methodology Note

The Assumptions Note describing the assumptions taken into account in the calculations (materials, definition of loads, etc.) must be accompanied by a Modeling Methodology Note describing how these assumptions are taken into account in the modeling (application of active earth pressure, calculation method, etc.).

The Methodology Note sets out the principles implemented in the modeling and allows all project participants to validate them before modeling them. This avoids the long and laborious modifications that often occur when the model is finished. To simplify, this is equivalent to writing the modeling note before it is completed.

Part C: Modeling

A.1 Geometric modeling principle

A.1.1 Breakdown into three independent parts

The modeling has been broken down into three independent parts, assembled during the final phase:

Partial modeling

Complete model

A.1.2 Coordinate system

The general reference frame is taken in the direction of the rear wall, which corresponds to the axes of the tower and overall to the directions of the active earth pressures, in order to make the seismic calculation coherent as it will be carried out according to the main axes of the tower.

Global reference frame

Tower axes

A.1.3 Using the BIM model

It could have been interesting to use the PRO file including a BIM model to generate the geometry of the model, but it soon appeared it was much simpler and more rigorous to study each level separately from the AutoCAD files to define the average lines of the panels.

This helps understanding how the structure works and ensures the proper transfer of loads between levels or between the elements themselves.

This manual step is important because it simplifies the modeling by removing local details that have no effect on the overall distribution of the forces, which will then be the subject of local studies. It mainly deals with the alignment of walls, slabs, the removal of small reservations, the removal of secondary walls, etc.

A.2 Modeling of the rear zone of the "large excavation" base

A.2.1 Model features

Model view of the rear area of the base: large excavation

It is the most delicate zone because it is subjected to earth pressure, and it is done from the top to the bottom with the following phasing:

Diaphragm walls and drilled shafts
Upper slab (tower support)
First level earthworks levelling
1st floor concreting
Lower levels according to the same principle

The active earth pressures asymmetry between upstream and downstream requires a partial active earth pressures resumption by the central drilled shafts during the levelling, such resumption not being calculable by conventional 2D methods – hence the need to proceed to a 3D phased calculation.

The main features of this modeling are:

Modeling of the diaphragm wall in shell elements with the installation of springs at the junction between panels
Modeling of the buttresses into shell elements, with springs modeling the support of the diaphragm wall on these buttresses
Taking into account passive earth pressure zones in areas that do not affect the surrounding areas
Taking lateral earth pressure into account in areas that don’t affect the surrounding areas
Making 4 seismic calculations (+X -X +Y +Y directions)
Phased calculation of earthworks phases

View of the large excavation without the upper slabs

A.2.2 Soil modeling by springs

The connection of the diaphragm wall to the soil depends on the direction of the force:

Either the wall presses on the soil, the spring is then in passive earth pressure, and its stiffness is in passive earth pressure
Either the wall pulls on the soil, there is then a detachment, the stiffness of the spring is thus null (the wall is in fact in an active earth pressure state)

Active and passive earth pressures of walls framing a floor

There are therefore active and passive earth pressure zones for each load case.

We have considered 2 methods:

Either define manually by iterations the passive earth pressure zones for each load combination.
Or use non-linear springs working only under passive earth pressure.

This non-linear second method was adopted, as the calculation times proved to be acceptable.

Two laws of physics are used for soil modeling springs:

Springs in passive earth pressure. Friction springs (passive earth pressure at the bottom of the excavation).

The friction springs are horizontal: there is no friction in the vertical direction.

These springs are relative to frontal stiffnesses and friction stiffnesses, and they vary according to the soil layers.

Example of soil spring location

A.2.3 Connections between panels of molded walls

The connection between diaphragm wall panels and drilled shafts or between diaphragm wall and buttress is modeled by a gap between the elements: 0.20m between panels and 0.5m between wall and buttress. The 2 panels are then connected by a non-linear spring connection with the following behavior law:

Connection between panels of the diaphragm wall

A friction coefficient of 0.7 is added to model friction in the panel contact plane with a limit of 0.7 x normal stress to the surface.

A.2.4 Connections between the buttresses and the diaphragm wall panels

They are carried out according to the same principle than for the connection between diaphragm wall panels.

Connection between the buttresses and diaphragm wall panels

A.2.5 Loading

A.2.5.1 Weight loads

They are simple to describe: dead weight, additional permanent loads, and overloads.

A.2.5.2 Static active earth force

They are derived from 3D geotechnical modeling

A.3 Modeling of the front area of the base (school and dwelling)

This modeling is much more conventional and traditional.

It is made up of shell elements (floors and sails) and wire elements (posts and beams).

The foundations are modeled entirely as for the rear area.

This area is only subjected to weight loads.

General view of the school zone model

It should be noted that the lengths of the lower levels exceed 100 ml, thus exceeding the regulatory lengths for taking into account the shrinkage effect.

A calculation of this zone under the shrinkage effect will have to be carried out during the second phase of the study, in order to determine the longitudinal reinforcement of the walls and floors.

For homogeneity with the large excavation, the piles of the foundations are modeled entirely with the installation of horizontal and vertical springs according to the soil layers.

A.4 Modeling of the tower

The modeling of the tower is conventional and traditional, consisting of shell elements for the sails and floors and wire elements for the beams and posts.

The main problem is the large size of the number of elements due to the large number of levels.

In the first step of this foundation calculation, the tower only interacts by its effects at its base (upper base level). The size of the meshes does not interact much, it will thus be large meshes.

View of a typical level of the tower

One of the peculiarities of the tower is the design of the slab edge which is very complex and variable at each level. There are no two identical slab edges.

The layout of the slab edge had to be worked on in order to remove many points from the architect's original DWG file, which had very small distances between two points – even down to the millimeter.

Meshing of the slab before purge the useless points on the slab edge

This example shows the problems encountered during the automatic recovery of DWG or REVIT files.

Although it does not initially study the effects of the wind, the modeling includes at each floor the definition of a "WIND" node positioned at the center of gravity of the floor and connected to the core walls by rigid links.

These nodes will then be used to introduce the wind load torsors calculated in the wind report for each level of the tower.

A.5 Modeling of the optional second tower

This second tower is identical to the first one and may be built in the future.

Whereas for the first tower the need to model it entirely by shell elements quickly appeared, for this optional second tower, we studied solutions limiting the model size.

A.5.1 Solution 1: modeling of the 2nd tower by its forces torsor at its base

This is the simplest solution which consists in calculating the resulting torsors at the base (O2 point below) for each load case and applying them directly to the general model.

The resulting seismic torsors of the 2nd tower are then calculated on a model of the tower alone which is embedded at its base.

This method could not be implemented because it directly adds up the seismic forces of the two towers, thus generating inadmissible forces in the diaphragm wall. Indeed, it appeared during the PRO file that there was no seismic interference between the 2 towers.

A.5.2 Solution 2: modeling of the 2nd tower by a skewer model

We realized a skewer model of the isolated tower.

This model consists of a vertical bar modeling the core whose characteristics are defined from test cases of the tower model by arranging horizontal loads at the head (according to X and Y), then by studying the equivalent inertias producing the same deformations.

Given the asymmetries of the floors, it soon became clear that the conventional skewer modeling consisting in assigning masses at each level is not suitable, because torsion is then not taken into account.

Each floor has been cut into 4 parts to which the corresponding masses are assigned.

Visualization of the skewer model

We then compared and validated the resulting torsors between the 2 calculation models under the CQC seismic cases, and compared the main modes.

Mode 1: transverse according to X:

f= 0.68 Hz with 56% of the mass f=0.63 Hz with 62 % of the mass

Mode 2: Longitudinal Y:

f= 0.77 Hz with 66% of the mass f=0.70 Hz with 62 % of the mass

Torsion mode:

f=2.2 Hz f=1.3 Hz

Vertical seismic mode:

f= 5.0 Hz with 73% of the mass f=5.5 Hz with 82 % of the mass

The validated skewer model was implemented in the general modeling by having rigid joints between the base of the skewer, and the diaphragm walls and bearing drilled shafts of the large excavation.

Compared to the first solution, a decrease in the forces in the diaphragm walls appeared. On the other hand, the rigid connection has generated very significant not admissible forces in the diaphragm wall, which do not appear in the connection of the first tower.

Therefore, the first level of the second tower should be modeled in shells to obtain consistent results.

This solution has therefore been abandoned in favor of the third solution.

A.5.3 Solution 3: modeling of the 2nd tower entirely by shells

It is the solution that we were trying to avoid that was used!!, the calculation times have increased while being reasonable.

Rear view of the model showing the anchoring of the 2nd tower in the diaphragm wall

Part D: Global modeling calculations

A.1 Global model features

The global model is meshed with elements of 1.50m size, except for the foundations (diaphragm wall, drilled shafts) with smaller meshes of 1m.

In the end, the model includes 168,000 nodes.

The total calculation with phasing and seismic calculations takes one night.

A.2 Phasing calculation

The calculation takes into account the 18 construction phases (earthworks) of the large excavation.

Then the school zone and the tower are activated.

Operating overloads can thus be applied to all floors of the model.

A.3 Seismic calculation

4 seismic calculations are performed in the directions +X, -X, +Y, and -Y, neutralizing the linear springs in tension in each case. These cases are then studied twice; with or without the 2nd tower. There are therefore 8 modal spectral analyses.

The 2 calculations with or without the second tower are quite close, the 1st mode is 0.471Hz with 2 towers, and 0.582Hz with only one tower.

First modes visualization (with 2 towers)

A.3.2 Seismic active earth pressure

Dynamic increments are applied in the 3 directions +X, -X, and -Y.

They are added to the static active earth pressure.

Cumulative dynamic increments with static active earth pressure

The seismic active earth pressures are then added to the inertial seismic forces from modal/spectral studies.

A.4 A few results

Cumulative phasing deformations

Deformations of dynamic increments

Seismic CQC deformations +X direction

A.5 Iron framework of the foundations: diaphragm walls, drilled shafts and buttresses

The global forces are calculated for the SLS and ULS limit states, and ULS seismic.

Cuts are made over the entire height of each panel to deduce the global resulting forces.

We visualize below the graphs of the forces in a buttress in the SLS state.

Normal stress in a buttress

Bending moment on high inertia

Bending moment on low inertia

The iron framework is then calculated by applying the usual and regulatory rules related to reinforced concrete.

Part E: Modeling validation

This is the fundamental question of complex modeling: how can we show the validity of the results?

Several types of validation were carried out.

A.1 Comparison with PRO file studies

The main results were compared with those in the PRO file:

Mass balance
Torsor of support reactions for elementary load cases
Deformations under permanent loads and earthquakes
Specific modes
Etc.

A.2 Internal validations during modeling

They are carried out during the modeling and during the verification of the main results

Moreover, they relate to:

Geometry visualization, local frames, thicknesses, etc.
Graphical visualization of the loads applied to the model,
Visualization of steel mapping to show any problematic zones identified by large steel sections
Visualization of the deformations of elementary load cases

A.3 Internal validations by a partner not involved in the modeling team

A person external to the modeling team checked several points:

Activation and deactivation of groups of elements (surface, wire, or spring elements) in the calculation phase
Behavioral laws according to input data
Behavior law assignment for all passive earth pressure or friction springs, depending on panel location and level.
Orientation of non-linear springs which only work in compression
Respect of the springs’ plastic zone during the different phases
Loading of elements

A.4 Modeling validation meeting

Outside the modeling team, it is absolutely impossible for other project participants (project managers, technical controllers, construction site, other technical design offices, etc.) to understand the details of this "black box" and to be able to validate the results of the model.

A general meeting was therefore scheduled "live" in front of the modeling computer. Everyone was then able to request data visualizations, request additional results, understand the model structure, see all the parameters included in the calculation data, access intermediate results, etc.

The aim of such a meeting is to answer all the questions raised by the participants directly with the modeling computer.

Part F: Calculations of the structure’s iron framework

The modeling will be completed in a second phase by the calculation of wind and shrinkage forces.

The mesh will be refined for the tower’s walls by adopting 3 meshes on the height (i.e. a 1m mesh).

The walls will then be calculated directly from the results of the modeling by making cuts at their base.

The bending forces of the floors will be calculated "manually", i.e. with local modeling, which will be added to the membrane forces (N and FXY) determined by the modeling in order to determine their iron frameworks.

FXY membrane forces to be taken into account in the slab calculation