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
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