Anchorage effect of NPR cable based on second-order work criterion
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摘要: NPR锚索因其具有恒定工作阻力和较大变形量的特性,已广泛应用于巷道的加固和监测预警中。为了研究NPR锚索在露天矿山边坡中的支护效果,首先基于有限差分软件FLAC3D中的锚索单元开发出NPR锚索单元,并通过数值拉伸试验验证了NPR锚索比普通锚索具有更优异的吸能特性；之后引入二阶功作为边坡稳定性评价准则,并将其植入显式动力学算法中,详细讨论了其合理性和可靠性；最后,以浩尧尔忽洞金矿西采场北帮开挖诱发的滑坡为研究对象,对现有普通矿用锚索和NPR锚索支护体系下的边坡稳定性进行对比分析。根据数值模拟结果可知,NPR锚索支护体系下的边坡稳定性明显优于普通矿用锚索。Abstract: Due to the characteristics of constant working resistance and steady large deformation, the NPR cable has been widely applied in monitoring and reinforcement of a large number of roadways. In order to study the anchorage effect of NPR cables in open-pit slope, firstly, the NPR cable element is developed based on the cable element in the finite difference software FLAC3D, and it is proved by the tensile tests that the NPR cable has better energy absorbing capacity than the traditional one. Secondly, the second-order work criterion is then implemented, and the rationality and advantages of the second order work criterion as a safety factor in explicit numerical algorithm are discussed. Finally, the rock slope induced by the excavation at the north side of the west stope in Haoyaoerhudong Opencast Gold Ore is taken as the research object, and the stability of rock slope under the existing traditional mine cable support system and NPR cable support system is compared and analyzed. According to the numerical results, the global second-order work and kinetic energy of each loading step have the opposite variation tendency, and the slope stability of NPR cable support system is obviously better than that of the traditional mine cable.
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Keywords:
- NPR cable /
- safety factor /
- stability of rockslope /
- second-order work /
- instability criterion
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0. 引言
近年来,国内外学者针对经历循环荷载历史后土体的剪切特性进行了大量研究[1-5]。一般来说,循环荷载会使土体的超孔隙水压力增大,平均有效应力降低,从而导致土体的循环后强度降低。王淑云等[1]针对重塑粉质黏土,在不同围压下进行了一系列静三轴和动-静三轴不排水试验,发现粉质黏土的振后不排水强度衰减程度取决于动载引起的动应变和孔压值；郑刚等[2]认为原状土样的振后不排水抗剪强度显著衰减,而重塑土的抗剪强度变化不甚明显；Moses等[3]发现土体的振后不排水强度随循环荷载幅值的增加而减小；Yasuhara等[5]研究了重塑Ariake黏土的循环后剪切特性,发现循环荷载作用后土体累积孔压可以很好地评价振后不排水剪切强度,并提出了预测土体振后抗剪强度的经验模型。
然而,经历循环荷载作用后的土体往往处于未固结和完全固结的中间状态,该状态可用振后固结度这一概念进行描述。目前针对原状软土在不同振后固结度条件下的剪切特性研究较少。因此,有必要针对不同振后固结度下的软土振后剪切特性进行研究。本文选取珠江入海口原状软土,通过一系列的动-静三轴试验,分析了初始围压,循环应力比以及振后固结度对土体振后剪切特性的影响,以期加深对软土振后静力特性的理解,为工程设计提供试验基础。
1. 土体试样和试验方案
1.1 土样基本物理力学特性
试验选取珠江入海口原状软土为研究对象,土壤呈深灰色,取土深度为0～7 m。依据《土工试验规程（GB/T 50123—2019）》获得土体的基本物理力学指标和土体的粒径分布曲线分别见表1和图1所示。
表 1 原状软土基本物理力学指标值Table 1. Indices of basic physical and mechanical properties of undisturbed soft soils物理力学特性 取值 天然密度ρ/(g·cm-3) 1.54~1.79 含水率w/% 38.3~69.1 孔隙比e 1.12~1.91 相对质量密度Gs 2.71 液限wL/% 38.5~61.8 塑限wP/% 19.4~28.0 塑性指数IP 19.1~33.8 渗透系数K/(10-7cm·s-1) 8.79~10.80 压缩系数av/MPa-1 0.48~1.15 侧压力系数K0 0.44 1.2 试验方案
通过薄壁取土器进行现场取土,并将原状土样保存在恒温恒湿箱中。按照《土工试验方法标准（GB/T 50123—2019）》的要求,将土体制成直径38 mm,高76 mm的原状试样,并采用真空饱和及反压饱和法对试样进行饱和。首先对所有圆柱试样进行真空饱和,然后将试样置于压力室内进行反压饱和,当B值达到0.95以上时,可认为土体已经饱和。随后,对试样施加一定的固结压力,进行等向固结,当试样排水体积速率小于100 mm3/h时,认为土样固结完成。为研究有效固结围压对振后强度的影响,本次试验中选取有效固结围压分别为20,40,60 kPa。
对固结完成后的土体在不排水状态下开展循环三轴试验,并采用Sakai等[6]提出的循环应力比CSR描述循环偏应力大小,即
CSR=q/2p′0=q/2σ′3, (1) 式中,q为循环偏应力幅值,
p′0 为固结完成后的有效围压。为研究CSR对振后土体强度的影响,在围压为60 kPa下,CSR值分别取0.08,0.17,0.25,0.33。循环轴向偏应力采用半正弦波形,频率为0.1 Hz,且循环振次为1000次。对振动后的试样再次进行固结过程,并采用振后固结度这一概念描述振后土体固结程度。试验过程中为得到不同振后固结度的土体,可通过向振后试样施加不同的反压。具体为：向经历循环荷载作用后的土体施加一定的反压pu,此时,振后土体在一定围压作用下进行固结,振动过程中产生的超孔隙水压力将逐渐降低直至与反压相等。因此,振后不同固结度Ur可通过下式计算得到,
Ur=1−pu(Δu)cy, (2) 式中,pu为再固结过程中施加在试样上的反压,(∆u)cy为振动过程中产生的超孔隙水压力。
当试样再次固结完成后,对土体进行三轴固结不排水剪切试验。其中,剪切过程中均采用应变控制,剪切速率为0.1%/min。当应变达到20%时,试验结束。对于经历和未经历循环荷载作用的土体而言,若静力剪切过程中应力应变曲线出现峰值点,其不排水抗剪强度为峰值偏应力的1/2；若未出现峰值点,则土体不排水抗剪强度取20%应变处对应偏应力的1/2。整个试验方案如表2所示,其中ST-20,ST-40和ST-60为未经历循环荷载作用的土体在不同围压条件下的静三轴试验。经历和未经历循环荷载作用的土体强度用Su表示。
表 2 试验方案Table 2. Test schemes试样编号 p′0 /kPaqampl/kPa CSR 循环次数 Ur/% Su/kPa U01 20 10 0.25 1000 0 20.2 U02 20 10 0.25 1000 25 24.4 U03 20 10 0.25 1000 75 22.8 U04 20 10 0.25 1000 100 33.0 U05 40 20 0.25 1000 100 40.4 U06 60 30 0.25 1000 100 39.5 U07 60 10 0.08 1000 100 32.7 U08 60 20 0.17 1000 100 31.5 U09 60 40 0.33 1000 100 42.9 ST-20 20 — — — — 28.5 ST-40 40 — — — — 33.4 ST-60 60 — — — — 33.5 2. 试验结果
2.1 固结围压对振后土体强度的影响
图2展示了循环荷载后完全固结试样在不同围压下的偏应力-应变曲线。其中,CSR=0.25,Ur= 100%。可以看出,不同围压下的q-ε曲线变化趋势相同。当应变较低时,应力在小应变范围内迅速增加。随着应变的增加,应力增速放缓,当轴向应变为20%左右时,偏应力趋于稳定。不同围压下完全固结的振后试样强度大于相同围压无循环荷载作用历史的土体静强度。例如,当围压为60 kPa时,试样的振后强度比未经历循环荷载作用下的强度大6.0 kPa。此外,对比发现,实验条件相同的情况下,振后土体的抗剪强度随着围压的增加基本呈增大趋势。具体为完全固结的振后试样在初始固结围压为20,40,60 kPa时,对应的抗剪强度分别为33.0,40.4,39.5 kPa。
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图 2 不同围压下振后土体的偏应力-应变曲线Figure 2. Post-cyclic deviator stress-strain curves under different confining pressures2.2 循环应力比对振后土体强度的影响
图3展示了不同循环应力比循环荷载作用后完全固结试样（Ur=100%）的偏应力-应变曲线。其中,初始固结围压为60 kPa。可以看出,初始应变随着CSR的增加而增加。当CSR值分别为0.08,0.17,0.25和0.33时,对应的初始应变分别为0.24%,0.43%,0.66%,4.27%。当CSR>0.25时,试样的振后剪切强度明显大于静态剪切强度（表2）。相较于未经历循环荷载的土体静强度,当CSR=0.08时,振后土体强度增幅为-0.8 kPa；当CSR=0.33时,振后土体强度增幅为9.4 kPa。同样地,土体振后剪切强度随着CSR的增大而增大。当CSR从0.08增大到0.33时,土体振后剪切强度从32.7 kPa增大到42.9 kPa。
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图 3 不同循环应力比下振后土体的偏应力-应变曲线Figure 3. Post-cyclic deviator stress-strain curves under different CSRs2.3 振后固结度对振后土体强度的影响
图4为不同振后固结度下土体的偏应力-应变曲线。其中,初始固结围压为20 kPa,CSR=0.25。通过与未经历动荷载的试样q-ε曲线对比发现,Ur在75%～100%存在临界值,使得振后土体强度等于相同围压下未经历动荷载作用的土体强度。当固结围压为20 kPa,固结度为0%,25%,75%,100%时,抗剪强度分别为20.2,24.4,22.8,33.0 kPa。试验结果表明土体的振后抗剪强度随Ur的增大而增加。
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图 4 不同振后固结度下振后土体的偏应力-应变曲线Figure 4. Post-cyclic deviator stress-strain curves under different degrees of reconsolidation3. 结论
本文通过对珠江入海口原状软土开展一系列动、静三轴试验,对其振后强度特性进行了研究。
（1）经历循环荷载作用后的土体,不同因素影响下对应的偏应力-应变曲线变化趋势基本一致。不同固结围压影响下,振后完全固结试样的振后抗剪强度大于未经历动荷载土体静强度。另一方面,土体振后抗剪强度随初始固结围压的增大呈增加趋势。
（2）当循环应力比大于0.25时,振后完全固结状态下土体剪切强度明显大于相同围压下未经历循环荷载作用的土体静态剪切强度。另一方面,振后完全固结的土体,其振后剪切强度随着循环应力比的增大而增加。
（3）土体振后抗剪强度随振后固结度的增加而增大,且振后固结度存在某一临界值,使得土体的振后抗剪强度与相同围压条件下未经历循环荷载作用的土体抗剪强度基本一致。
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图 4 锚索拉伸荷载-变形量曲线
Figure 4. Tensile force-axial deformation curves of traditional and NPR cables
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图 7 岩质边坡三维地质模型及锚杆（索）布置图
Figure 7. Geometric model for rock slope in 3D and distribution of bolts and cables
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图 9 4种工况下整体二阶功和动能对比图
Figure 9. Comparison between global second-order work and kinetic energy of rock slope under 4 working conditions
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图 10 传统矿用锚索及NPR锚索加固下边坡的整体二阶功对比图
Figure 10. Comparison of global second-order work of rock slope reinforced by traditional and NPR cables
表 1 锚杆（索）物理力学参数
Table 1 Physical and mechanical parameters for bolts and cables
锚固类别 强度/kN 杨氏模量/GPa 长度/m 预应力/kN 横截面/m2 恒阻力/kN 变形量/mm NPR锚索 1500 205 27 750 0.2238 850 1000 矿用锚索 1500 205 27 750 0.2238 — — 矿用锚杆 800 205 8 0 0.373×10-3 — — 
下载: 导出CSV
表 2 边坡岩体物理力学参数
Table 2 Physical and mechanical parameters of involved rockmass
类型 ρ /(kg·cm-3)E/GPa ν c/MPa φ /(°)TS/MPa Ⅲ级片岩 2.7 4.54 0.25 0.40 35 0.12 Ⅳ级片岩 2.5 4.11 0.30 0.15 28 0.10 Ⅳa级片岩 2.5 4.11 0.30 0.15 28 0.10 片岩破碎带 2.4 2.50 0.35 0.02 18 0.10 开挖区 2.5 4.11 0.30 0.15 28 0.10
下载: 导出CSV
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