LEBANESE UNIVERSITY DOCTORATE SCHOOL OF SCIENCES AND TECHNOLOGIES

1. LEBANESE UNIVERSITYDOCTORATE SCHOOL OF SCIENCES AND TECHNOLOGIES

2. Research Master’s Degree Report on: Evaluation of the Equivalent Height of the Basement Structure when Subjected to Seismic Excitation Considering the Type of the Soil Surrounding Basements For the graduation from the Research Master’s Program in Civil Engineering Done by Eng. Wassim J. Elias Supervised by Dr. Michel F. Khouri

3. Introduction An earthquake generates elastic vibration or waves which causes movement in all directions from the point of origin and cause earthquake. There are four basic causes of earthquake: ground shaking (ii) ground failure (iii) tsunamis (iv) fire. - Consequently,

4. Introduction (Cont’d) To achieve economy in tall buildings special systems to resist lateral load should be adopted. Some of the systems are:  Moment Resistant Frames  Braced Frames  Shear Wall Structures  Tube Structures

5. Introduction (Cont’d) There are different types of shear walls such as given below:  Cantilever shear walls  Flanged cantilever shear walls  Coupled shear walls  Shear wall with openings  Box system

6. Objectives of the Research The objectives of the research are: 1- Evaluate the effect of the interaction between basements and surrounding soil for certain earthquake forces. 2- Evaluate the equivalent height of the basement structure, for a variety of soil types and basements number. 3- Generate a model for a Tuned Mass Damper (TMD) that can be used to reduce vibration levels in Tall Structures.

7. Soil Structure interaction and Getting the equivalent Height To realize these targets, the methodology involves the computer modeling of different buildings constituting of many floors above ground surface level with different basements levels and different soil bearing capacities. The computer model involves three-dimensional dynamic analysis of the combined superstructure and its foundation.

8. Theoretical Review Seismic Codes give a simple approximations. a- French Seismic Code PS92:

9. Theoretical Review (Cont’d) Seismic Codes give a simple approximations. a- French Seismic Code PS92: H=H0 if the structure is constructed on a category “a” soil. H=H0 + H1/2 if the structure is constructed on a category “b” soil. H=H0 + H1 if the structure is constructed on a category “c” soil.

10. Theoretical Review (Cont’d) Seismic Codes give a simple approximations. b- Uniform Building Code UBC97:-Box effect  zero equivalent basement heights.

11. History of Seismic Drift Older Codes In 1961, the first deflection requirement was added to the Uniform Building Code (UBC), which required that buildings either be designed to act as an integral unit or be designed with sufficient separation to avoid contact under deflections caused by wind or seismic loads.

12. History of Seismic Drift (Cont’d) Older Codes Engineers were also required to “consider” lateral deflections or drift of a story relative to its adjacent stories in accordance with “accepted engineering practice.”

13. History of Seismic Drift (Cont’d) Older Codes The 1976 UBC further increased drift and deflection requirements by imposing a drift limit of 0.005 times the story height and requiring that the calculated drift be multiplied by a 1.0/K term, where K was analogous to the reciprocal of the more modern R or Rw factors.

14. History of Seismic Drift (Cont’d) Older Codes In 1988, the UBC underwent a dramatic change, switching from K’s to Rw’s, and modifying drift requirements. For structures under 65 feet in height, story drift was limited to 0.04/Rw or 0.005 times the story height. For structures over 65 feet in height, story drift was limited to 0.03/Rw or 0.004 times the story height.

15. History of Seismic Drift (Cont’d) Current Approach By the 1997 UBC, R-factors had replaced the Rw-factors. The nominal displacements resulting from these strength-level forces were then defined as ∆S. The maximum inelastic displacements, ∆M, were then calculated by multiplying ∆S by 0.7R.

16. Effective Stress in Soil The principle of effective stress is one of the most important concepts in geotechnical engineering. The total normal stress in soil is equal:

17. Effective Stress in Soil (Cont’d) The effective or inter-granular stress is the sum of the contact forces between the granular particles (P′) of the soil divided by the total or gross area (A). 𝑃=𝑃′+(𝐴−𝐴𝑐)𝑢

18. Lateral Earth Pressure These lateral forces are caused by lateral earth pressure, which has three different cases: at rest, active and passive, and will be described below. At Rest Conditions Active Conditions Passive Conditions

19. Lateral Earth Pressure (Cont’d)

20. The shear strength of a soil mass is the internal resistance per unit area that the soil mass can offer to resist failure and sliding along any plane inside it. The most popular strength criterion applied to soils is the Mohr-Coulomb strength criterion as follows: Shear Strength of Soil

21. Shear Strength of Soil (Cont’d) The criterion of Mohr-Coulomb is illustrated in the Figure below where found a stress block having the axial and shear stresses.

22. Terzaghi (1943) was the first to present a comprehensive theory for the evaluation of the ultimate bearing capacity. He suggested that for a foundation, the failure surface in soil at ultimate load may be assumed to be similar to that shown . Bearing Capacity

23. Bearing Capacity(Cont’d) Terzaghi The effect of soil above the bottom of the foundation may also be assumed to be replaced by an equivalent surcharge . The failure zone under the foundation can be separated into three parts (as shown in Figure 5): 1- The triangular zone ACD which is immediately under the foundation 2- The radial shear zones ADF and CDE, with the curves DE and DF being arcs of a logarithmic spiral. 3- Two triangular Rankine passive zones AFH and CEG.

24. According to Winkler’s hypothesis, the constant of proportionality k is usually called the modulus of sub-grade reaction or the Winkler spring stiffness. Winkler Spring Model As per Terzaghi the soil rigidity is to be taken as: Ksv=120.q Ksh=(2/3).Ksv

25. Deformation is the key parameter in performance-based seismic design rather than force or strength that is used in conventional code design approaches because performance is characterized by the level of damage and damage is related to the degree of elastic and inelastic deformation in components and systems. Deformation Based Design Philosophy

26. Deformations can be classified into three types: 1. Overall building movements 2. Story drifts and other internal relative deformations 3. Inelastic deformations of structural components and elements Deformation Based Design Philosophy (Cont’d)

27. In high-rise buildings it is important to assess these relative movements in each story as components due to: Deformation Based Design Philosophy (Cont’d) 1. Rigid body displacement 2. Racking (shear) deformation

28. Deformation Based Design Philosophy (Cont’d) In low rise building, a rigid body displacement will occurs.

29. Deformation Based Design Philosophy (Cont’d) Tube high rise building

30. Deformation Based Design Philosophy (Cont’d) Wall-frame high rise building

31. Importance of determining the position of the start of the displacement in the design of structures in order to determine: a- Base shear positionb- Proper seismic design ( to be used in Analysis)c- Soil-structure interaction (evaluate the structural behavior and its interaction with soil surroundings as related to global Stiffness and Mass. Importance of the Research

32. We want to generate a simple and empirical equation that can be used by engineers and designers to determine the equivalent height and start of the displacement based on various soil-structural factors and boundary conditions. 1440 Finite element calculations were done using Arche-Effel software for several models for different soil types on different upper and lower structure heights: a- Soil bearing capacity vary from 0.5 Kg/cm2 to 4 Kg/cm2 by increment of 0.5 Kg/cm2 and taking an 8 Kg/cm2 as rigid soil. Using Winkler spring model soil vertical and horizontal rigidity can be determined as per Terzaghi. b- All Basement heights were 3m. c- Basement numbers vary from 2 to 5 basements. Procedure of calculation

33. d- The case study was done for various buildings with 15 floors, 20 floors, 25 floors and 30 floors; each story height is 3m. e- Shear walls inertia varies from two shear walls 0.5m x 5m to four shear walls 0.5m x 10m. f- Various slab masses were considered (from D.L=0.4T/m2 to 1.2 T/m2). g- Seismic zone acceleration of 0.2g is taken in the calculations. Procedure of calculation (Cont’d)

34. Procedure of calculation (Cont’d) a- Equations that leads to evaluate it, depends on several factors: -Mass of the typical slab structure “M”. -Surface of the typical slab of the building “S”. -Concrete modulus of elasticity “E”. -Shear walls inertia in the direction of the earthquake “I”. -Bearing capacity of the soil surrounding basement walls “q”. -Superstructure height “H0”. -Basements total height “H1”.

35. Finite Element Model for 20 floor building with 3 basements embedded on 1Kg/cm2 bearing capacity soil type. Procedure of calculation (Cont’d)

36. Procedure of calculation (Cont’d)

37. Procedure of calculation (Cont’d)

38. Procedure of calculation (Cont’d) A regression analysis was done to all the output data for the position of the displacement in order to determine the equivalent height of the basements structure. Many steps were proceeded to obtain a general linear equation relatively to the bearing soil capacity coefficient q, and the following procedure steps are: Step 1: by changing the bearing capacity, the starting position of the displacement h varies linearly with q. Step 2: by changing the total height of the basements H1, the coefficients “a” and “b” of the equation Eq.(1) varies linearly with H1 as shown in the equations Eq.(2) and Eq.(3) below.

39. Procedure of calculation (Cont’d) Step 3: by changing the superstructure height H0, the coefficients “α” and “β” of the equation Eq.(2) varies to the power with H0 as shown in the equations Eq.(4) and Eq.(5) below. Step 4: by changing the a-dimensional coefficient (, the coefficients “α1” and “α2” of the equation Eq.(4)varies linearly with ( as shown in the equations Eq.(6) and Eq.(7) below.

40. Procedure of calculation (Cont’d) Step 5: by changing the a-dimensional coefficient (, the coefficient “β1”of the equation Eq.(5)varies linearly with ( as shown in the equations Eq.(8) below. Step 6: by changing the a-dimensional coefficient (, the coefficient “β2”of the equation Eq.(5)varies to the logarithmic with ( as shown in the equations Eq.(9) below. Step 7:by changing the superstructure height H0, the coefficients “γ” and “δ” of the equation Eq.(3) varies to the logarithmic with H0 as shown in the equations Eq.(10) and Eq.(11) below.

41. Procedure of calculation (Cont’d) Step 8: by changing the a-dimensional coefficient (, the coefficient “γ1” of the equation Eq.(10) varies to the exponential with ( as shown in the equations Eq.(12) below. Step 9: by changing the a-dimensional coefficient (, the coefficient “γ2” of the equation Eq.(10) varies linearly with ( as shown in the equations Eq.(13) below. Step 10: by changing the a-dimensional coefficient (, the coefficient “δ1” of the equation Eq.(11) varies to the logarithmic with ( as shown in the equations Eq.(14) below.

42. Procedure of calculation (Cont’d) Step 11: by changing the a-dimensional coefficient (, the coefficient “δ2” of the equation Eq.(11) doesn’t varies with ( as shown in the equations Eq.(15) below. Boundary Condition The a-dimensional coefficient ( defines the type of the structure’s displacement function.

43. Design Procedure Given a structure with ( ratio, the structure contains basements with H1 depth founded in a soil with a bearing capacity q, formed from many floors with H0 height, a design procedure would look as follow:

44. Design Procedure (Cont’d) This is an example that shows how calculations are done using these equations:

45. The Third Objective:Methods of Decreasing the Vibration Base Isolation Reducing vibration through the use of Dampers, Isolators, Pendulum Tuned Mass Dampers (PTMD), etc.

46. How exactly does Base Isolation Work? Most types of Isolators exhibit nonlinear behavior • Isolators have large deformation potential allowing for large drift on the Isolation Interface Objective is to Lengthen the Structure’s Period and to increase Damping that results in a large decrease of the Seismic Response.

47. Response of Base Isolated Buildings versus Fixed Base Response Reduced Structural Deformations for Base Isolated Structure

48. Elastomeric Isolators Sliding Isolator Friction Pendulum Lead Core Rubber Bearings

49. Example: Oakland City Hall Constructed 1914, about 100 m high Earthquake Response Retrofitted through the use of an Isolation System: • 111 rubber isolation bearings • 36 of them with lead cores Fixed Base Base Isolated

50. Pendulum Tuned Mass Damper (PTMD) mostly for high-rise structures • A proper method is realized to evaluate the PTMD motion in relation with the ground motion due to the earthquake acceleration. • Let us take a tower building constructed on a soil layer with a thickness H, density ρ, modulus of elasticity E and a poison ratio ϑ, where the soil layer is subjected to a ground motion Ug as shown in the Figure below.