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1、STRUCTURAL ELEMENTS1-1 1STRUCTURAL ELEMENTS 1.1Overview Animportantaspectofgeomechanicalanalysisanddesignistheuseofstructuralsupporttostabilize a rock or soil mass. Structures of arbitrary geometry and properties, and their interaction with a rock or soil mass, may be modeled with FLAC. This section
2、 describes the structural elements available in FLAC. Generic concepts, such as geometry specifi cation, linkage of elements to the grid and to each other, options for specifying end conditions, and specifi cation of properties, are discussedfi rst. Eachtypeofstructuralelementisthendescribedindetail
3、, includingadescriptionof the numerical formulation and the properties required for each element type. Example applications are also provided at the end of each section.* All vector quantities in this section are expressed using indicial notation with respect to a fi xed right-handed rectangular Car
4、tesian coordinate system. Thus, the position vector is denoted by xi, where it is understood that the indices range over the set 1,2. Notethat,becauseFLACisatwo-dimensionalcode,thethree-dimensionaleffectofregularlyspaced elements is accommodated by scaling their material properties in the out-of-pla
5、ne direction. This procedure is explained in Section 1.9.4. 1.1.1Types of Structural Elements Seven forms of structural support may be specifi ed. 1. Beam Elements Beam elements are two-dimensional elements with three degrees of freedom (x-translation, y-translation and rotation) at each end node. B
6、eam elements can bejoinedtogetherwithoneanotherand/orthegrid. Beamelementsareusedtorepresenta structuralmember,includingeffectsofbendingresistanceandlimitedbendingmoments. Tensile and compressive yield strength limits can also be specifi ed. Beams may be used to model a wide variety of supports, suc
7、h as support struts in an open-cut excavation and yielding arches in a tunnel. Interface elements can be attached on both sides of beam elements in order to simulate the frictional interaction of a foundation wall with a soil or rock. Beam elements attached to sub-grids via interface elements can al
8、so simulate the effect of geotextiles. (See Section 1.2.) * Thedatafi leslistedinthisvolumearecreatedinoneoftwoways: eitherbytypinginthecommands inatexteditor; orbygeneratingthemodelintheGIICandexportingthefi leusingtheFile/Export Record menuitem. Thefi lesarestoredinthedirectory“ITASCAFLAC500STRUCT
9、URES”with the extension “.DAT.” A project fi le is also provided for each example. In order to run an example and compare the results to plots in this volume, open a project fi le in the GIIC, by clicking on the File/Open Project menu item and selecting the project fi le name (with extension “.PRJ”)
10、. Click on the Project Options icon at the top of the Project Tree Record, select Rebuild unsaved states and the example data fi le will be run and plots created. FLAC Version 5.0 1-2Structural Elements 2. Liner Elements Liner elements, like beam elements, are two-dimensional elements with three deg
11、rees of freedom (x-translation, y-translation and rotation) at each end node, and these elements can be joined together with one another and/or the grid. Liner elements are also used to represent a structural member in which bending resistance, limited bending moments and yield strengths are importa
12、nt. The primary difference betweenlinerelementsandbeamelementsisthatlinerelementsincludebendingstresses to check for yielding, whereas beam elements only base the yielding criterion on axial thrust. Liner elements are recommended for modeling tunnel linings, such as concrete or shotcrete liners. (Se
13、e Section 1.3.) 3. CableElementsCableelementsareone-dimensionalaxialelements that may be anchored at a specifi c point in the grid (point-anchored), or grouted so that the cable element develops forces along its length as the grid deforms. Cable ele- ments can yield in tension or compression, but th
14、ey cannot sustain a bending moment. If desired, cableelementsmaybeinitiallypre-tensioned. Cableelementsareusedtomodel a wide variety of supports for which tensile capacity is important, including rock bolts, cable bolts and tiebacks. (See Section 1.4.) 4. Pile Elements Pile elements are two-dimensio
15、nal elements that can transfer normal and shear forces and bending moments to the grid. Piles offer the combined features of beams and cables. Shear forces act parallel to the element, and normal forces perpen- dicular to the element. The three-dimensional effect of the pile interaction with the gri
16、d can be simulated. A user-defi ned FISH function describing the load versus deformation at the pile/medium interface normal to the pile can also be specifi ed. The element does not yield axially, but plastic hinges can develop. Pile elements are specifi cally designed to represent the behavior of f
17、oundation piles. (See Section 1.5.) 5. Rockbolt Elements Rockbolt elements, like pile elements, are two-dimensional ele- ments that can transfer normal and shear forces and bending moments to the grid. Rock- bolt elements have the same features as pile elements. In addition, rockbolt elements can ac
18、count for: (1) the effect of changes in confi ning stress around the reinforcement; (2) the strain-softening behavior of the material between the element and the grid material; and (3) the tensile rupture of the element. Rockbolt elements are well-suited to represent rock reinforcement in which nonl
19、inear effects of confi nement, grout or resin bonding, or tensile rupture are important. (See Section 1.6.) 6. StripElementsStripelementsrepresentthebehaviorofthinreinforcingstripsplaced in layers within a soil embankment to provide structural support. The strip element is similar to the rockbolt el
20、ement in that strips can yield in tension or compression, and a tensile failure strain limit can be defi ned. Strips cannot sustain a bending moment. The shear behavior at the strip/soil interface is defi ned by a nonlinear shear failure envelope thatvariesasafunctionofauser-defi nedtransitionconfi
21、ningpressure. Stripelementsare designedtobeusedinthesimulationofreinforcedearthretainingwalls. (SeeSection1.7.) 7. Support Members Support members are intended to model hydraulic props, wooden props or wooden packs. In its simplest form, a support member is a spring connected between two boundaries.
22、 The spring may be linear, or it may obey an arbitrary relation FLAC Version 5.0 STRUCTURAL ELEMENTS1-3 between axial force and axial displacement, as prescribed from a table of values. The support member has no independent degrees of freedom: it simply imposes forces on the boundariestowhichitiscon
23、nected. Asupportmembermayalsohaveawidthassociated with it. In this case, it behaves as if it were composed of several parallel members spread out over the specifi ed width. (See Section 1.8.) In all cases, the commands necessary to defi ne the structure(s) are quite simple, but they invoke a very po
24、werful and fl exible structural logic. This structural logic is developed with the same fi nite-difference logic as the rest of the code (as opposed to a matrix-solution approach), allowing the structure to accommodate large displacements and to be applied for dynamic as well as static analysis. 1.1
25、.2Geometry The geometries of all structural elements are defi ned by their endpoints. The user defi nes the endpoints for beams, liners, cables, piles, rockbolts and strips, whereas the endpoints for support elements are found automatically by FLAC. Note that cable, pile, rockbolt and strip endpoint
26、s have different mechanical behaviors, depending on the form of specifi cation grid or x,y (see below). 1.1.2.1Beam, Liner, Cable, Pile, Rockbolt and Strip Elements The primary format to specify each beam, liner, cable, pile, rockbolt or strip element is of the form: STRUCTbegin .end. where type is
27、beam, liner, cable, pile, rockbolt or strip. Note that an optional format, using from and to, is also available to facilitate geometry creation for beams and liners along model boundaries. See Section 1.1.2.2. In general, endpoints may be placed at any location inside or outside the FLAC grid. The b
28、eginning and ending locations are identifi ed by the keywords begin and end, respectively. One of three types of linkage may be defi ned by phrases following begin and end: grid = i, j x,y node = n grid = i, j denotes that the beginning (or ending) of the element is linked to gridpoint (i, j) of the
29、 host medium. For example, in Figure 1.1, two beam elements are connected to the grid at gridpoints (1,2) and (1,3), and at (1,3) and (1,4). The only way that beam and liner elements can interact with the grid is by linking their nodes to gridpoints with the grid keyword, or via a connection through
30、 interface elements (see Section 1.1.2.2). If the grid keyword is specifi ed for one end of a cable, then that end of the cable is bonded rigidly to the specifi ed gridpoint; the grout properties are not used at such an attachment point. This also applies for the pile, rockbolt and strip elements an
31、d coupling-spring properties. FLAC Version 5.0 1-4Structural Elements If x- and y-coordinates are specifi ed, the endpoint is located at any selected location within or outside the grid. In Figure 1.1, a cable element (Cable 1) is located with endpoints at (x = 0, y = 3.5) and (x = 3, y = 3.5). If c
32、oordinates are used to specify one end of a cable, even if the coordinates coincide exactly with a gridpoint, then grout stiffness and strength will operate at the connection e.g., the cable may “pull out.” Likewise, if x- and y-coordinates are specifi ed for a pile, rockbolt or strip node, the coup
33、ling-spring properties will operate. Beam 1 Beam 2 Cable 1 Cable 2 FLAC grid y 5 4 3 2 j=1 i=12345 x Figure 1.1Placement of element end nodes (FLAC zones are 1 unit square) node = n links the beginning (or ending) of the beam, liner, cable, pile, rockbolt or strip to another node of the structure. T
34、he node numbers are assigned sequentially, starting with one, when the linkage phrase grid = i, j or x, y is used. Alternatively, nodes can be created at any location and assigned node numbers by the user via the command STRUCT node n x, y to position a node at a specifi c location, or via the comma
35、nd STRUCT node n grid i,j to link the node to a gridpoint. These nodes can then be included in the structural element. Node numbers can be identifi ed by issuing either the PRINT struct node position or PLOT struct node command. For example, cable 2 in Figure 1.1 is defi ned by endpoints at node num
36、bers 1 and 6. Node 6 is fi rst located at (x = 3, y = 2). Note that all nodes (and all elements) have unique numbers. Example 1.1 shows the commands to produce the geometry in Figure 1.1. Structural element groups are assigned unique ID numbers automatically. A group is a collection of structural el
37、ements of the same type that contains a contiguous set of nodes, and the adjoined element segments have the same property number (see Section 1.1.6). The group ID numbers can befoundviathePLOTstructnumbercommand. Forexample, inExample1.1therearethreegroups FLAC Version 5.0 STRUCTURAL ELEMENTS1-5 bec
38、ause the two beam elements are connected by a common node (node 2). Note that cable 2 has a separate group ID number even though it is connected to beam 1 at node 2. Example 1.1Specifying structural elements grid 4 4 mo el struct beam begin grid 1,2 end grid 1,3 ; beam 1 struct beam begin grid 1,3 e
39、nd grid 1,4 ; beam 2 struct cable begin 0,3.5 end 3,3.5; cable 1 struct node 6 3,2; individual node struct cable begin node 1 end node 6; cable 2 Asingleelementmaybedividedatitscreationintoanumberofsmallerelementsorsegmentsusing the segment = n keyword. Each segment represents a structural element.
40、If n = 1, then only one segment (and, thus, one element) is created. If n 1, then FLAC divides the specifi ed beam, liner, cable, pile, rockbolt or strip into n elements of equal length. The coordinates and node numbers for each element are automatically determined by FLAC. The PLOT struct element c
41、ommand plots the individual elements and their identifying numbers. Themostcommonreasontospecifyn1istoimproveaccuracy,especiallywithcable,pile,rockbolt and strip elements that are interacting with the host medium. In this case, the distribution of shear forcesalongtheelementisafunction, tosomeextent
42、, ofthenumberofnodalpoints. Thefollowing rules-of-thumb can be used to determine the number of element nodal points and, thus, segments for cables, piles, rockbolts and strips. 1. Try to provide approximately one element-nodal point in each FLAC zone. The reasoning here is that since the zones are c
43、onstant-stress elements, it is not necessary to have more than one interaction point within a zone. 2. Try to provide at least two to three structural elements within the develop- ment length of the cable or rockbolt. The development length is determined by dividing the specifi ed yield force by the
44、 unit bond value. By following this procedure, failure by “pull-out” can occur if such conditions arise. For example, if cable elements are too long, then only the yield failure mode of the axial element is possible. (There is no yield in the piles at this time.) 3. If a cable, pile, rockbolt or str
45、ip crosses a grid interface, and the calculation is to be performed in large-strain mode, then enough element segments must be provided in the part of the element that is distorted by the interface, so that the proper shear restraint is captured. At least fi ve element segments in this region must b
46、e provided. FLAC Version 5.0 1-6Structural Elements Structural element segments can be deleted at any time in the calculation process by specifying the keyword phrase delete n1 n2 following the name of the element type. For example, to delete beamelementsegmentsbeginningwithsegment(i.e.,element)numb
47、er10andendingwithsegment number 15, use the command struct beam delete 10 15 If only n1 is given, one element segment is deleted. If neither n1 nor n2 is specifi ed, all segments are deleted. If the segments to be deleted are connected by a slave (or master) node, the node must fi rst be “unslaved”
48、(see Section 1.1.5). All information related to the geometry and properties of structural elements can be printed with the PRINT struct command, with appropriate keywords. 1.1.2.2Beam and Liner Elements Created along Boundaries Beams and liners can only interact with the FLAC grid in one of two ways
49、: either by directly connecting nodes to gridpoints (via the grid = i, j linkage), or by using interfaces to connect the nodes to the grid. If a beam or liner is to be attached along a grid boundary, either every node must be individually connected to a corresponding gridpoint, or an interface must be created, with one side of the interface attached to the structural element and the other side attached to the grid. Geometry creation can become quite tedious in either case. See Section 1.1.4 for details on the procedures for linking beams and liners to the grid. An optional