Elasticplastic FEM Simulation and Analysis of the Entire Construction Process of Culvert

1
Elastic-plastic FEM Simulation and Analysis of
the Entire Construction Process of Culvert
The 1st China-Japan Seminar for Graduate Students
in Civil Engineering

• By LI Jun-wei
• E-mail 0310020154_at_smail.tongji.edu
  .cn
• or lijunwei76_at_163.com
• Department of Geotechnical
  Engineering
• Tongji University, Shanghai,
  China, 200092
• Nov.6, 2004

2
Outline

• 1. Research Background
• 2. The Theory of Elastic-plastic FEM
  Simulation of the Entire Construction Process of
  Culvert
• The Mode of Elastic-plastic Finite Element Method
• The types of elements used in FEM simulation
• The basic theory of FEM simulation
• Loading process simulation by step by step
  construction
• 3. Case Study
• Simplification of case

3
Outline

• 4. Analysis on the simulation results
• Results analysis on the simulation of
  foundation excavation
• Results analysis on the stress contour of
  excavation step by step.
• Results analysis on the displacement field
  contour of excavation step by step.
• Simulation results analysis on the
  foundation-pits filling
• The settlement and vertical stress contour
  analysis after the backfilling completion.
• Discussion on the simulation results.
• 5. Conclusion

4
1. Research Background

• Much research work on
• ? Foundation-pit excavation.
• ? Mechanics characteristics of the culvert
  structure under earth pressure or live loadings.
• ? Interaction between the culvert and the
  soil.
• ? The designing methods and procedures.

5

• But, as for the construction of the culvert,
  including ?foundation-pit excavation, ?casting
  structure concrete and ?the backfilling the
  foundation-pit and covering fill layers, this
  continuous construction process is always been
  ignored.
• Although some research work had involved the
  backfilling computation, yet, after the
  excavation completion, the primary stress field
  was assumed as the self-weight stress field. This
  kind of solution is not reasonable. The main
  reason is that their stress history and stress
  path are distinct from each other.
• So, present research on the entire construction
  process of culvert is needed very much in
  practical construction, design and analysis.

6
2. The Theory of Elastic-plastic FEM Simulation
of the Entire Construction Process of Culvert

• 2.1 The Model of Elastic-plastic Finite Element
  Method
• In this research work, elastic-plastic
  hardening constitutive finite element (FE) model
  and Drucker-Prager yield criteria are used. The
  yield function of it could be expressed the
  following
• 2.2 The types of elements used in FEM
  simulation
• Beam elements, quadrilateral isoparametric
  elements and Goodman contact elements etc.

7
2.3 The basic theory of FEM simulation

• The method of generating initial stress
  field in this research is according to the
  following steps
• 1) According to the formula of initial
  stress, compute the initial Gauss stress in
  different depth. Thus a hypothesis initial stress
  field was formed
• Formula of initial stress
• 2) Compute the equivalent nodal stress
  vector
• 3)Carry out the FEM computation. At this
  time, the loading is only q , which is divided
  into several increments and added to the
  structure system. It is noted that at the
  beginning of the increment, the stress is zero.
• Using above, a modified initial stress
  field and initial elastic-plastic distribution
  were obtained, which could be presented the
  entire characteristics of the stress field and
  confirm with the yield criterion.

8
The Method of Simulating Release Loading

• The Modified Manas Method is used in this
  research work. Owing to the influence of the
  volume force (such as self-weight, seepage force,
  etc.) on the releasing loading caused by
  excavation is taken into consideration. It can be
  expressed
• Where, N - the displacement interpolation
  function
• B - the strain matrix
• - the equivalent nodal force
  caused by excavation
• - all elements that will be
  excavated
• - area load (the
  excavation loading) acting on the
• - the excavated boundary
  surface.

9

• 2.4 Loading process simulation by step by step
  construction
• In the simulation, the influence of
  the gravity of backfilling soil only applies on
  the soil that has been filled before this
  construction, but it has no influence on the
  future filling soil.
• Using the method of increasingly
  adding the number of elements in computation
  domain to simulate backfilling the foundation-pit
  is an important construction process. By applying
  the self-weight loading of the newly backfilling
  elements and construction grinding force in every
  backfilling layer, the displacement increment and
  stress increment of every newly added element are
  obtained By this way, the backfilling
  construction process is really simulated in
  practice.

10
3. Case Study

• A horseshoe-shaped culvert (see right
  Fig.1) was designed for the soil dam with the
  length 110m, entry elevation 463.00m, outlet
  elevation 461.17m.
• The foundation is the original state
  silty clay. The slope degree of open-excavation
  is 11.5, and the width of the bottom of it is
  12m. The fill is the silty clay. The elevation on
  the top dam is 489.86m. The maximum height above
  the culvert is 20.46m.

Fig.1 the section of culvert. / cm
11
3.1 Simplification of case

• Structural characteristicTake the unit
  length to solve
• the problem as a plane strain problem.
• Structural symmetry The computation is
  carried on by taking the half of the culvert
  along with the vertical symmetrical axis.
• The computation domain is taken by 2 to 3
  times diameter of culvert.
• The constraint condition the vertical
  displacements of nodes on the symmetry and
  lateral side are freedom and their horizontal
  displacements are constraint and the
  displacements of the nodes on the bottom of the
  side are fixed horizontally and vertically.

12
4. Analysis on the simulation results

• The mesh used to simulate foundation-pit
  excavation in FE computation is given in Fig.2.

13
4.1 Results analysis on the simulation of
foundation excavation

• A) Results analysis on the stress contour of
  excavation step by step

?Seen from the Fig.3 and Fig.4, we can
conclude that the contour of are nearly
parallel with the ground surface away from the
free face. At the end of excavation, stress
concentration occurs.
14
A) Results analysis on the stress contour of
excavation step by step

• ?With the free face increasing, near
  the free face, the stress contour tends to
  parallel with the free face.
• Theoretically, with the formation of
  free face increasingly, excavation makes the soil
  unload, as result, near the free face, the soil
  column pressure acting on the soil decreases. So,
  in the Fig.4 and Fig.5 the contour of stress
  shows this law. When excavation is finished, in
  the vertical direction, the soil pressure
  decreases by 1018 compared with the soil
  column stress. So, if use the self-weight stress
  field as the primary stress field before filling
  the foundation-pit, then, the results will be not
  accurate and not agreement with the practice.

15
B) Results analysis on the displacement feild
contour of excavation step by step
Elevation of foundation-pit /m
With the formation of the foundation-pit
slope step by step, shear deformation of the soil
towards free face occurs and increase. From Fig.7
,Fig.8 ,Fig.9 and Fig.10, we can drawn the
conclusions
? The horizontal displacements of the soil
increase with the excavation depth increasing
near the free face. But the maximum horizontal
displacement does not occur on the free face, it
occurs at a certain depth under the foot of the
slope. At the same time, the maximum horizontal
displacement shifts towards the central of the
excavation.
16
Elevation of foundation-pit /m
Elevation of foundation-pit /m
Distance from the central axis of the foundation
d/m
Distance from the central axis of the foundation
d/m
Fig.9 At ?h13m the contour of vertical
displacement /cm
Fig.10 The contour of vertical displacement after
excavation completion. /cm

• ? Because the soil is at the state of
  unloading at this period, resilience will occur,
  and the displacement in y-direction at a certain
  point will increase with the depth of excavation
  increasing. In different construciton period, the
  displacement in y-direction show that the
  maximum resilience occurs in the place of central
  symmetry axis, and the resilience decreases with
  the distance from the symmetry axis increasing.
  On the slope surface, the displacement in
  y-direction tends to increse with the depth of
  excavation increasing. At the place away from the
  excavation area, a small settlement occurs, which
  will expand with the the depth of excavation
  increasing. This law is agreement with the
  theoretical analysis results.

17
4.2 Simulation results analysis on the
foundation-pits filling

• After the completion of foundation-pit
  excavation, firstly, the culvert structure is
  constructed, at this time, assuming the force
  acting on the foundation by the culvert bodys
  weight is loaded only by once in the FE
  computation. After this FE computation, the
  obtained stress field and displacement field is
  treated as the primary state of filling
  foundation-pit. Then, the backfilling begins
  layer by layer and the roller applies the
  grinding force to make the fill compact. The FEM
  simulates the entire process., the results shown
  in the Fig.11 and Fig.12.

18
A) The settlement and vertical stress contour
analysis after the backfill completion

• 1)The Settlement and Vertical stress contour
  analysis after the backfill completion.

Elevation of foundation-pit /m
Distance from the central axis of the foundation
d/m
Fig.11 Contour of vertical stress after
backfilling completion. /kPa
19

• Due to the larger stiffness and little
  deformation of the culvert compared with the
  soil, during the backfilling, the culvert
  structure has the behavior of holding back the
  settlement of the fill. So, near the tunnel wall
  of the culver, the settlement is smaller than the
  settlement away from the tunnel wall. In the
  Fig.11, the settlement on the top of the culvert
  is smaller than the settlements on the two sides
  of it. So, in the contour of vertical stress
  field, the stress concentration occurs on the top
  of it, however, beside two side-walls, the stress
  is smaller.
• Additionally, owing to the uplifting
  effect of the culvert structure on the settlemt
  of around soil, the vertitcal stress on the
  lining structure increases. As result of it, the
  relatively tangential displacement between
  side-wall and the fill and frictional contact
  force occures . The manifestation of the
  frictional contact is to holdback the settlement
  of the fill on the two side of tunnel wall.
  Therefore, the vertical earth pressure on the two
  sides of the tunnel wall is smaller than the
  earth column pressure. Besedes these, because of
  the increment of friction contact and the
  increment of vertical stress on the top of the
  culvert, the compression stress on the bottom of
  culvert base and settlement deformation compared
  with its side increases with it as well.

20
2)Discussion on the simulation results
Conventional method
Fig.13 Settlement comparison between
step-by-step loading and one-step
loading
Using this method
21
2) Discussion on Conventional Method

• In the conventional FE computation, the fill
  was assumed to backfill directly to the top of
  the dam instead of using backfilling layer by
  layer, and the loading was applied the structure
  entirely for only one time. So, the structure
  would bear every part of the loading. And the
  displace-ment of every point is the result of the
  self-weight of the entire fill. within the
  compression layer (h-z), the stress presents the
  trapezoid shape distribution ABCD. Assumed
  the soil is elastic medium, the unit weight of
  soil is , the deformation modulus for unit
  volume is ,and the coefficient of bulk
  compressibility is constant, thus, the settlement
  of A point is

22
2)Discussion on the simulation results in this
work

• In fact, the force applied the culvert increased
  step by step. When the real construction reaches
  a certain A point, the self-weight of newly
  backfilled elements and the construction grinding
  force is only applied to the soil that has been
  constructed fill, however, the up layer soil will
  not undertake any loading At the FE simulation
  process, the meshes will be created only with the
  respect of the soil that bad been backfilled,
  which can embody the real construction process.
  This is the characteristics of the procedure in
  this paper. When the backfilling construction was
  complete, above this surface, there is no any
  loading, so there is no settlement. Therefore,
  the settlement of A point is zero. When the
  height of the fill reach another height above the
  A point, then, the settlement will occur at the A
  point. When the fill reached the top of the
  designed elevation, the stress caused settlement
  of A point in the compression layer presents
  rectangular distribution, see ABED in the Fig.13.
  so, the settlement of A is

23
2)Discussion on the simulation results in this
work

• In fact, backfilling the culvert
  foundation is not an one dimensional problem.
  Owing to stress distribution is not always
  echelon shape, and the material has the
  non-linear characteristic, the maximum settlement
  is always located between h/3 and h/2. The
  relationship between the settlement of the fill
  above the top of the culvert and the height of
  fill is shown in the Fig.14.
• Additionally, due to the interaction
  between the culvert and the fill, the maximum
  settlement is not located at the top of the
  culvert. From the Fig.14, it could be drawn a
  conclusion that the simulation results is
  agreement with the theoretical analysis results.

24
(No Transcript)
25
5. CONCLUSION

• From the FE simulation results of the
  example of the Huihe Reservoir reinforcement
  engineering construction process, some concluding
  remarks can be drawn
• (1) The programmed procedure can reflect the
  continuity of the loading or unloading applied
  and the deformation of the soil. And the general
  changing laws were obtained using these
  simulation methods. The methods embody the
  interacting relationship between the
  structure-soil-foundation and the harmony
  relationship of deformation. The simulation
  results are agreement with the theoretical
  analysis.
• (2) With the depth of the excavation
  increasing, the vertical resilience of soil and
  lateral displacement on the slope increase. The
  results show that the resilience at the central
  axis of basement is maximal and the maximum
  lateral displacement occur near the foot of the
  slope of the foundation-pit. But the maximum
  would drift towards the central of the
  foundation-pit. The stress field decrease about
  10 to 18 compared with the self weight stress
  field.

26
5. CONCLUSION

• (3) As the backfilling soil is finished,
  due to the uplifting effect of the culvert, the
  state of the soil around the crown becomes small
  displacement and large stress domains. The
  maximum settlement is not located the top of the
  culver, but at the 1/3 to 1/2 height of the fill.

27
Our Beautiful Campus
28

• Thank You !
• Hope you have a pleasant
• time in Tongji University