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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; *** Profe
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  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: http://web.eng.fiu.edu/prieto/ Email: prietol@fiu.edu © Copyright by L. Prieto-Portar, October, 2009  i Table of Contents Table of Contents.................................................................................................................i  Chapter 1 Soil Exploration..................................................................................................1  Symbols for Soil Exploration..........................................................................................1  *Exploration–01. Find the required number of borings and their depth........................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 cohesion........................9  *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 Soil.....................................................................................16  Symbols for Phase Relations of soils............................................................................16  Basic Concepts and Formulas for the Phases of Soils...................................................17  *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................................................25  *Phases of soils–06: Find γ d , n, S and W w ...................................................................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 m 3 ................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 data.....................................38  **Phases of soils–18: Find the voids ratio of“muck” (a highly organic soil)...............40  Chapter 3 Classification of Soils and Rocks.....................................................................41  Symbols for Classification of soils................................................................................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 USCS..........................................................44  *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 Improvement..................................................................54  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 required........................................................61  *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....................65  **Compaction-09: Ranges of water and fill required for a road...................................66  **Compaction-10: Find the family of saturation curves for compaction......................68  **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 units...............................79   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...............85  *Permeability-08: Permeability as a function of the voids ratio e................................86  *Permeability–09: Uplift pressures from vertical flows................................................87  *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 h c  in a silt stratum using Hazen...................91  *Permeability-13: Back-hoe trench test to estimate the field permeability...................92  **Permeability-14: Seepage loss from an impounding pond........................................93  Chapter 6 Seepage and Flow-nets.....................................................................................97  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 wall............................99  *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 size................................................105  *Flow-nets-08: Drainage of deep excavations for buildings.......................................108  *Flow-nets-09: Dewatering a construction site...........................................................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 Pressure............................................117  *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 
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