Module 15: Comprehensive Review and Practice Exams on Mohammad Movahedi

Corridor Design Integration

Mon, 04 May 2026 00:00:00 +0000

Corridor Design Integration

Corridor design integration represents the synthesis of horizontal alignment, vertical alignment, cross-section design, drainage, and earthwork balancing into a unified roadway project. A successful corridor balances vehicle safety, constructability, costs, and environmental impacts.

Roadway Cross-Section Elements

A standard roadway cross-section integrates multiple components that must comply with AASHTO’s A Policy on Geometric Design of Highways and Streets (the Green Book):

Travel Lanes: Standard width is 12 feet (minimum 9 to 11 feet on low-volume local roads).
Shoulders: Provide structural support, emergency parking, and lateral clearance. Width ranges from 2 feet (minor rural roads) to 10 or 12 feet (freeways).
Fore-slope: The slope extending down from the shoulder edge to the ditch. Slopes of 1:4 or flatter are preferred to allow vehicles to recover if they leave the roadway. Slopes steeper than 1:3 are non-recoverable and require guardrail shielding.
Ditch: Sized to convey storm runoff without overtopping the shoulder.
Back-slope: The slope rising from the ditch bottom to meet the natural terrain.
Clear Zone: The unobstructed, traversable area provided beyond the edge of the travel lane for recovery of errant vehicles. Sized based on design speed, ADT, and side slopes (using AASHTO Roadside Design Guide tables).

Earthwork Sizing and Material Volumes

Roadway construction involves excavation (cut) and embankment (fill). Because soils change volume when excavated and compacted, engineers must adjust raw volumes:

Design Exception Reasoning

Mon, 04 May 2026 00:00:00 +0000

Design Exception Reasoning

When a roadway project cannot meet the minimum design standards due to physical, environmental, or economic constraints, designers must seek a formal Design Exception. This process requires documentation demonstrating that safety and operations will not be significantly compromised, or that suitable mitigation measures are implemented.

FHWA Controlling Design Criteria

In 2016, the Federal Highway Administration (FHWA) updated the list of “controlling design criteria” that require formal design exceptions on the National Highway System (NHS).

Standards Conflict Resolution

Mon, 04 May 2026 00:00:00 +0000

Standards Conflict Resolution

Highway engineering projects frequently involve multiple reference manuals, state specifications, local guidelines, and federal regulations. When these standards conflict, engineers must apply a systematic hierarchy to determine which standard governs.

Hierarchy of Standards and Guidelines

In the United States, geometric design and traffic engineering standards follow a defined hierarchy:

Federal Law & Civil Rights Regulations:
- Examples: Americans with Disabilities Act (ADA), Section 504 of the Rehabilitation Act.
- Status: Sovereign law. ADA/PROWAG guidelines always override state, local, or contract standards. If a state standard allows a $10.0\%$ ramp slope but ADA limits it to $8.33\%$, the ADA standard governs.
Federal Rules & Manuals (Federal Aid Projects):
- Examples: MUTCD (Manual on Uniform Traffic Control Devices).
- Status: The MUTCD is the national standard for all traffic control devices on public roads. States must adopt either the federal MUTCD or a state-specific manual in substantial compliance.
State DOT Design Standards:
- Examples: State Roadway Design Manuals, Standard Plans, Standard Specifications.
- Status: For state highway projects, the state-specific manual governs over national guidelines. AASHTO policies (the Green Book) are guidance, whereas state manuals are specifications.
National Guidelines:
- Examples: AASHTO Green Book, AASHTO Roadside Design Guide, Highway Capacity Manual (HCM).
- Status: Used as baseline reference and best-practice guides when state or local specific standards do not address a design feature.

Order of Precedence in Contract Documents

During construction, conflicts often arise between different parts of the project contract documents. Unless otherwise stated in the contract, the standard order of precedence is:

Mixed Calculation Set: Traffic and Signals

Mon, 04 May 2026 00:00:00 +0000

Mixed Calculation Set: Traffic and Signals

This calculation set covers core traffic engineering and signal design problems typical of the PE Civil Transportation exam.

Problem 1: Greenshields Traffic Flow Parameters

A freeway segment’s traffic stream is modeled using the Greenshields linear speed-density relationship:

$$u = 65.0 - 0.45 \cdot k$$

Where:

$u$ = Space-mean speed (mph)
$k$ = Density (vehicles per mile, veh/mi)

1. Determine the free-flow speed ($u_f$) and the jam density ($k_j$). 2. Calculate the maximum flow rate (capacity, $q_{max}$) of the segment in vehicles per hour (veh/h). 3. Find the speed ($u_{cap}$) and density ($k_{cap}$) at capacity.

Mixed Calculation Set: Geometry and Safety

Mon, 04 May 2026 00:00:00 +0000

Mixed Calculation Set: Geometry and Safety

This calculation set covers geometric alignment design and roadside safety calculations typical of the PE Civil Transportation exam.

Problem 1: Horizontal Curve Stationing

A simple horizontal curve is being designed for a two-lane highway.

The intersection angle (deflection angle) $\Delta = 38^{\circ} 30' = 38.5^{\circ}$.
The degree of curve (arc definition) is $D_a = 4.0^{\circ}$ (measured over a 100-foot arc length).
The station of the Point of Intersection (PI) is $244 + 50.00$.

Calculate the following:

Mixed Calculation Set: Drainage and Pavement

Mon, 04 May 2026 00:00:00 +0000

Mixed Calculation Set: Drainage and Pavement

This calculation set covers hydrology/drainage and pavement design calculations typical of the PE Civil Transportation exam.

Problem 1: Flexible Pavement Structural Number (SN)

A highway agency is designing a flexible pavement cross-section. The design structural number ($SN$) required for the design ESALs and soil conditions is $SN_{req} = 4.2$. The proposed pavement structure consists of three layers:

Asphalt Concrete Surface Course: Layer coefficient $a_1 = 0.44$, thickness $D_1$ to be determined.
Granular Base Course: Layer coefficient $a_2 = 0.14$, drainage coefficient $m_2 = 1.0$, thickness $D_2 = 8.0\text{ inches}$.
Soil-Cement Subbase Course: Layer coefficient $a_3 = 0.11$, drainage coefficient $m_3 = 0.8$, thickness $D_3 = 10.0\text{ inches}$.

1. Write the AASHTO structural number equation. 2. Calculate the minimum thickness ($D_1$) of the asphalt surface course required to meet the design structural number. 3. Round $D_1$ to the nearest half-inch (as is standard in highway specs) and verify the final SN.

Full Mini-Exam 1

Mon, 04 May 2026 00:00:00 +0000

Full Mini-Exam 1

This exam is designed to simulate the PE Civil Transportation morning and afternoon sessions. It contains five representative multiple-choice questions spanning hydrology/drainage, nonmotorized design, and corridor integration.

Exam Questions

Question 1 (Hydrology)

A design engineer is calculating the peak runoff flow rate ($Q$) for a 35-acre industrial park watershed to size a stormwater channel. The site has a design return period of 50 years.

Paved parking and roofs ($C = 0.90$): 20 acres
Gravel storage lot ($C = 0.60$): 5 acres
Grass lawns ($C = 0.25$): 10 acres
The 50-year rainfall intensity for a duration equal to the time of concentration is $i = 4.2\text{ in/hr}$.
Use the standard NCEES frequency adjustment factor ($C_f$) for a 50-year storm.

Which of the following is closest to the 50-year peak runoff flow rate ($Q$)?

Full Mini-Exam 2

Mon, 04 May 2026 00:00:00 +0000

Full Mini-Exam 2

This exam is designed to simulate the PE Civil Transportation morning and afternoon sessions. It contains five representative multiple-choice questions spanning open channel hydraulics, transit stop design, traffic flow theory, hydraulic jumps, and earthwork balancing.

Exam Questions

Question 1 (Open Channel Flow)

A trapezoidal concrete-lined channel ($n = 0.013$) has a bottom width $b = 8.0\text{ feet}$ and side slopes of 2:1 (2H:1V). The longitudinal slope of the channel is $S = 0.16\% = 0.0016\text{ ft/ft}$.

Final Review and Formula Recognition

Mon, 04 May 2026 00:00:00 +0000

Final Review and Formula Recognition

Success on the PE Civil Transportation exam depends on quickly recognizing formulas in the NCEES Reference Handbook and matching them to the problem statement. This lesson serves as a final review guide, mapping critical equations across hydrology, drainage, traffic, geometry, and pavements.

1. Hydrology and Hydraulics

Formula Name	USCS Form	SI (Metric) Form	Variables & Crucial Units
Rational Method	$Q = C i A$	$Q = 0.00278 C i A$	$Q$ [cfs or $m^3/s$], $C$ [dim], $i$ [in/hr or mm/hr], $A$ [ac or ha]
SCS Runoff Depth	$Q = \frac{(P-0.2S)^2}{P+0.8S}$	Same	$Q$ [in], $P$ [in], $S$ [in] (Potential Max Retention)
SCS Retention	$S = \frac{1000}{CN} - 10$	$S = \frac{25400}{CN} - 254$	$S$ [in or mm], $CN$ [dim, 0-100]
Manning’s Velocity	$V = \frac{1.486}{n} R^{2/3} S^{1/2}$	$V = \frac{1}{n} R^{2/3} S^{1/2}$	$V$ [ft/s or m/s], $n$ [dim], $R = A/P_w$ [ft or m], $S$ [ft/ft]
Gutter Flow (Izzard)	$Q = \frac{0.56}{n} S_x^{5/3} S^{1/2} T^{8/3}$	$Q = \frac{0.376}{n} S_x^{5/3} S^{1/2} T^{8/3}$	$Q$ [cfs or $m^3/s$], $S_x$ [cross slope, ft/ft], $S$ [long slope, ft/ft], $T$ [spread, ft or m]
Broad-Crested Weir	$Q = C_w L H^{1.5}$	Same	$Q$ [cfs], $C_w$ [roadway default $\approx 2.6$ to $3.0$], $L$ [width, ft], $H$ [head, ft]
Hydraulic Jump (Conjugate)	$\frac{y_2}{y_1} = 0.5 (\sqrt{1+8Fr_1^2}-1)$	Same	$y_1$ [supercritical depth, ft], $y_2$ [subcritical depth, ft], $Fr_1$ [Froude number, dim]

2. Traffic Engineering and Signals

Formula Name	Equation Form	Variables & Crucial Units
Traffic Flow Relation	$q = u \cdot k$	$q$ [flow, veh/h/lane], $u$ [speed, mph], $k$ [density, veh/mi/lane]
Greenshields Model	$u = u_f (1 - k/k_j)$	$u_f$ [free-flow speed, mph], $k_j$ [jam density, veh/mi]
Greenshields Capacity	$q_{max} = \frac{u_f \cdot k_j}{4}$	$q_{max}$ [capacity, veh/h/lane]
Yellow Change Interval	$Y = t + \frac{V}{2a + 2gG}$	$t$ [reaction time, 1.0 s], $V$ [speed, ft/s], $a$ [deceleration, 10.0 $\text{ft/s}^2$], $G$ [grade, decimal]
Red Clearance Interval	$R_c = \frac{w+L}{V}$	$w$ [intersection width, ft], $L$ [vehicle length, 20 ft], $V$ [speed, ft/s]
Webster’s Cycle Length	$C_{opt} = \frac{1.5L + 5}{1 - Y_{sum}}$	$L$ [total lost time per cycle, s], $Y_{sum}$ [sum of critical flow ratios, dim]

3. Roadway Geometry

Formula Name	Equation Form	Variables & Crucial Units
Horizontal Radius	$R_{min} = \frac{V^2}{15(e + f)}$	$V$ [design speed, mph], $e$ [superelevation, ft/ft], $f$ [side friction factor, dim]
Curve Stationing	$T = R \tan(\Delta/2)$ and $L = \frac{\pi R \Delta}{180}$	$T$ [tangent length, ft], $L$ [curve length, ft], $\Delta$ [deflection angle, degrees]
Vertical Curve Profile	$y = y_{PVC} + g_1 x + \frac{r x^2}{2}$	$y$ [elevation, ft], $g_1$ [initial grade, ft/ft], $r = \frac{g_2-g_1}{L}$ [ft/ft$^2$], $x$ [distance, ft]
High/Low Point Location	$x_{hp} = \frac{g_1 L}{g_1 - g_2}$	$x_{hp}$ [distance from PVC, ft], $g_i$ [grades, percent], $L$ [curve length, ft]

4. Pavement and Earthwork

Formula Name	Equation Form	Variables & Crucial Units
Flexible Pavement SN	$SN = a_1 D_1 + a_2 D_2 m_2 + a_3 D_3 m_3$	$a_i$ [layer coeff, dim], $D_i$ [thickness, inches], $m_i$ [drainage coeff, dim]
Earthwork Shrinkage	$V_C = V_B (1 - S_h)$	$V_C$ [compacted volume], $V_B$ [bank volume], $S_h$ [shrinkage factor, decimal]
Earthwork Swell	$V_L = V_B (1 + S_w)$	$V_L$ [loose volume], $V_B$ [bank volume], $S_w$ [swell factor, decimal]

Formula Recognition Drills

Identify the Speed Units: In geometric radius $R_{min} = \frac{V^2}{15(e+f)}$, $V$ is in mph. In signal clearance $Y = t + \frac{V}{2a+2gG}$, $V$ is in ft/s. Double-check your units before squaring or dividing.
Identify the Grade Form: In vertical curve high point formulas, $g_1$ and $g_2$ are entered in percent (e.g. $3.0$). In signal timing and hydraulic slope equations, grades are entered in decimal form (e.g. $0.03$).
Verify the Area Units: Rational Method $Q = CiA$ uses area in acres. The SCS Peak flow equation $q_p = \frac{484AQ}{t_p}$ uses area in square miles.

Exam Day Decision Drills

Mon, 04 May 2026 00:00:00 +0000

Exam Day Decision Drills

This lesson features five qualitative “decision drills” designed to test engineering judgment, reference navigation, and qualitative reasoning. These drills simulate conceptual questions on the PE Civil Transportation exam where calculations are minimal but understanding context and standards is critical.

Drill 1: Identifying Culvert Control Conditions

Scenario:

A maintenance engineer inspects a concrete culvert under a highway embankment during a design storm event:

The headwater is ponded well above the top of the culvert inlet ($HW/D = 1.5$).
The tailwater level is low and does not submerge the outlet invert.
Flow inside the barrel is flowing shallow and fast, and a hydraulic jump is observed downstream of the outlet.

Decision: Is the culvert operating under Inlet Control or Outlet Control? How would you proceed to increase the capacity of this culvert?