(a) What do you understand by the effective CBR value ? Discuss its significance. How is it calculated as per the latest IRC…

(a) Effective CBR of the subgrade (10 marks)

Meaning. The effective CBR is the single CBR value that represents a layered subgrade, that is, the CBR at which a uniform subgrade would give the same surface deflection as the actual layers. It is needed when the 500 mm subgrade has two layers of different strength, or when the subgrade differs significantly from the embankment or natural soil beneath it. IRC:37-2018 defines it through the effective resilient modulus of the subgrade.

Significance. The subgrade is the foundation of the pavement. Its strength controls the thickness of the granular and bituminous layers needed, and, in the mechanistic method, it sets the vertical compressive strain at the top of the subgrade that governs rutting. Using the CBR of the top layer alone over a weak embankment overestimates the support and gives an under-designed pavement, while using the weakest value alone wastes material.

Calculation as per IRC:37-2018.

• Design CBR of each layer. Determine the 4-day soaked CBR of the soil remoulded at the placement density (97% of the maximum dry density from the heavy compaction test) and moisture content, for the top 500 mm subgrade and for the embankment or natural soil below. Adopt the 90th percentile value for expressways, national and state highways, and for other roads the 80th percentile when the design traffic is below 20 msa and the 90th percentile otherwise.
• Convert each CBR to a resilient modulus. M_RS = 10.0 CBR (MPa) for CBR ≤ 5%, and M_RS = 17.6 (CBR)^0.64 for CBR > 5%.
• Two-layer analysis. Compute the maximum surface deflection δ for the two-layer system (500 mm subgrade over a semi-infinite embankment or soil layer) using IITPAVE, for a 40 kN wheel load with 0.56 MPa contact pressure (loaded radius a = 150.8 mm).
• Effective modulus. Take the modulus of a uniform half-space that gives the same deflection: M_RS(eff) = 2p a (1 − μ²)/δ, with μ = 0.35.
• Limits and use. The effective modulus is limited to a maximum of 100 MPa, and the corresponding effective CBR (from the equations above) is used in the design, and should exceed 5% for roads with more than 450 commercial vehicles per day.

(b)(i) Applications of origin and destination (O&D) studies (10 marks)

O&D data show where trips start and end, along with their purpose, mode and volume. They are collected by roadside or home interviews, post-card and licence-plate surveys, and now also by GPS, mobile-phone and ANPR data. Their applications are:

• Planning. Identifying desire lines and the main travel corridors, and finding the traffic generated and attracted by each zone. Forecasting future travel with growth-factor and gravity models. Deciding new links, bypasses and ring roads, and the phasing of road improvements.
• Design. Deciding the location and alignment of a bypass by the volume of through traffic. Choosing the type and geometry of intersections, flyovers and grade separations. Determining the number of lanes, and the capacity needed.
• Terminals and facilities. Locating bus stops and bus, truck and railway terminals, parking areas, toll plazas and airports. Planning public-transport routes and frequencies.
• Modelling. Building and calibrating the four-stage transport model (trip generation, distribution, mode split and assignment), and validating the assignment against observed flows.
• Traffic management. Planning one-way schemes, turn bans, diversions and parking restrictions. Coordinating signals, routing freight traffic away from congested areas, and assessing the effect of new policies or new facilities.
• Other. Estimating the share of through, local and internal traffic; studying the travel pattern of freight and passengers; and evaluating road-user costs and the economic viability of projects.

(b)(ii) Orientation in plane table surveying (10 marks)

Process. Orientation is the process of setting the plane table at a station so that all lines on the sheet are parallel to the corresponding lines on the ground. It is necessary because details plotted from different stations fit together on one sheet only if the table has the same orientation at every station. Without it, the plotted map is distorted.

Methods.

• By magnetic needle (trough compass). The trough compass is placed along the magnetic-meridian line drawn on the sheet at the first station, and the table is turned until the needle points to the ends of the trough. This is quick and simple, and is suited to small-scale surveys in areas free from local attraction. It is the least accurate, because the needle is affected by local attraction from iron and electrical lines, so it is not suitable for large-scale work.
• By backsighting. At a new station B, the alidade is placed along the plotted line ba, and the table is turned until the ranging rod at the previous station A is bisected, and then clamped. This is accurate and is the standard method for traversing, but it requires the line to be already plotted and the previous station to be visible. Any error in orientation at the earlier station is carried forward.
• By resection. The table is oriented at an unknown station using well-defined points already plotted on the sheet. It is suited to stations that are inaccessible or that have to be fixed from existing control points.
• Three-point problem. The station P is found by sighting three known points A, B and C. It is solved by the tracing-paper (Bessel) method, by Lehmann's trial-and-error rules using the triangle of error, or by the mechanical method. It is accurate if the points are well placed, but the solution fails if P lies on the circle through the three points (the danger circle), and it needs three visible, well-defined points.
• Two-point problem. Two known points A and B are used with an auxiliary station Q, from which rays to A and B are drawn with the table roughly oriented. The table is then set at P and oriented by backsighting Q, and back-rays are drawn from A and B, the intersection giving the position of P. This is used when only two points are visible, but it involves more work and trial and error, and is less accurate.

(c)(i) Accelerators and retarders (10 marks)

Difference. An accelerator is a chemical admixture that shortens the setting time and speeds up early hardening and strength gain. Examples are calcium chloride, calcium formate, triethanolamine and sodium silicate. A retarder is an admixture that slows down the setting and hydration. Examples are gypsum in excess, sugar, calcium lignosulphonate, tartaric acid and borax.

Effect on the properties of concrete.

• Accelerators. In fresh concrete, they shorten the initial and final setting time, and so the time available for placing. In hardened concrete, they raise the early strength, so that formwork can be struck sooner, but they may slightly reduce the later strength and increase shrinkage. Calcium chloride corrodes reinforcement, so it should not be used in reinforced or prestressed concrete. They are used in cold weather concreting, emergency repair, shotcrete, and where quick reuse of the formwork is needed.
• Retarders. In fresh concrete, they lengthen the setting time and keep the mix workable for longer, and they reduce the rate of heat release. In hardened concrete, they lower the early strength but usually improve the later strength. They are used in hot weather, in long hauls of ready-mixed concrete, in large pours, and in slip-form work, to avoid cold joints, and in grouting.

(c)(ii) Creep of hardened concrete (10 marks)

Definition. Creep is the gradual increase in strain of hardened concrete with time under a sustained constant stress, in addition to the instantaneous elastic strain on loading. It is mainly due to the movement of gel water and the viscous flow of the cement gel. The creep coefficient is φ = ε_c/ε_e, taken in IS 456 as about 2.2, 1.6 and 1.1 for loading at 7 days, 28 days and 1 year.

Diagram. The strain-time diagram is shown.

On loading at t₀ there is an instantaneous elastic strain ε_e. Under the sustained load, the strain then increases with time at a decreasing rate, giving the creep strain ε_c, which approaches a limiting value. On removal of the load at t₁, there is an instantaneous recovery, roughly equal to the elastic strain, followed by a slow creep recovery, which is only partial. A residual (permanent) strain remains. Creep increases with a higher stress, w/c ratio and cement paste content, and with earlier age at loading and lower humidity, and it is reduced by strong, stiff aggregate.