D R A F T
of the course CEB5061/Lecture GEOENGINEERING – FOUNDATIONS
by
Włodzimierz Brząkała, PhD, DSc, Associate Professor
contents
Subject
1. Examples of soil-foundations interaction 2. Linear models of the subsoil behaviour
3. Foundations on the Winkler subsoil – continuous modelling 4. Calculation examples
5. Beams and slabs on elastic subsoil – simple discrete modelling 6. Underground mine workings and surface subsidence
7. Structures liable to the effects of mining subsidence 8. Types, applications and construction of retaining structures 9. General stability criteria of retaining structures
10. Earth pressure calculations 11. Reinforced earth constructions
12. Dynamical excitations in geoengineering 13. Case histories
14. Repetition and examples; the course synthesis 15. Final completion tests; marks.
General outcomes: the course completes the scope of the graduate course called Foundations (Level I) focusing on the presentation of selected new geoengineering technologies and some relevant calculation techniques. Special attention is paid to the soil-foundation interaction which enables a more realistic evaluation of actions. Both basic models, the elastic settlements and the ultimate bearing capacity, are developed. Special methods are required for mining influences.
Students get the background knowledge to cope with more advanced problems of geoengineering and gain a skill in foundation design.
1. Examples of soil-foundations interaction (1 hr)
• Statically indeterminate foundation beam on 3 elastic supports
• Elastic supports and fixities of a frame structure
• Long beam loaded with a moving force
• Long pipeline resting on an inhomogeneous subsoil
• Contact forces under stiff plates and water pressure effects Outcomes:
Students discover that structural calculations can be loaded with errors of the range up to 20-40%, if the soil-structure interaction is ignored; the foundation (or structure) stiffness – related to the subsoil stiffness – governs the redistribution of contact forces for design purposes, the rising of the water horizon introduces new calculation situations.
2. Linear models of the subsoil behaviour (2 hrs)
• The Winkler model, the subsoil coefficient
• The Pasternak model
• Elastic half-plane
• Finite elastic layers
• Evaluation of parameters – the inverse analysis
• Limitations of the linear models, no-tension joints Outcomes:
Students look for a balance between model simplicity and acceptable accuracy for design purposes;
shortcomings of the linear models are discussed in detail, global and local models (analogs) of the subsoil are introduced;
the question “When the Winkler model (hypothesis of the elastic subsoil coefficient) can be acceptable?” is addressed.
3. Foundations on the Winkler subsoil – continuous modelling (3 hrs)
• The Euler-Bernoulli beam (strip foundation)
• The force fundamental solution (infinite beam, concentrated loading force)
• The moment fundamental solution (infinite beam, concentrated loading moment)
• Boundary conditions
• Semi-finite and finite beams – the Bleich virtual forces
• Variable subsoil coefficient – solutions in terms of polynomial expansions
• Foundation beams as virtual strips within rectangular slabs supporting an array of columns
• Equations and analytical solutions for slabs Outcomes:
A bridge to the courses Strength of Materials and Ordinary Differential Equations, practicing with the superposition principle and the Green functions, application of virtual loadings as a prototype for the Boundary Element Method, longitudinal variability of internal forces in beams on the elastic subsoil, design of deformable continuous footings.
4. Calculation examples (1 hr)
• Distributed loads
• Bending of piles and deformable retaining walls
• Beams of variable bending stiffness
• Action of mining subsidence Outcomes:
Students acquire training and practice in the analytical treatment of simple geoengineering tasks, building of “the engineering intuition” of the foundation behaviour under actions, redistribution of contact forces, variability of internal forces for design purposes.
5. Beams and slabs on elastic subsoil – simple discrete modelling (2 hrs)
• Discretization of contact stresses
• Influence coefficients for beams and slabs
• Influence coefficients for linearly deformable elastic subsoil
• Completing a required set of algebraic equations
• Examples – calculation code ZEM-SIN (public domain) Outcomes:
Useful applications of the Force Method for statically indeterminate problems, approaching continuous problems using a discrete approximation (towards numerical methods), approximation error and discussion of approximation shortcomings, practical skills – correlated with the parallel course CEB3261/Design Project.
6. Underground mine workings and surface subsidence (2 hrs)
• Mining technologies
• Area of influence and subsidence curves
• Parameters of the ground surface subsidence, mining categories
• Tolerance of engineering objects to deformations
• Time factor – “traveling” mining area and rheological effects
• Discontinuous mining deformations Outcomes:
15-20% of Poland’s territory is in contact with mining influences (including dewatering of open-pits, historical mining activity, mining induced quakes, etc.) – and close to urban regions or industrial ones, students acquire a description and classification of CE-problems;
students get a background for further contacts with mining engineers and municipal authorities.
7. Structures liable to the effects of mining subsidence (2 hrs)
• Subsoil redistributed actions on foundations
• Subsoil additional actions on foundations
• Precautions against mining damage
• Fundamental construction principles:
structural accommodation or high resistance?
• Mining dynamical excitations Outcomes:
Design in difficult geoengineering conditions, evaluation of bending moment changes (mining curvature) and tensile/compressive axial forces (mining strains); individual analysis of the allowable differential settlements of CE-objects, shape optimization of foundations; some aspects are also useful for foundations on swelling and shrinking soils or other origins of ground movements
8. Types, applications and construction of retaining structures (2 hrs)
• Massive abutments and gravity walls
• Concrete cantilever retaining walls
• Slurry walls
• Soil anchors Outcomes:
Students acquire technical information (useful to make a rational selection) about characteristic features of each construction type in the context of: required functions, safety, bearing capacity, durability and costs; most recent technologies, such as the “Top & Down” construction processes and the floor strutting method, are discussed; soil anchors are also useful for masts, suspension bridges, hydrotechnical structures, deep tunnels (against up-lift).
9. General stability criteria of retaining structures (2 hrs)
• Setting of loadings, positioning of the structure, eccentricity reduction
• Sliding failure
• Rotation failure
• Bearing failure
• Failure by (rotational) slip in surrounding soil
• Other failure criteria: anchors, slurry trench, concrete design, etc.
Outcomes:
The criteria meet the geotechnical requirements of the Eurocode EC7 design code, minimal values of allowable safety margins confirm the correct position and shape of the construction; other failure criteria that are of interest: pull-out capacity of anchors, slurry trench stability, design of concrete elements, etc.)
10. Earth pressure calculations (3 hrs)
• The Coulomb-Poncelet theory
• The Prandtl solution and its applications
• Cohesive soils – the method of corresponding states of stresses
• Technical methods for the earth-pressure reduction
• The EC7 approach to the earth pressure evaluation
• Commercial codes analyzing full soil-structure interaction Outcomes:
The limit equilibrium equations formulated in stresses can be solved only for several simple cases – most frequently, some additional simplifications are necessary; for the ultimate passive earth pressure such simplifications can be dangerous (overestimated values by the Poncelet approach), solutions for cohesive soils result from corresponding solutions for noncohesive ones; the rational shape of the wall can reduce the earth pressure substantially; elastic-plastic numerical modelling is more universal, if it uses adequate values of soil parameters.
11. Reinforced earth constructions (2 hrs)
• Geosynthetics and their applications
• Rupture, creep and pull-out tests of geogrids
• Partial safety coefficients
• Homogenization: reinforcement as a pseudo-cohesion
• Macro-modelling: Design of reinforced-sand cushion
• Macro-modelling: Design of reinforced-sand retaining walls
• Construction details Outcomes:
Students gain experience within a popular geoengineering technology of soil improvement – useful for shallow foundations, retaining walls, road embankments, etc.; get familiar with fundamental reinforcing materials, calculation methods and design principles
12. Dynamical excitations in geoengineering (2 hrs)
• Natural earthquakes, mining quakes, dynamic compactions, driven piles
• Propagation of waves in soils
• Soil liquefaction
• Design of block machine foundations
• Damping of vibrations: passive, semi-active, active Outcomes:
Impact of vibrating surrounding soils to foundations and vice versa – from foundations to surrounding soils, increasing pore pressure and soil subsidence, allowable amplitudes and frequencies for buildings, screening of vibrations, monitoring
13. Case histories (2 hr)
• Was The Babel Tower made of reinforcerd earth? – ziggurats (XXIc. BC) in Babilon/Iraq
• The Leaning Tower of Pisa – a sequence of geoengineering faults
• Old monumental buildings in Mexico City – very large settlements
• Reclamation of a pond with liquid uranium wastes in Kowary – reinforced soil cover Outcomes:
Some spectacular situations as a background for profound geoengineering analyses: role of human errors, insufficient geological data, lack of experience with new technologies, poor prediction of environmental changes
14. Repetition and examples; the course synthesis (2 hr)
• List of fundamental problems to be addressed
• Questions and answers, discussion Outcomes:
The last chance to explain problems, difficulties and to sum up what students learned;
preparation for the credit test.
15. Credit test (2 hrs)
• 2 calculation tasks (20min+10min, 7pts.+4pts)
• 3 detailed questions (3x5min, 3x3pts)
• marks (at least 10 pts. to pass) Outcomes:
It is expected that students – engineers to be - become skilful in simple calculations for design purposes; therefore 11 pts. - of the total of 20 pts. – are assigned to the calculation part of the test.
