1，項目描述

本項目為落石沖擊堆滿沙土和EPS泡沫防護的橋墩，其中沙土采用spg算法。橋墩為鋼筋混凝土結構，內含縱筋和箍筋鋼筋，EPS泡沫采用24號材料的試驗曲線模擬。

2，幾何模型

首先利用workbench的dm模塊建立沙土、EPS泡沫、橋墩及鋼筋的幾何模型，其中鋼筋為1D線體。模型如下圖所示。

3，材料

落石為剛體，采用rigid本構

*MAT_RIGID_TITLE

luoshi

$#     mid        ro         e        pr         n    couple         m     alias

         4    2730.02.00000E10       0.3       0.0       0.0       0.0          

$#     cmo      con1      con2    

       0.0         0         0

$#lco or a1        a2        a3        v1        v2        v3  

       0.0       0.0       0.0       0.0       0.0       0.0

沙土采用可壓縮泡沫崩MAT_CRUSHABLE_FOAM，沙漏采用5號，系數0.03.

*MAT_CRUSHABLE_FOAM_TITLE

shatu

$#     mid        ro         e        pr      lcid       tsc      damp    

         7    1628.04.000000E7       0.3         2       0.0       0.0

*HOURGLASS_TITLE

shatu

$#    hgid       ihq        qm       ibq        q1        q2    qb/vdc        qw

         7         5      0.03         0       1.5      0.06      0.03      0.03

EPS泡沫采用24號多線性彈塑性本構，借助試驗曲線；

*MAT_PIECEWISE_LINEAR_PLASTICITY_TITLE

eps

$#     mid        ro         e        pr      sigy      etan      fail      tdel

         9      20.0   6000000      0.12  100000.0  600000.01.00000E21       0.0

$#       c         p      lcss      lcsr        vp  

       0.0       0.0         3         0       0.0

$#    eps1      eps2      eps3      eps4      eps5      eps6      eps7      eps8

       0.0       0.0       0.0       0.0       0.0       0.0       0.0       0.0

$#     es1       es2       es3       es4       es5       es6       es7       es8

       0.0       0.0       0.0       0.0       0.0       0.0       0.0       0.0

橋墩采用混凝土材料，使用jhc本構，采用4號0.03沙漏。并定義額外的失效參數。

*MAT_JOHNSON_HOLMQUIST_CONCRETE_TITLE

hunningtuban

$#     mid        ro         g         a         b         c         n        fc

         1    2650.01.68000E10      0.79       1.6     0.007      0.618.400000E7

$#       t      eps0     efmin     sfmax        pc        uc        pl        ul

   6000000       1.0      0.01       7.02.800000E7     0.0011.400000E9       0.1

$#      d1        d2        k1        k2        k3        fs  

      0.04       1.08.50000E10-1.7100E112.08000E11     0.004

*HOURGLASS_TITLE

hunningtuban

$#    hgid       ihq        qm       ibq        q1        q2    qb/vdc        qw

         1         4      0.03         0       1.5      0.06      0.03      0.03

*MAT_ADD_EROSION_TITLE

hunningtuban-shixiao

$#     mid      excl    mxpres     mneps    effeps    voleps    numfip       ncs

         1       0.0       0.0       0.0       0.0       0.0       1.0       1.0

$#  mnpres     sigp1     sigvm     mxeps     epssh     sigth   impulse    failtm

       0.0       0.0       0.0      0.06       0.0       0.0       0.0       0.0

$#    idam         -         -         -         -         -         -    lcregd

         0         0         0         0         0         0         0         0

$#   lcfld      nsff   epsthin    engcrt    radcrt   lceps12   lceps13   lcepsmx

         0        10       0.0       0.0       0.0         0         0         0

$#  dteflt    unused     mxtmp     dtmin     

       0.0                 0.0       0.0

鋼筋采用彈塑性本構，定義0.2的有限塑性應變失效參數。

*MAT_PLASTIC_KINEMATIC_TITLE

pingmian-gangjin

$#     mid        ro         e        pr      sigy      etan      beta    

         2    7850.02.00000E11       0.35.000000E82.000000E9       0.0

$#     src       srp        fs        vp  

       0.0       0.0       0.2       0.0

4，單元及有限元網格

沙土采用SPG算法，其他均采用lagrange算法。

*SECTION_SOLID_SPG

7,47

$DX,DY,DZ,,KERNEL,,SMSTEP

1.8,1.8,1.8,,2,,2

$IDAM,FS失效，

1,0.004

workbench下劃分lagrange網格，網格數5萬以上。

5，接觸建立

泡沫與橋墩之間采用綁定接觸，沙土與泡沫之間為摩擦接觸，球與沙土為自動接觸。

*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE_ID

$#     cid                                                                 title

         1luoshi-shatu

$#    ssid      msid     sstyp     mstyp    sboxid    mboxid       spr       mpr

         7         4         3         3         0         0         0         0

$#      fs        fd        dc        vc       vdc    penchk        bt        dt

       0.4       0.4       0.0       0.0       0.0         0       0.01.00000E20

$#     sfs       sfm       sst       mst      sfst      sfmt       fsf       vsf

       1.0       1.0       0.0       0.0       1.0       1.0       1.0       1.0

$#    soft    sofscl    lcidab    maxpar     sbopt     depth     bsort    frcfrq

         1       0.1         0     1.025       2.0         2         0         1

*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE_ID

$#     cid                                                                 title

         4ban-duntai

$#    ssid      msid     sstyp     mstyp    sboxid    mboxid       spr       mpr

         5         1         3         3         0         0         0         0

$#      fs        fd        dc        vc       vdc    penchk        bt        dt

       0.4       0.4       0.0       0.0       0.0         0       0.01.00000E20

$#     sfs       sfm       sst       mst      sfst      sfmt       fsf       vsf

       1.0       1.0       0.0       0.0       1.0       1.0       1.0       1.0

*CONTACT_TIED_SURFACE_TO_SURFACE_ID

$#     cid                                                                 title

         9tie eps-huxingban

$#    ssid      msid     sstyp     mstyp    sboxid    mboxid       spr       mpr

         2         1         0         0         0         0         0         0

$#      fs        fd        dc        vc       vdc    penchk        bt        dt

       0.4       0.4       0.0       0.0       0.0         0       0.01.00000E20

$#     sfs       sfm       sst       mst      sfst      sfmt       fsf       vsf

       1.0       1.0       0.0       0.0       1.0       1.0       1.0       1.0

$#    soft    sofscl    lcidab    maxpar     sbopt     depth     bsort    frcfrq

         1       0.1         0     1.025       2.0         2         0         1

6，邊界及載荷

施加z方向重力；

*LOAD_BODY_Z

$#    lcid        sf    lciddr        xc        yc        zc       cid   

         1       1.0         0       0.0       0.0       0.0         0

*DEFINE_CURVE_TITLE

zhongli

$#    lcid      sidr       sfa       sfo      offa      offo    dattyp     lcint

         1         0       1.0       1.0       0.0       0.0         0         0

$#                a1                  o1  

                 0.0                 9.8

                10.0                 9.8

落石Z方向速度偽18.8m/s。

*INITIAL_VELOCITY_GENERATION

$#nsid/pid      styp     omega        vx        vy        vz     ivatn      icid

         4         2       0.0       0.0       0.0 -18.80632         0         0

$#      xc        yc        zc        nx        ny        nz     phase    irigid

       0.0       0.0       0.0       0.0       0.0       0.0         0         0

7，求解設置

計算時間0.2s。為防止容易負體積，時間步因采用0.5

*CON*T*ROL_TERMINATION

$#  endtim    endcyc     dtmin    endeng    endmas     nosol     

       0.2         0      0.05       0.01.000000E8         0

*CON*TROL_TIMESTEP

$#  dtinit    tssfac      isdo    tslimt     dt2ms      lctm     erode     ms1st

       0.0       0.5         0       0.0       0.0         0         1         0

$#  dt2msf   dt2mslc     imscl    unused    unused     rmscl     

       0.0         0         0                           0.0

施加全局阻尼0.05

*DAMPING_GLOBAL

$#    lcid    valdmp       stx       sty       stz       srx       sry       srz

         0      0.05       0.0       0.0       0.0       0.0       0.0       0.0

$

8，求解

6核cpu求解時間1.5小時。

9，結果分析

通過計算，沙土由于采用可壓碎泡沫本構MAT_CRUSHABLE_FOAM，非常容易出現負體積，因此采用了SPG算法，經過計算可見沙土的成坑性能非常好，也與試驗進行了對比，接觸反力與試驗測得值非常接近。

落石打擊沙土、橋墩等的變形應力如下圖所示：

落石與沙土之間的接觸力如下：

沙土沙漏能幾乎為0；精度非常高。

 

sph對比spg優劣勢：

? Sph效率高但是精度低；spg反之；

? Sph難以與fem耦合，spg容易與fem耦合；

? Sph用于高速問題，spg低速高速問題都適用；

? Sph支持2D-3D，spg只支持3D；

? Fem失效后動量能量不守恒，spg在失效后仍然守恒。