# Shear Strength of Soil

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LEBANESE UNIVERSITY DOCTORATE SCHOOL OF SCIENCES AND TECHNOLOGIES

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

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IntroductionAn 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,

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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

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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

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Objectives of the ResearchThe 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.

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Soil Structure interaction and Getting the equivalent HeightTo 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.

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

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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.

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

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History of Seismic DriftOlder 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.

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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.”

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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.

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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.

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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.

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

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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

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Lateral Earth PressureThese 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

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Lateral Earth Pressure (Cont’d)

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Shear Strength of SoilThe 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:

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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.

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Bearing Capacity 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 .

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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.

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

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Deformation Based Design PhilosophyDeformation 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.

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Deformation Based Design Philosophy (Cont’d) 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

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Last Updated: 8th March 2018