SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

SCHEDULE 13D/A
Under the Securities Exchange Act of 1934
(Amendment No. 16)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of Rule 13d-1(e), 13d-1(f), or 13d-1(g), check the following box.  / /

NOTE: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See § 240.13d-7(b) for other parties to whom copies are to be sent.

The information required on the remainder of this cover page shall not be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange Act of 1934 ("Act") or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

CUSIP No. 74762E102

*

This representation is qualified by the fact that, as described in Item 4 of the Schedule 13D, UtiliCorp has the ability to vote or direct the vote of the shares subject to the Stockholder's Voting Agreements only in two limited, tax-related circumstances. UtiliCorp expressly disclaims beneficial ownership to any shares of Common Stock that are subject to the Stockholder's Voting Agreements.

2

**

The percentage reflected in row 13 above is obtained by using 75,923,049 shares as the denominator (in accordance with Rule 13(d)3(d)(1)(i)(D)). This denominator includes: (a) 58,698,244 shares of Issuer's issued and outstanding Common Stock (as indicated in Issuer's Form 10-Q filed on August 14, 2001), and (b) 17,224,805 shares of Common Stock into which Issuer's Convertible Preferred Stock held by UtiliCorp is convertible.

    Also note that the percentage of Common Stock owned by UtiliCorp on a partially diluted basis is approximately 37.69%. This percentage is obtained by using 77,550,547 shares as the denominator, which includes (a) the 75,923,049 shares discussed in the previous paragraph, and (b) 1,627,498 shares of Limited Vote Common Stock (as indicated in Issuer's Form 10-Q filed on August 14, 2001). UtiliCorp's ownership can be further diluted by (x) other classes of Issuer's securities that can be converted into Common Stock and (y) shares of Common Stock issuable under Issuer's Stock Option Plan.

3

AMENDMENT NO. 16 TO
STATEMENT ON SCHEDULE 13D

INTRODUCTION

    All information herein with respect to UtiliCorp United Inc., a Delaware corporation ("UtiliCorp"), and the common stock, par value $0.00001 per share (the "Common Stock"), of Quanta Services, Inc., a Delaware corporation ("Issuer"), is correct to the best knowledge and belief of UtiliCorp. The Schedule 13D originally filed on October 4, 1999 on behalf of UtiliCorp and fifteen amendments thereto filed on October 8, 1999, October 14, 1999, October 20, 1999, October 26, 1999, November 9, 1999, January 13, 2000, April 27, 2000, May 25, 2000, June 20, 2000, July 17, 2000, May 23, 2001, October 1, 2001, October 4, 2001, October 8, 2001 and October 11, 2001, respectively, on behalf of UtiliCorp are incorporated by reference and amended as follows.

ITEM 6. CONTRACTS, ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH RESPECT TO SECURITIES OF THE ISSUER.

    On October 19, 2001 UtiliCorp and Issuer amended the Standstill Agreement dated October 8, 2001, which was attached as an exhibit to Amendment No. 14 to UtiliCorp's Schedule 13D/A, to extend the term through 9:00 a.m. (U.S. Eastern Standard Time) on October 29, 2001.

4

SIGNATURE

    After reasonable inquiry and to the best of the undersigned's knowledge and belief, the undersigned hereby certifies that the information set forth in this statement is true, complete and correct.

5

QuickLinks