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FORM 836 (10/96)

LA-UR-01-0737 Approved for public release; distribution is unlimited.

Title: Modeling Underground Structure Vulnerability in Jointed Rock

Author(s): Robert P. Swift and David W. Steedman

Submitted to: http://lib-www.lanl.gov/la-pubs/00357121.pdf

1 INRODUCTION

Today, many nations protect their critical assetsthrough deep burial in hard rock formations. Thevulnerability of these underground facilities -- in-cluding command and control facilities, weaponproduction and storage areas, testing facilities, nu-clear waste burial facilities, and others -- to groundmotions caused by explosions and earthquakes is ofpriority national interest. However, the response ofthese facilities to ground shock environments ispoorly understood, and high confidence in vulner-ability assessments from these stimuli is impededwith uncertainty.

For tunnels, current vulnerability/survivability es-timates rely on the application of a semi-theoretical-continuum method of Hendron & Aiyer (1972) topredict failure criteria related to a prescribed level ofplastic deformation in the tunnel walls assumingstatic loading. This approach has been previouslyapplied to tunnels in ductile media, and even insome brittle media where joint conditions were as-sumed to provide for a relative ÒductileÓ response ona macroscopic scale. However, for many hard rocksettings, failure occurs in a ÒbrittleÓ manner, and theapplication of static, elastic-plastic failure criteria tostructures in hard jointed rock will most likely giveerroneous results. We believe that a more authenticresponse behavior can be captured with the use ofbrittle response models with dynamic loading. Byincluding explicit joint representations — such as

spaceing, orientation, and mechanical behavior —that can have a significant affect on the response andstability of underground structures, improved failurecriteria for underground structures will evolve. Thisis the focus of the present paper.

Several studies (Cundall & Hart 1985, Vaughn &Isenberg 1991, Schwer & Linberg 1992, Senseny &Simons 1994) have attempted to use numericalmodeling to better analyze the response of structuresin jointed rock. A recent program reported by Sen-seny & Pucik (1999) focused on the development,validation, and application of computer codes withsophisticated elastic-plastic constitutive models fornumerical simulation of the response of tunnels injointed-rock to ground shock loading. Includingtheoretical studies and laboratory testing, the pro-gram culminated in the MIGHTY NORTH (MN)event-- explosive loading of an aluminum-lined tun-nel within a jointed test bed fabricated of limestoneÒbarsÓ (Gran et al. 1999). The rock studied was Sa-lem limestone, from an Indiana formation with con-sistent, well-characterized material behavior. Post-test observations revealed that the jointed rock failedby brittle cracking with no plastic behavior evident.While the sophisticated models applied to this ex-periment did capture certain elements of the struc-tural deformation, only through Òsubstantial inter -pretation of the simulation outputÓ, Senseny & Pucik(1999), were reasonable brittle regions defined thatreflected the observed damage and fracturing.

Modeling Underground Structure Vulnerability in Jointed Rock

Robert P. SwiftLos Alamos National Laboratory, EES Division, Los Alamos, NM 87545

David W. SteedmanLos Alamos National Laboratory, D Division, Los Alamos, NM 87545

ABSTRACT: The vulnerability of underground structures and openings in deep jointed rock to ground shockattack is of chief concern to military planning and security. Damage and/or loss of stability to a structure injointed rock, often manifested as brittle failure and accompanied with block movement, can depend signifi-cantly on jointed properties, such as spacing, orientation, strength, and block character. We apply a hybridDiscrete Element Method combined with the Smooth Particle Hydrodynamics approach to simulate theMIGHTY NORTH event, a definitive high-explosive test performed on an aluminum lined cylindrical open-ing in jointed Salem limestone. Representing limestone with discrete elements having elastic-equivalence andexplicit brittle tensile behavior and the liner as an elastic-plastic continuum provides good agreement with theexperiment and damage obtained with finite-element simulations. Extending the approach to parameter varia-tions shows damage is substantially altered by differences in joint geometry and liner properties.

Similarly, we are examining buried structuredamage assessment criteria and performing numeri-cal simulations of ground shock tunnel response. Toincrease our understanding of this problem and togain confidence in numerical results, our studies in-clude both continuum Finite Element Method (FEM)and a hybrid Discrete Element Method(DEM)/Smooth Particle Hydrodynamics (SPH) ap-proaches. FEM simulations by Steedman & Swift(2000) suggest that the above modeling deficienciespartly result from restricting constitutive model con-siderations to the high-stress ductile response of thejointed material and neglecting the low-stress (i.e., ≤100Mpa) brittle behavior that the material actuallyexperienced in the test. These simulations demon-strate that a simpler elastic-brittle-tensile-failuremodel for the intact rock replicates the MN behav-ior. They included a Coulomb friction model appliedto the contact conditions for the test bed ÒjointsÓ andcontact separations (i.e., gaps between adjacent bars)to account for non-planarity and asperities of barsurfaces, implicit from test bed measurements.

The FEM and the DEM/SPH approaches arecomplementary for studies in rock. While the FEMapproach is applicable to a more universal set of pa-rameters, the DEM approach allows for larger dis-placement, block motion response, such as might beexpected in rock. In this paper we validateDEM/SPH results with comparisons to MN obser-vations and to the FEM results. We then expand theDEM/SPH approach to examine the effects of vari-ous parameters of joint geometry and liner variation.The DEM/SPH simulations modeled individual barsas clusters of DEM elements having elastic contin-uum-equivalent behavior coupled with an explicitbrittle-tensile failure condition between elements.The aluminum liner was modeled as an elastic-plastic continuum with SPH particles. The resultsreveal the rock damage and structure responses are

significantly influenced by joint and liner parametervariations.

2 MIGHTY NORTH EXPERIMENT

The MIGHTY NORTH experiment, Figure 1, con-sisted of milled limestone bars, stacked around analuminum-lined Òtunnel.Ó A concrete container su r-rounded the jointed test bed. The concrete containerwas loaded with an explosive-driven cylindricalshock wave. In addition to active data, precisionmeasurements of individual ÒbarÓ dimensions weremade both during construction of the test article andduring post-test decomposition.

Analysis of active gage data verified uniform re-sponse throughout the central portion of the test arti-cle along the tunnel axis, confirming two-dimensional response in that section (Gran et al.1998, Gran & Groethe 1997). The data also verifiedsymmetrical response about the vertical plane run-ning along the tunnel axis. Additionally, the meas-urements and inspection of individual bar/bricks in-dicated that no plastic deformation occurred in therock. On the contrary, deformation was fully attrib-uted to development of vertical rock fractures in in-dividual bars, forming an apparent Òchimney,Ó com -bined with liner deformation and accompanying slipalong the chimney fractures (Gran et al. 1998). Fig-ure 2a displays the qualitative description of thebrittle failure from Gran & Groethe (1997), showingthe chimney formed above and below the tunnelspringline. Vertical displacements are exaggeratedby a factor of two for this plot. Modal fit from Fou-rier coefficients to the liner radial deformation isshown in Figure 2b. Test liner deformation wasdominated by ovaling, mode 2, with a significantbreathing mode 0 contribution. Contributions ofother modes were observed to be insignificant.

Figure 1. MIGHTY NORTH test bed and jointed-rock detail (Gran et al. 1998)

(a) Damage, Gran & Groethe (1997)

0 1 2 3 4 5 6 7 8 9 10(b) Modal number, (Gran et al. 1998)

Figure 2. MIGHTY NORTH experiment (a) deformation and (b) modal amplitudes for aluminum liner.

3 HYBRID APPROACH

The SPH method employs collocated particles todefine a Lagrangian, meshless continuum and wasoriginally formulated for the treatment of astro-physical problems (Gingold & Monaghan, 1977).It has been used over the past decade to modelsolid mechanics problems such as bomb-casefragmentation (Randles et al, 1995) and brittlefracture (Mandell & Wingate, 1995, Hiermaier &Riedel, 1997). Each particle, governed by the con-tinuum equations of motion and constitutive mod-els, obtains values of velocity, density, deforma-tion rate, acceleration and energy through aninterpolation function with neighboring particles.Stresses are updated from specific constitutive rep-resentations. The particulate nature of SPH easilyaccounts for large deformation and accommodatesthe mixing of multi-materials in a more naturalway. Overviews of the SPH approach are given by(Swegle et al, 1995, Randles & Libersky, 1996).

The DEM approach originated as a technique fordescribing behavior of granular assemblies inwhich elements are treated as rigid bodies withtranslation and rotation degrees of freedom. Theyinteract via Hertzian contact (Cundall and Strack,1979) or spring force-displacement laws to con-serve momentum. It has been applied to a widerange of applications (Williams and Mustoe,1993). Recently, the method has been advanced toapproximate dynamic fracture where element in-teractions behave in an Hookian elastic-continuummanner with tensile debonding of elements to pro-vide explicit fracture (Potapov and Campbell,1997)

3.1 Setup for MN

The hybrid DEM/SPH approach was implementedinto the SPHINX code (Crotzer et al, 1995) andhas been used to simulate the dynamic fragmenta-tion of explicit grain-pore structures (Swift et al.2000) and applied to many other applications. Inthe FE simulations of MN, Steedman & Swift(2000), the limestone-jointed bars were modeledwith a continuum brittle failure model and an elas-tic-plastic model for the aluminum liner.

DEM elements experience normal and sheartranslation forces along their interfaces in terms ofpair-wise relative displacement and experiencemoments in terms of the evolving vector offset ofthe translation forces between element centroids.These forces are determined from stresses andstrains at element interfaces that obey HookeÕs lawof elasticity. An estimate of forces between ele-ment pairs is made by assuming stresses act overthe area of their adjoining interfaces. Interactionsbetween DEM elements and SPH particles aretreated by a penalty method. More complete detailsof this DEM approach are given by (Greening, inprep).

For the hybrid simulations presented here, lime-stone bars are modeled as clusters of DEM ele-ments having elastic continuum-equivalent be-havior coupled with an explicit brittle-tensilefailure, while the liner is modeled as an elastic-plastic continuum with SPH particles. Figure 3shows the DEM/SPH setup configuration for theMN simulations. Each limestone bar, with a 5.071-cm x 5.071-cm cross-section, consists of eight tri-angular elements. The aluminum liner (1.27 cmthick) and the velocity boundary particles are rep-resented by SPH particles. The 4-cm thick concreteliner shown with DEM elements is used in pa-rameter cases discussed below.

Am

plitu

de

4

3

2

1

0

SPH boundary velocity particles

DEM limestone elements

SPH or DEM liner DEM limestone bars Aluminum liner Concrete liner SPH particles DEM elements.

Figure 3. DEM/SPH setup for MN simulations.

Fracture modeling for DEM elements considersthe normal stress acting between elements and theareas of adjoining interfaces. If the normal force Fn

value exceeds a threshold value, σth, a crack isassumed to grow at a fixed rate. Formally, ifFn A theff> σ (1)

then,

Aeff A t= −γ ∆ (2)

where, A denotes the initial interfacial tension areaand γ is a rate parameter for area reduction. Be-cause of a slight random variation in the elementsizes there exists varying interface areas, thus, pro-viding a slight variation in tensile threshold. As theeffective area decreases the tensile force is reduceduntil complete fracture occurs, which is denoted asan explicit separation, causing free surfaces, be-tween element pairs. When the normal strain iscompressive the original area is used to computethe normal force, but the effective tension area isalways used in to compute the shear force.

Material properties given by Gran et al. (1998)are used. The limestone has a bulk density and agrain density of 2.34 g/cc and 2.71 g/cc, respec-tively, YoungÕs modulus = 30 GPa, and Poisson’sratio = 0.24. Tensile parameters for the limestonefailure are σth = 8 MPa and γ = 1e-3 sq-cm/s. Con-crete liner elastic properties are the same with ten-sile parameters σth = 4 Mpa and γ = 1.0 sq-cm/s.

The aluminum liner has density = 2.7 g/cc,YoungÕs modulus = 75 GPa, and Poisson’s ratio =0.25. The elastic-plastic behavior is modeled witha strain rate-dependent model in Johnson & Cook(1985) with a threshold strength = 75 MPa.

The velocity boundary SPH particles used todrive the jointed limestone region were specifiedwith the vertical and horizontal velocity historiesmeasured in the MN event, as shown in Figure 1.Interpolation was used for the particles betweenmeasured stations. Velocity histories measured atthe top center crown and bottom center in the lime-stone are shown in Figure 4. The data Gran et al.(1998) shows very good symmetry. Because of thiscylindrical symmetric loading, the simulationswere performed in the plane-strain configuration.

Figure 4. Velocity histories from V3, top center and V13, bottom center. (Gran et al. (1998)

3.2 Comparison with MN and FEM Results

Two simulations are compared to MN that affordssomewhat bounding variations of the actual jointconditions, where the bar surfaces are not perfectlyplanar. One case models the joints in full contact,while the other considers prescribed gaps separat-ing individual bars. The gaps were derived frommeasurements made during the MN construction,which showed the final vertical and horizontal di-mensions of the joint regions to be greater than thesum of the individual bars. Measurements indi-cated an average gap of 0.163 mm between rowsof bars and the side-by-side gap to be 0.188 mm.

Comparisons of the DEM computed crackingpatterns for the no-gap and gap cases with the pat-terns obtained by Steedman & Swift (2000) inFEM simulations are given in Figures 5. Bothcases exhibit the chimney cracks pattern above andbelow the springline similar to the FEM pattern.The DEM patterns replicate well the observed re-sult for the MN experiment, shown in Figure 2a.

The differences between the two DEM cases arenot great, the gap case having a more symmetricalpattern. The FEM case with no gaps, Figure 5b, in-cluded Coulomb friction along the bar contact sur-faces, while the case with gaps, Figure 5d, had nofriction. Presently, friction is unavailable in theDEM approach, but FEM simulations show themain influence of friction is to reduce the extent of

chimney cracking below the springline. This is ob-served in MN also, indicating friction to be a fac-tor. However, the major factor affecting thecracking pattern is the joint pattern. Vertical jointsabate the buildup of hoop-tension stress from thecylindrical loading. The square joint pattern allowsslumping in crown region and up-heaving in theinvert region, that leads to bending of the bars inthe chimney regions. Above the springline bendingis downward and below it bending is upward. Themanner in which DEM cracking proceeded, topdownward for bars above the spring line and bot-tom upward for bars below the springline, is a con-sequence of this behavior.

Figure 6 shows results of modal analysis of thecomputed liner deformations. Similar to the MNtest liner in Figure 2b, the simulated modal re-sponse is dominated by modes 2 and 0. The maindifferences are that the case without gaps has a lit-tle higher breathing mode-0 amplitude, while thecase with gaps has much higher ovaling mode-2amplitude. The high ovaling is attributed to higherinvert upheaval that occurs for the gap case. Theincreased joint stiffness associated with joint con-tacts in the no-gap case tends to lessen invert up-heaval. Friction would also reduce upheaval. Thisis attested to by the MN liner crown/invert reduc-tion of 11.4 mm vs. 13.4 mm and 16.3 mm for theno-gap and gap cases, respectively. FEM simula-tions showed similar modal amplitude results.

(a) - DEM WO gaps (b) — FEM WO gaps (c) — DEM with gaps (d) — FEM with gaps Figure 5. Comparison of calculated crack patterns without gaps (a) DEM and (b) FEM and with gaps (c) DEM and (d) FEM.

0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8modal number modal number

(a) — DEM without gaps (b) — DEM with gapsFigure 6. DEM calculated MN liner modal amplitude for (a) no gaps and (b) gaps.

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9

3.3 Joint Geometry Effects

We examine DEM computed fracture patterns forcases where the joint character is varied from thatof MN. Parameter variations include substituting aconcrete liner or being unlined, varying joint char-acter (e.g., joint aspect ratio of bar cross-section,joint size, joint orientation and joint gaps), andtreating the limestone as a continuous mass withand without a lined tunnel. Table 1 gives the de-tails of these variations and a brief description ofthe damage obtained with comments restricted tocases only simulated thus far. The MN aluminumliner is considered for all joint conditions. Theterm AR denotes aspect ratios for the bars. A sec-ond AR=1 case is examined with bars twice thesize, 10.142-cm square, of those for MN. TheAR=2 bars considered have dimensions 5.071-cmvertically by 10.142-cm horizontally.

Because of limited space we will only view afew selected cases. Figure 7 show the fracture pat-terns for AR=1 with the MN liner and bar orienta-tions of 30 degrees and 90 degrees. The effect of

(a) — AR=1, 30 degree tilt (b)—AR=1, 90 degree tilt Figure 7. Fracturing for tilt of (a) 30 & (b) 90 degrees.

the 30 degree tilt, Figure 7a, is to offset the chim-ney cracking in a asymmetric fashion, reorient thecracks normal to the tilted vertical bedding, andreduce the amount of cracking in comparison tothe zero degree tilt cases in Figure 5. The 90-degree condition, Figure 7b, shows significantbroadening in the chimney-cracking pattern alongwith slumping and upheaval which increases theovaling mode of deformation. This case is analo-gous to lateral loading for the zero degree orienta-tion. Damage was not evident in simulations fororientations of 45 and 60-degree cases for AR=1.

Figure 8 shows three fracture sequences for thecase AR=1 with a 4-cm thick concrete liner inplace of the MN aluminum liner. At 2 ms, chimneycracks are well developed, cracking occurs belowthe invert, and the liner is starting to fragment. At

Table 1. DEM simulations for varying joint geometry.

LinerType

Al Concrete Unlined No adit

Joints Damage Description

AR = 15x5 sqcmθ = 0 deg

Chimneyfracture

Collapse,chimneyfracture &liner failed

Collapse &chimneyfracture

VerySlight

AR = 15x5 sqcmθ=30 deg

Offsetchimneyfracture

AR = 15x5 sqcmθ=45 deg

None

AR = 15x5 sqcmθ=60 deg

None

AR = 15x5 sqcmθ=90 deg

Extensivechimneyfracturing

AR = 15x5 gapsθ = 0 deg

Symchimneyfractures

AR = 15x5 gapsθ=45 deg

none

AR = 110x10θ = 0 deg

Chimney,crown &invert frac

AR = 25 x 10θ = 0 deg

Crown &invertfractures

Collapse,crown , in-vert fracs,liner failed

Collapse,crown &invert fracs

None

AR = 25 x 10θ=45 deg

Very littlearoundliner & 45deg invert

Some col-lapse, linerfailed &bridge fracs

Some col-lapse &a lot ofbridge fracs

AR = 25 x 10θ=90 deg

Chimneyfracturing,

Collapsewith littlefracturing

Non-jointed

Extensivefracturingall over

Exten-sivefracs

4ms, the totally failed liner is falling downward,slumping occurs in the crown region with bridging,

�

2 ms 4 ms 8 msFigure 8. Failure sequence for AR=1 with concrete liner.

and upheaval begins in the invert region. Finally,at 8 ms the liner has nearly closed off the openingdriven by the slumping crown and upheaving in-vert. These results illustrate the consequence of astronger ductile liner, Figs. 5a-d, versus a weakerbrittle one here.

The influence of modifying the bar size is nowexamined. Figure 9 shows fracture patterns forcases AR=1 (10.142-cm square) and AR=2, bothoriented at zero degrees and with the MN Al liner.��

(a) — AR=1, Big 10 cm x10 cm (b) — AR=2, 10 cm x 5 cm Figure 9. Effect of size change on damage.

Damage for the big AR=1, Figure 9a, case isgreatly different from the small AR=1 case, Figure5a. The chimney cracks are quite slight with fewsevering individual bars. Also, there is crackingabove the crown and below the invert, but removedby the thickness of two bars. In Figure 9b, AR=2case, damage proceeded vertically upward fromthe crown and downward from the invert, also withslight chimney cracking. For both cases, the cracksinitiate according to bending buildup of tensilestress as discussed above for the small AR=1 case.

Damage patterns for cases AR=2 oriented at 45and 90 degrees are shown in Figure 10. In Figure10a, cracking is significantly reduced compared tothe zero degree orientation in Figure 9b. With theexception of slight cracking around the liner, dam-age is oriented below the rotated invert and normalto the tilted bedding. In Figure 10b, for the 90 de-gree case, slight cracking occurs around the liner,�

(a)—AR=2, 45 degree tilt (b)—AR=2, 90 degree tilt Figure 10. Fracturing for tilt of (a) 45 and (b) 90 degrees.

and wing-like chimney cracking occurs above andbelow the springline. Cracks are vertical and ori-ented parallel to the tilted bedding with only one ortwo bars completely broken through. Again, moreliner ovaling occurs for the 90-degree orientation.

Figure 11 shows the influence of the weakerconcrete liner on fracturing for AR=2 at zero and45 degrees orientation. Similar to the AR=1 case inFigure 8 the liners are totally damaged. For zerodegree tilt, Figure 11a, considerable damage oc-curs above the crown and below the invert alongwith noticeable invert heave. For 45-degree orien-tation, Figure 11b, the cracking again occurs belowthe rotated invert and slumping takes place inwardalong the tilted bedding planes.�

(a)—zero degree tilt (b)-45 degree tilt Figure 11. AR=2 concrete liner (a) zero & (b) 45 degrees.

For comparison to the jointed cases, Figure 12shows damage for intact rock with and without atunnel opening. The damage imparted is mainlydue to the hoop stress from the cylindrical loading.The influence of the opening is readily noted bycracking in the crown and invert regions in Figure12a with the MN liner. A compressive shadowzone is noted outward from the springline region.Little or no damage was obtained in simulationcases having joints but no opening. The significantdecrease in damage for jointed conditions illus-trates their effectiveness to mitigate fracturing. Onthe other hand, the movement of blocks is muchgreater for the jointed cases.

(a) — with opening (b) — without openingFigure 12. Damage for non-jointed rock (a) with opening &

(b) without an opening.

4 CONCLUSIONS

We examined damage imparted by ground shockto underground openings in jointed rock with a hy-brid DEM/SPH approach. Damage observed in theMN experiment and that from FEM simulationswas well replicated using an elastic model with anexplicit fracture feature for the discrete elements.Good agreement was obtained with the measureddeformation of the MN liner. Extending the modelto account for the effects of varied joint geometry,a weaker liner, and for non-jointed rock foundbrittle failure to be significantly sensitive to jointedmedia properties, such as spacing, orientation, andblock size. The responses were often accompaniedwith block movement.

For example: In the AR=1 5-cm x 5-cm casedamage is manifested by vertical ÒchimneyÓ typecracking above and below the springline. Doublingthe bar size leads to increased damage in the crownand invert regions at the expense of the chimneycracking. For the AR=2 case, progressive increasein damage occurs in the crown and invert regions.For the concrete liner cases, significant damage ofthe liner occurs, accompanied by crown collapseand invert upheaval along with more rock-mass re-gion damage. The more forgiving ductile alumi-num liner greatly mitigates the degree of damage.For joint orientation of 30 degrees, the groundshock is sufficiently disrupted to diminish damageand it is non-evident for the 45 and 60-degreecases. For the non-jointed case, extensive damageoccurs well over the entire rock medium.

This hybrid approach readily captures the effectsof rock joints by illustrating how the tensionbuildup in the diverging ground shock is relieved,thus, alleviating brittle failure. In concert with de-finitive experiments, it offers a way to enhance un-derstanding of the vulnerability of deep buriedstructures in hard-jointed rock.

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This work was supported by the U.S. Departmentof Energy under Contract No W-7405-ENG-3