Mixture Temperature during Compaction

Almost all publications on SMA underline the necessity of carefully observing the temperature of the mixture during placement and rolling. The expected range of mixture temperature is determined in different ways; it chiefly depends on the kind of binder, but such factors as the layer thickness and weather conditions are impor­tant, too. However, the most important factor is the temperature of the mixture deliv­ered to the construction site and the temperature at the end of effective compaction, below which further rolling becomes ineffective and even harmful.

Minimum temperatures for mixture supplied to a work site according to the European standard EN 13108-5 (which applies only to selected [unmodified] bitu­mens after EN 12591) are as follows:

• 160°C for paving grade bitumen 40/60

• 150°C for paving grade bitumen 50/70

• 140°C for paving grade bitumen 70/100

In the German DAV SMA handbook (Druschner and Schafer, 2000), the afore­mentioned temperatures are presented in a more general way; the suggested tem­perature of an SMA mixture in a paver hopper should not be lower than 150°C. The same rule is presented by Bellin (1997).

Different temperatures at the end of the compaction time have been assumed in various publications, from 80-100°C for ordinary binder, and from 120-138°C for modified ones. The U. S. NAPA SMA Guidelines QIS 122 stipulates no rolling when the temperature of a layer drops below 116°C. A temperature of about 100°C has been stated in German documents as the point at which to stop rolling. The mini­mum temperature at the end of the compacting time may be roughly calculated by adding 50°C to the Ring and Ball (R&B) softening point of the binder used in the mix (Daines, 1985; Read and Whiteoak, 2003).

Other relevant points include the following:

• Problems related to a mix temperature that is either too low or too high are elaborated on in Chapter 11. Additional comments may be found in Section, which deals with rolling time.

• Optimum compaction temperatures are related to the viscosity of the added binder. That implies the significance of not only the lower temperature limit of rolling but also the initial temperature of rolling (already described while discussing SMA laydown on a hot underlying layer). A mixture that is too hot also causes problems at placement.

• Remember that spreading mixtures with substantial temperature differ­ences (e. g., from a truck with a hot mixture alternated with another truck with a cool mixture) cause changes in the resistance offered by such mix­tures at spreading.

• Appearing here and there in a layer being placed, pieces of a cool mixture may cause the development of an increased content of air voids and hence decrease the pavement’s lifespan (Pierce et al., 2002).

All these remarks concerning temperatures do not apply to cases that involve the use of special additives for lowering mixture temperatures that create the so-called warm mixes.

Embankment Construction

Where a pipe is required as part of an embankment construction, it may be installed by compacting layers of fill uniformly on either side. It is important to bring the layers up uniformly on either side of the pipe. After a sufficient layer is compacted over the top of the pipe, ordinary embankment construction may proceed. Alternatively, some agencies require that the embankment be constructed first, then a trench dug for the installation of the pipe.

5.10.1 Trench Construction

The open-trench method is commonly used for culvert construction. It is more cost – effective than tunneling except when a pipe must be constructed in an existing high fill. Shoring may be necessary, particularly if the installation is under a traveled way. This will keep the limits of excavation to a minimum and, by the use of steel cover plates, allow the roadway to remain open during nonworking hours. Where it is necessary to use an open-trench method of construction in urban areas, it is wise for the designer to make available to the contractor options for the type of structure to be placed. For example, if a box culvert is deemed necessary by the engineer because of hydraulic considerations and physical constraints, a precast concrete or a prefabricated metal box, as alternatives to cast-in-place construction, should be permitted. In this manner, the traveling public expe­riences a minimum of disruption of service when open-trench construction is used. AASHTO recommends a trench width equal to 1.25 times the outside diameter of the pipe plus 1 ft (300 mm) for concrete pipe and a width to provide for 2 ft (600 mm) mini­mum on each side of the pipe for flexible culverts. However, some states simply recom­mend a constant clearance between the outside of the pipe and the trench wall to ensure that there is room for compaction and compaction-testing equipment.


Underground structures may be built by a variety of means including embankment construction, open-trench construction, jacking, tunneling, and microtunneling.

The proper design and installation of the foundation, bedding, and backfill for embankment and trench installations are critical to the performance of underground structures. They are also essential factors for achieving an accurate structural analysis of the system. The foundation preparation, bedding, and backfill of underground structures should be done in accordance with standards established by local and state transportation agencies. These standards vary from region to region, but the important aspects of typical practices are reviewed below.

Regardless of whether the pipe is installed in an embankment or a trench, the foun­dation must provide relatively uniform resistance to loads. If rock is encountered, it should be excavated and replaced with soil. If soft material is encountered, it should be removed for a width of three pipe spans and replaced with suitable material. Care must be taken to ensure that the foundation under the pipe is not stiffer than the adjacent zones, because this will attract additional load on the pipe.

The bedding is then placed above the foundation. Bedding thickness and material is contingent upon the type of pipe and the quality of the installation required. Pipe-arch structures require excellent soil support at the corners, because pressures are higher there. For most applications 3 to 6 in (75 to 150 mm) of bedding is sufficient. Some agencies require a shaped bedding for all pipe because of the difficulties in compacting the backfill in the haunch area. More recently, for most round pipes, in lieu of a shaped bedding, specifications call for the bedding under the middle one-third of the pipe diameter to be left uncompacted. This is so that the pipe can properly seat itself in the bedding, resulting in a greater length of support along the bottom circumference of the pipe. Pipe arches and large span structures should always be placed on a shaped bedding.

The backfill should be placed in 6- to 8-in (150- to 200-mm) compacted layers around the structure. Each backfill layer must be compacted to the minimum density required in the construction specifications. Densities less than 90 percent standard Proctor density should not be permitted. The backfill must be kept in balance on each side of the pipe. A granular material free of organic content and with little or no plasticity makes good backfill.

Complete installation requirements for the various pipe materials can be found in AASHTO, ASTM, and state DOT specifications.


In some very old houses, you may find that the neutral wires were attached to a switch— rather than the hot wires, as required by codes today. Thus, when working on old switches or fixtures, test all wires for current. Even if you’ve flipped a fixture switch off, there could still be a hot conductor in the fixture outlet box.


Подпись: TIP
Подпись: Miscellaneous tools. From left:two slot-head screwdrivers, tapper (to cut threads in metal box holes), offset screwdriver, nut driver, utility knife, small pry bar/nail puller, plaster chisel, drywall saw, and hacksaw.


when an outlet is too distant. Cordless tools now have all the power you could want. Besides, they don’t need an extension cord and won’t electrocute you if you inadvertently drill or cut into a live wire. Cordless reciprocating saws can cut anything from plaster lath to studs; but use

a cordless jigsaw if you want to preserve the plaster around a cut-in box opening.

Miscellaneous tools. Other necessary tools include a hammer, tape measure, Speed Square, hacksaw, plaster chisel, drywall saw, nut driver, small pry bar, and spirit level.

Electrical cable. From top:type NM (Romex), type UF (underground), armor clad (AC), and metal clad (MC). Note: The silver wire in the AC cable is a bonding wire, not a ground. In the MC cable, the green wire is ground, the white is neutral, and the red and black are hot.



Design Considerations

For a waterway crossing, the designer must consider the backwater elevation and flow velocity for both the proposed and existing structures. It is recommended that the same hydraulic model be utilized for both the existing and proposed structure. Any increase in backwater elevation or stream velocity must be thoroughly analyzed and the upstream and downstream effects considered. For a grade separation structure the designer must consider both horizontal and vertical clearances. The shape of the replacement structure must be considered when determining the minimum clearances.

It is imperative that an accurate and complete survey of the existing structure be conducted. This will aid the designer in determining the maximum prefabricated struc­ture size that can be installed at a particular site.

In certain situations it may be possible to reuse portions of the existing structure in the design of the replacement structure. The most obvious example is reuse of the existing foundation. If the foundation type is known (i. e., concrete spread footer, con­crete on piling, etc.) standard geotechnical engineering calculations for assessing the suitability of the foundation must be completed. The designer is cautioned against using existing unknown foundation types.

One of the primary benefits of utilizing a prefabricated culvert as a bridge replace­ment is that much of the existing structure can remain in place. This reduces construction time and reduces the work limits required for the structure installation. For single-span structures with vertical wall-type abutments, it is typical to leave the existing abutments in place. It may also be possible to leave the deck in place. For multiple-span structures, existing abutments, piers, foundations, and deck may all be left in place depending on site constraints. The required size of the replacement structure, along with site access will typically control how much of the existing structure can be left in place.

Another consideration for the designer is the void space between the existing and proposed structure. If there is insufficient void space to properly place, compact, and test soil backfill, the use of flowable fill is common. Where flowable fill is utilized, it is recommended that the proposed structure size be maximized. This is because the cost of the additional structure size is typically far less expensive then the cost of the flowable fill.

Lastly the designer must determine the structural capacity of the replacement struc­ture and the existing structure. If the two structures are very close or if the existing deck is left in place, then the composite strength of the two may be considered. The finite element method is well suited for this complex analysis. In the absence of sophisticated computer methods, the designer can conservatively ignore the contribu­tion of the existing structure. However, typical design assumptions regarding sur­rounding soil support must be verified prior to the use of the closed form design methodologies presented in Art. 5.8. The designer must also consider external grout­ing pressures when flowable fill is used as the backfill material.

Orthogonal Transformation Techniques

The orthogonal transformation is an important tool for treating problems with correlated stochastic basic variables. The main objective of the transformation is to map correlated stochastic basic variables from their original space to a new domain in which they become uncorrelated. Hence the analysis is greatly simplified.

Orthogonal Transformation Techniques

Consider K multivariate stochastic basic variables X = (Xі, X2,, XK)t having a mean vector fj, x = (jx1, /г2 …, /гкУ and covariance matrix Cx as


011 012 013 021 °22 023





Cr =


0K1 Ok2 0K3




in which oij = Cov(Xi, Xj), the covariance between stochastic basic variables Xi and Xj. The vector of correlated standardized stochastic basic variables X’ = D-1/2(X – fxx), that is, X’ = (X1, X2,…, XKУ with Xk = (Xk – /xk)/ok, for k = 1,2,…, K, and Dx being an K x K diagonal matrix of variances of stochastic basic variables, that is, D x = diag(o12, o|, …, o^), would have a mean vector of 0 and the covariance matrix equal to the correlation matrix Rx:


Orthogonal Transformation Techniques

Y = T-1X ’ (4C.1)

where Y is a vector with the mean vector 0 and covariance matrix I, a K x K identity matrix. Stochastic variables Y are uncorrelated because the off- diagonal elements of the covariance matrix are all zeros. If the original stochas­tic basic variables X are multivariate normal variables, then Y is a vector of uncorrelated standardized normal variables specifically designated as Z’ be­cause the right-hand side of Eq. (4C.1) is a linear transformation of the normal random vector.

It can be shown that from Eq. (4C.1), the transformation matrix T must satisfy


Rx = TTt




There are several methods that allow one to determine the transformation matrix in Eq. (4C.2). Owing to the fact that Rx is a symmetric and positive – definite matrix, it can be decomposed into

Rx = LLt (4C.3)

in which L is a K x K lower triangular matrix (Young and Gregory, 1973; Golub and Van Loan, 1989):

l11 0


. . . 0 ‘

l21 l22


. . . 0

Ik 1 Ik2 Ik3

. . . Ikk _


which is unique. Comparing Eqs.(4C.2) and (4C.3), the transformation matrix T is the lower triangular matrix L. An efficient algorithm to obtain such a lower triangular matrix for a symmetric and positive-definite matrix is the Cholesky decomposition (or Cholesky factorization) method (see Appendix 4B).

The orthogonal transformation alternatively can be made using the eigenvalue-eigenvector decomposition or spectral decomposition by which Rx is decomposed as

Rx = Cx = VAVt (4C.4)

where V is a K x K eigenvector matrix consisting of K eigenvectors as V = (v i, v 2,…, vK), with vk being the kth eigenvector of the correlation matrix Rx, and Л = diag(X1, Л2,…, XK) being a diagonal eigenvalues matrix. Frequently, the eigenvectors v’s are normalized such that the norm is equal to unity, that is, vt v = 1. Furthermore, it also should be noted that the eigenvectors are or­thogonal, that is, v t v j = 0, for i = j, and therefore, the eigenvector matrix V obtained from Eq. (4C.4) is an orthogonal matrix satisfying VVt = Vt V = I where I is an identity matrix (Graybill, 1983). The preceding orthogonal trans­form satisfies

Vt Rx V = Л (4C.5)

To achieve the objective of breaking the correlation among the standardized stochastic basic variables X’, the following transformation based on the eigen­vector matrix can be made:

U = VtX’ (4C.6)

The resulting transformed stochastic variables U has the mean and covariance matrix as

E(U) = V tE(X’) = 0 C (U) = VtCx V = Vt RxV = Л







As can be seen, the new vector of stochastic basic variables U obtained by Eq. (4C.6) is uncorrelated because its covariance matrix Cu is a diagonal ma­trix Л. Hence, each new stochastic basic variable Uk has the standard deviation equal to V^k, for all k = 1, 2,…, K.

The vector U can be standardized further as

Y = Л-1/2и (4C.8)

Based on the definitions of the stochastic basic variable vectors X – (vx, Cx), X’ – (0, Rx), U – (0, Л), and Y – (0,1) given earlier, relationships between them can be summarized as the following:

Y = Л-1/2и = Л-1/2 V1X’ (4C.9)

Comparing Eqs.(4C.1) and (4C.9), it is clear that

T-1 = Л-1/2 V1

Applying an inverse operator on both sides of the equality sign, the transfor­mation matrix T alternatively, as opposed to Eq. (4C.3), can be obtained as

T = VЛ1/2 (4C.10)

Using the transformation matrix T as given above, Eq. (4C.1) can be expressed as

X ‘ = TY = VЛ1/2Y (4C.11a)

and the random vector in the original parameter space is

X = vx + D1/2 VЛ1/2Y = vx + D1/2 LY (4C.11b)

Geometrically, the stages involved in orthogonal transformation from the orig­inally correlated parameter space to the standardized uncorrelated parameter space are shown in Fig. 4C.1 for a two-dimensional case.

From Eq. (4C.1), the transformed variables are linear combinations of the standardized original stochastic basic variables. Therefore, if all the original stochastic basic variables X are normally distributed, then the transformed stochastic basic variables, by the reproductive property of the normal random variable described in Sec. 2.6.1, are also independent normal variables. More specifically,

X – N(vx, Cx) X’ – N(0, Rx) U – N(0, Л) and Y = Z – N(0,1)

The advantage of the orthogonal transformation is to transform the correlated stochastic basic variables into uncorrelated ones so that the analysis can be made easier.

Orthogonal Transformation Techniques
The orthogonal transformations described earlier are applied to the stan­dardized parameter space in which the lower triangular matrix and eigenvector matrix of the correlation matrix are computed. In fact, the orthogonal transfor­mation can be applied directly to the variance-covariance matrix Cx. The lower triangular matrix of Cx, L, can be obtained from that of the correlation matrix L by

L = D1/2 L (4C.12)

Following a similar procedure to that described for spectral decomposition, the uncorrelated standardized random vector Y can be obtained as

Y = Л-1/2 Vг (X – цх) = Л-1/2£7 (4C.13)

where V and Л are the eigenvector matrix and diagonal eigenvalue matrix of the covariance matrix Cx satisfying

Cx = УЛ V/1

and U is an uncorrelated vector of the random variables in the eigenspace having a zero mean 0 and covariance matrix Л. Then the original random vector X can be expressed in terms of Y and L:

X = fix + VA1/2Y = fix + L Y (4C.14)

One should be aware that the eigenvectors and eigenvalues associated with the covariance matrix Cx will not be identical to those of the correlation matrix Rx.

STEP 8 Seal the Roof with Felt Paper

Now that the house has been framed and sheathed, its time to seal it from the elements.

As long as you are able to work safely on a roof, voucan cover it with rooting felt and shingles. It’s best if all the plumbing and beating vents are through the root before you install the felt.

If that isn’t possible, just make sure they’re installed before you begin shingling.

Roll out the felt paper

Felt paper, sometimes called tar paper or builder’s felt, is the first protective layer installed over roof sheathing. This material has evolved in a fashion similar to that of a candvbar. In the old davs, you could buv a good-size candy bar for a nickel. Today, you getamuch smaller bar at a higher price.

Similarly, the felt paper available today is much lighter, even though it’s sti. l sold as

15- lb. and 30-lb. felt. I like to use 30-lb. felt for theunderlayment because it provides extra protection and the cost difference isn’t that
great. Roofing felt has horizontal lines marked

О c?

on it. Follow a line that provides a minimum 4-in. lap as you roll one row over another.

Follow nailing guidelines

Some builders like lo snap a chalkline on the sheathing 36 in. up from the edge of the gutter or fascia board and lav the first roll of felt


Подпись: ІПодпись: Helping HandПодпись: Stay cool. Roofing can be hot work. Be sure to drink plenty of water, take breaks, and go down if you begin to feel weak. Remind others to do the same.to that line. This makes the roll lay down straight. Alternatively, you can hold the felt Hush with the edge of the roof. Unroll the felt Hat (with no bumps or wr nkles) and tack it down with roofing tacks. A roofing tack is a small nail with a large plastic button (gener­ally green, orange, or red) on top (see the bottom photo on p. 136). Stepping on felt that is not nailed well can cause you to slip off the roof, so use plenty of roofing tacks (6 in. o. c. at the bottom and ends and 10 in. o. c. from top to bottom every 24 in. o. c. across the roof). Roofing tacks hold the felt in place, which is especially important if the roof won’t be shingled for several days. Pick up any tacks that fall to the ground so that no one steps on them. Finally, trim the felt flush with the gable ends.

Подпись: ASPHALT PAPER IS THE FIRST LAYER OF PROTECTION. Known as builder's felt, this waterproof paper is applied over roof sheathing. Overlap each course by at least 4 in. Подпись: INSTALLING A DRIP EDGE. This L-profile flashing is installed around the edges of the roof.STEP 8 Seal the Roof with Felt PaperWhether you are tacking down roofing felt or nailing on shingles, it’s important in con­sider whether the nails can be seer, from below. When the eaves around t he house are open (no soffit), a long nail penetrates the roof sheathing and is visible to anyone who looks up. I kindreds of shiny nails sticking through the plywood or OSB is ur at tractive. Therefore, when tacking felt around the perimeter of the roof, take care to nail the tacks into the barge rafters and gable-end rafters—not just through the sheathing into the air. When nailing shingles, use %-in. nails at the gable overhangs and eaves. When work­ing over the house frame, nails that penetrate the sheathing in the attic are not a problem.

Seal twice around vents

The vent pipes that extend through the roof are flashed with special rubber or metal boots when the shingles are installed. But here in rainy Oregon, roofers take the time to make a double seal around these pipes. This is sort of like wearing a slicker and carrying an umbrella, too—but there’s no such thing as being too careful when it comes to roofs and water. To provide this extra protection, cut a 3-ft.-sq. piece of felt and cut a hole in the center the size of the vent pipe. Slip the felt over the vent and seal around the pipe with a tube of roofing tar. Do the same when you roll out the long strips of roofing felt. Cut the sec­ond layer of felt around each vent and again seal it around the pipe with roofing tar. You can lap the fell over the ridge, but remember to cut it away when you shingle to permit air­flow into the ridge vent.

Protect valleys and intersections

When a porch roof intersects the main root at a right angle, valleys are created on each side of the intersection. Valleys divert more water


Подпись: Felt paper on roofSTEP 8 Seal the Roof with Felt PaperПодпись: Cut the face of the metalПодпись: Bend and fit the drip edge to the ridge.STEP 8 Seal the Roof with Felt PaperПодпись: Cut a pie-shaped slice from the top of the drip edge arid bend it to fit around the corner.STEP 8 Seal the Roof with Felt PaperПодпись: The metal drip edge is placed on the fascia or gutter boards and barge rafters before shingles are nailed to the roof.Подпись: Helping HandПодпись: Cut elliptical holes in felt flashing. When you need to flash around a vent pipe, fold the felt in half and cut out half of an ellipse with a sharp utility knife. Because of the roofs slope, the hole is shaped more like an ellipse than a circle. The steeper the slope, the longer the ellipse.

than a regular gable roof does, so I always pro­vide extra protection in the form of flashing.

I like to roll at least two lavers of 30-lb. felt


right down the center of the valley. Even bet­ter is to cover the valley area with a sheet of 90-lb. rolled roofing. Then, when you install regular roofing felt, lay each row 12 in. or more beyond the valley and keep all roofing tacks at least 12 in. from the center of the valley. This technique provides a double layer of protection prior to shingling.

When working on a roof that butts into the sidewall of a house (a porch roof connected to a gable end, for example), lap the felt on the sidewall by at least 6 in. to prevent leaks at the intersection.

Install a drip edge

Once the fell is in place, make i: more secure around the edges bv installing sections of vinyl or metal drip edge. Drip edge is an L-shaped metal or vinyl flashing that comes in 10-ft. sections. One leg of the I profile extends about 13 in. up the roof; the other leg extends down the fascia or barge rafter by the same distance (see the bottom photo on the facing page). It has a slight lip on the lower edge to divert water from the roof.

Using roofing nails, install the drip edge wider the felt at the eaves and on top of the felt at the rakes, or gable ends. Space nails about 2 ft. apart. Where one length of edging joins another, overlap the joint by about 4in. Along the gable ends, make sure the top length of the drip edge laps over the one below. At the corners, cut a pie-shaped slice out of the top section. This allows you to bend the drip edge at a 90-degree angle and nail it around the corner. At the ridge, make a plumb nit in the vertical leg and bend the edge over the ridge, allowing the plumb cut to overlap, as shown in the illustration above.

Shapes and Materials

Shapes and Materials

Almost any size and shape of culvert can be utilized for the replacement of an existing bridge. However, reinforced concrete three – and four-sided box culverts, special shape reinforced concrete structures, metal box culverts, and long-span corrugated metal structures are particularly suited for this application. This is because they tend to have larger open-end areas with lower rises. General details on these structure types are given in Art. 5.6 and the structural design of these structures is given in Art. 5.8. Figures 5.42 and 5.43 show examples of reinforced concrete arches and a long-span corrugated steel culvert being used as bridge replacement structures.

Shapes and Materials

FIGURE 5.43 Corrugated steel culvert being used as a railroad overpass. (Photograph with permission of Viacon, Polska)


Corrections to mixture problems occurring during delivery of a mixture may be pos­sible up until the moment of placing the SMA. The moment the SMA layer appears behind the screed plate of a paver, the chances of improving the quality diminish to a minimum. After that time only compaction is possible; errors made during the design and manufacturing stages can no longer be corrected.

The vital elements of spreading an SMA layer include the following: [62]

10.3.1 image101
Layer Thickness

An SMA layer thickness should not be less than three times the maximum aggregate size in the mixture, and in principle, not greater than four times (higher ratios allow better compactability). An appropriately selected layer thickness with regard to gra­dation enables suitable compaction of the layer (reaching the expected compaction factor). For details on selecting SMA gradation, please refer to Chapter 6.

The layer thickness exerts a considerable influence on the speed of cooling of the layer, eventually involving temperature problems of various types (see Chapter 11). To put it briefly, the thinner the SMA layer, the more difficult the compaction. In addition, a thin layer cools off fast, magnifying compaction problems.

Preparing Pavement Facilities

The existing pavement facilities should be prepared prior to placing the mixture of a wearing course. This preparation should result in the following:

• Appropriate, tight, and durable bonding between asphalt course and facilities (e. g., with the use of suitable polymer modified asphalt tapes [Figure 10.7])

• Protection against damage or infiltration of excess asphalt mixture (e. g., around a drain or manhole)

10.2.5 Preparing Edges of the Courses

The edges of the course should also be prepared. The selected method should ensure durable joints at the transverse and longitudinal edges. Most previous experiences have proved the poor effectiveness of traditional methods like applying hot binder,

Preparing Pavement Facilities

image100FIGURE 10.8 PMB tape for sealing pavement joints (a) when bonding with a layer edge and (b) after application. (Photos courtesy of Slaskie Kruszywa Naturalne sp. z o. o., Poland.)

covering with emulsion, and other similar techniques. As in other cases, PMB tapes (Figure 10.8) put on manually or special PMB compounds spread mechanically (Figure 10.9) have been recommended.