1000 Solved Problems - SKYSCRAPERS

1 Ii 300 Solved Problems Soil / Rock Mechanics and Foundations Engineering These notes are provided to you by Professor Prieto-Portar, and in exchange, he will be grateful for your comments on improvements. All Problems are graded according to difficulty as follows: * Easy; defines general principles; typical of the PE examination; ** Slightly more difficult; typical of Master s level Problems ; ** Professional level ( real-life ) Problems . by Luis A. Prieto-Portar PhD, PE Professor of Civil and Environmental Engineering Florida International University, Miami, Florida Former Professor, United States Military Academy (West Point) Telephone 305-348-2825 / Fax 305-348-2802 Website: Email: Copyright by L. Prieto-Portar, October, 2009i Table of Contents Table of Contents .. i Chapter 1 Soil Symbols for Soil Exploration ..1 *Exploration 01. Find the required number of borings and their depth.

2 2 *Exploration 02. The sample s disturbance due to the boring diameter..3 *Exploration 03. Correcting the SPT for depth and sampling method..4 *Exploration 04. Three methods used for SPT depth corrections..6 *Exploration 05. SPT corrections under a mat foundation..7 *Exploration 06. The Shear Vane Test determines the in-situ *Exploration 07. Reading a soil boring log..10 *Exploration 08: Using a boring log to predict soil engineering parameters..11 **Exploration 09. Find the shear strength of a soil from the CPT Report..14 Chapter 2 Phase Relations of Symbols for Phase Relations of soils ..16 Basic Concepts and Formulas for the Phases of *Phases of soils-01: Convert from metric units to SI and US units..21 *Phases of soils 02: Compaction checked via the voids ratio..22 *Phases of soils 03: Value of the moisture when fully saturated..23 *Phases of soils 04: Finding the wrong data..24 *Phases of soils 05: Increasing the saturation of a soil.

3 25 *Phases of soils 06: Find d, n, S and Ww..26 *Phases of soils 07: Use the block diagram to find the degree of saturation..27 *Phases of soils 08: Same as Prob-07 but setting the total volume V=1 m3..28 *Phases of soils 09: Same as problem #5 with a block diagram..29 *Phases of soils 10: Block diagram for a saturated soil..30 *Phases of soils 11: Find the weight of water needed for saturation..31 *Phases of soils 12: Identify the wrong piece of data..32 *Phases of soils 13: The apparent cheapest soil is not! ..33 *Phases of soils 14: Number of truck loads..34 *Phases of soils 15: How many truck loads are needed for a project?..35 *Phases of soils 16: Choose the cheapest fill supplier..36 ii *Phases of soils 17: Use a matrix to the find the missing **Phases of soils 18: Find the voids ratio of muck (a highly organic soil)..40 Chapter 3 Classification of Soils and Symbols for Classification of soils.

4 41 *Classify 01: Percentage of each of the four grain sizes (G, S, M & C)..42 *Classify 02: Coefficients of uniformity and curvature of granular soils..43 *Classify-03: Classify two soils using the *Classify-04: Manufacturing a new soil..45 Classify 05 ..47 Classify 06 ..48 Classify 07 ..49 Classify 08 ..50 Classify 09 ..51 Classify 10 ..52 Classify 11 ..53 Chapter 4 Compaction and Soil Symbols for Compaction ..54 *Compaction 01: Find the optimum moisture content (OMC)..55 *Compaction 02: Find maximum dry unit weight in SI units..57 *Compaction-03: What is the saturation S at the OMC? ..59 *Compaction-04: Number of truck loads *Compaction-05: What is the saturation S at the OMC? ..62 *Compaction-06: Definition of the relative compaction (RC)..63 *Compaction-07: The relative compaction (RC) of a soil..64 *Compaction-08: Converting volumes from borrow pits and truck loads.

5 65 **Compaction-09: Ranges of water and fill required for a road..66 **Compaction-10: Find the family of saturation curves for **Compaction-11: Water needed to reach maximum density in the field..71 **Compaction-12: Fill volumes and truck load requirements for a levee..73 **Compaction-13: Multiple choice compaction problem of a levee..75 Chapter 5 Permeability of Soils ..78 Symbols for Permeability ..78 *Permeability 01: Types of permeability tests and common iii *Permeability-02: Use of Hazen s formula to estimate the k of an aquifer..80 *Permeability-03: Flow in a sand layer from a canal to a river..81 *Permeability-04: Find the equivalent horizontal permeability of two layers..82 *Permeability-05: Equivalent vertical and horizontal permeabilities..83 *Permeability-06: Ratio of horizontal to vertical permeabilities..84 *Permeability 07: Do not confuse a horizontal with a vertical permeability.

6 85 *Permeability-08: Permeability as a function of the voids ratio e..86 *Permeability 09: Uplift pressures from vertical *Permeability-10: Capillary rise in tubes of differing diameters..88 *Permeability-11: Rise of the water table due to capillarity saturation..90 *Permeability-12: Find the capillary rise hc in a silt stratum using Hazen..91 *Permeability-13: Back-hoe trench test to estimate the field **Permeability-14: Seepage loss from an impounding pond..93 Chapter 6 Seepage and Symbols for Seepage and Flow-nets ..97 *Flownets-01: Correcting flawed flow-nets..98 *Flow-nets-02: A flow-net beneath a dam with a partial cutoff *Flow-nets-03: The velocity of the flow at any point under a dam..100 *Flow-nets-04: Flow through an earth levee..101 *Flow-nets-05: Finding the total, static and dynamic heads in a dam..102 **Flow nets-06: Hydraulic gradient profile within an earth levee..103 **Flow-net-07: Flow into a cofferdam and pump *Flow-nets-08: Drainage of deep excavations for *Flow-nets-09: Dewatering a construction site.

7 110 *Flow-net-10: Dewatering in layered strata..111 **Flownets-11: Flow through the clay core of an earth dam..113 Chapter 7 Effective Stresses and Pore Water Pressure ..117 Symbols for Effective Stresses and Pore Water *Effective Stress 01: The concept of buoyancy..118 *Effective Stress 02: The concept of effective stress..119 *Effective Stress 03: The concept of effective stress with multiple strata..120 Effective Stress-03B ..121 Chapter 8 Dams and Levees ..122 iv Symbols for Dams and Levees ..122 *Dams-01: Find the uplift pressure under a small concrete *Dams-02: Determine the uplift forces acting upon a concrete dam..124 Chapter 9 Stresses in Soil Symbols for Stresses in Soil Masses ..127 *Mohr-01: Simple transformation from principal to general stress state..129 *Mohr 02: Find the principal stresses and their orientation..130 *Mohr 03: Find the principal stresses and their orientation.

8 131 *Mohr 04: ..132 *Mohr 05: Normal and shear stress at a chosen plane..133 **Mohr 07: Back figure the failure angle ..134 *Mohr 08: find the Principle pressure using Mohr ..135 *Mohr 09: Relation between and ..136 *Mohr 10: ..137 *Mohr 11: ..138 *Mohr 12: ..139 *Mohr 13: Data from Mohr-Coulomb failure envelope..140 **Mohr 14: ..141 *Mohr 15: Derive the general formula for horizontal stress..142 *Newmark 01: Stress beneath a tank at different *Newmark-02: The stress below the center of the edge of a footing..144 *Newmark-03: Stress at a point distant from the loaded footing..145 *Newmark-04: Stresses coming from complex shaped *Newmark-05: Stress beneath a circular oil tank..147 **Newmark-06: Use Newmark with a settlement problem ..148 *Stress 01: Stress increase at a point from several surface point *Stress-02: Find the stress under a rectangular *Stress-03: The effect of the WT on the stress below a rectangular *Stress 04: Finding the stress outside the footing *Stress-05: Stress below a footing at different points.

9 154 *Stress-06: Stress increase from a surcharge load of limited *Stress-07: Finding a stress increase from a surface load of limited width..156 **Stress-08: Stress increase as a function of depth..157 v Chapter 10 Elastic Settlements ..158 Symbols for Elastic Settlements ..158 *Elastic Settlement-01: Settlement (rutting) of a truck *Elastic Settlement-02: Schmertmann method used for granular soils..160 *Elastic Settlement-03: Schmertmann method used for a deeper footings..161 *Elastic Settlement-04: The 2:1 method to calculate *Elastic Settlement-05: Differential settlement between two *Elastic Settlement-06: Compare the settlements predicted by the Boussinesq, Westergaard, and the 2:1 *Elastic Settlement-07: Schmertmann versus the strain methods..169 *Elastic Settlement-08: The Schmertmann method in multiple strata..170 **Elastic Settlement-09: Settlement of a mat foundation.

10 172 Chapter 11 Plastic Symbols for Plastic Settlements ..174 *Plastic Settlement 01: Porewater pressure in a compressible soil..175 *Plastic Settlement-02: Total settlement of a single layer..177 *Plastic Settlement-03: Boussinesq to reduce the stress with depth..178 *Plastic Settlement -04: Surface loads with different *Plastic Settlement-05: Pre-consolidation pressure pc and index *Plastic Settlement-06: Final voids ratio after consolidation..183 *Plastic Settlement-07: Settlement due to a lowered WT..184 *Plastic Settlement-08: The over-consolidation ratio (OCR)..185 **Plastic Settlement-09: Coefficient of consolidation Cv..186 *Plastic Settlement -10: Secondary rate of consolidation..188 *Plastic Settlement-11: Using the Time factor Tv..189 *Plastic Settlement-12: The time rate of *Plastic Settlement-13: Time of consolidation *Plastic Settlement-14: Laboratory versus field time rates of settlement.